Abstract: This is a study of the fundamental physical processes of the runup of long waves with the objective to understand some coastal effects of tsunamis. The runup of nonbreaking long waves on plane beaches is studied and an exact solution is developed for the runup of solitary waves. The maximum runup predicted by this solution is compared to laboratory data from this and other investigations and it is found to be in good agreement. A runup transducer was developed and deployed in the laboratory to provide data for the shape of the runup tongue. The exact solution is shown to model the details of the climb of the wave satisfactorily. The runup of breaking long waves on plane beaches is investigated in the laboratory by studying different long waves and bores of [mite volume. The runup is shown to be a function of a momentum scale determined from the generation characteristics of the incoming wave. The runup number is introduced and it is demonstrated that it models the runup process adequately. It is also observed that arbitrary long waves have runup numbers smaller than, or at most equal to, the runup number of breaking solitary waves, suggesting that on a given plane beach breaking solitary waves run-up further than other long waves with similar generation characteristics. An exact result is established for the force on an accelerating plate in a fluid with a free surface. The result is used to explain some of the results of this study and other results on the hydrodynamic forces on moving partitions. A technique is developed to generate arbitrary, long, continuously evolving waves at any desired location in a laboratory model. The technique is applied in the laboratory and it is shown to be successful in reproducing complex waveforms.

ID: CaltechKHR:KH-R-61

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Abstract: This study considers the run-up of non-breaking and breaking solitary waves on a smooth sloping beach. A non-linear theory and a numerical model solving the non-linear shallow water equations (NLSW) were developed to model this physical process. Various experiments to obtain wave amplitude time-histories, water particle velocities, wave free surface profiles, and maximum run-up were conducted and the results were compared with the analytical and numerical models. A higher order theoretical solution to the non-linear shallow water equations, which describes the non-breaking wave characteristics on the beach, was sought and is presented in this study. The solution was obtained analytically by using the Carrier and Greenspan (1958) hodograph transformation. It was found that the non-linear theory agreed well with experimental results. The maximum run-up predicted by the non-linear theory is larger than that predicted by Synolakis (1986) at the order of the offshore relative wave height for a given slope. This correction for non-breaking waves on beach decreases as the beach slope steepens, and increases as the relative incident solitary wave height increases. A unique run-up gage that consists of a laser and a photodiode camera was developed in connection with this study to measure the time-history of the tip of the run-up tongue of a non-breaking solitary wave as it progresses up the slope. The results obtained with this run-up gage agree well with other measurements, and this technique provides a simple and reliable way of measuring run-up time-histories. The run-up of breaking solitary waves was studied experimentally and numerically since no fully theoretical approach is possible. The wave characteristics such as wave shape and shoaling characteristics, and, for plunging breakers, the shape of the jet produced are presented. The experimental results show that wave breaking is such a complicated process that even sophisticated numerical models cannot adequately model its details. Two different plunging wave breaking and resultant run-up were found from the experiments. The point where the tip of the incident jet produced by the plunging breaking wave impinges determines the characteristics of the resulting splash-up. If the jet impinges on a dry slope, no splash-up occurs and the plunging breaker simply collapses. If the impingement point is located on the free surface, splash-up including a reflected jet is formed, which further increases the turbulence and energy dissipation associated with wave breaking. It is hypothesized that both clockwise and counterclockwise vortices may be generated by the impinging plunging jet and the reflected jet associated with the splash-up when the jet impinges on the front face of a breaking wave or on the still water surface in front of the wave. If only the run-up process and maximum run-up are of interest, the wave and the water flow produced after breaking can be simplified as a propagating bore, which is analogous to a shock wave in gas dynamics. A numerical model using this bore structure to treat the process of wave breaking and propagation was developed. The non-linear shallow water equations were solved using the weighted essentially nonoscillatory (WENO) shock capturing scheme employed in gas dynamics. Wave breaking and propagation is handled automatically by this scheme and no ad-hoc term is required. A computational domain mapping technique proposed by Zhang (1996) is used in the numerical scheme to model the shoreline movement. This numerical scheme is found to provide a somewhat simple and reasonably good prediction of various aspects of the run-up process. The numerical results agree well with the experiments corresponding to the run-up on a relatively steep slope (1:2.08) as well as on a more gentle slope (1:19.85). A simple empirical estimate of maximum run-up based on energy conservation considerations is also presented where the energy dissipation associated with wave breaking was estimated using the results from the numerical model. This approach appears to be useful and the maximum run-up predicted agrees reasonably well with the experimental results. The splash-up of a solitary wave on a vertical wall positioned at different locations on a gentle slope was also investigated in this study to understand the degree of protection from tsunamis afforded by seawalls. It was found that the effect of breaking wave kinematics offshore of the vertical wall on the splash-up is of critical importance to the maximum splash-up. The maximum slope of the front face of the wave upon impingement of the wave on the wall, which represents the maximum water particle acceleration, was important in defining the maximum sheet splash-up as well as the trend for splash-up composed of drops and spray.

No.: 60
ID: CaltechKHR:KH-R-60

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Abstract: The exchange of nonlinearly adsorbing compounds between stream water and sediment beds covered with stationary bedforms was investigated in laboratory experiments. The dominant physical exchange process is advective pumping caused by dynamic pressure variations over dunes on the bed. Observations of net mass exchange of cationic surfactants in a 5-meter long recirculating flume were used to validate the exchange model, which is based on the hydraulics of advective pumping and nonlinear adsorption isotherms derived from batch experiments. The flume experiments were conducted under steady, uniform flow conditions. The pH and ionic strength of the flume water was controlled by adding sodium chloride and sodium bicarbonate to deionized water. The sand was washed prior to every experiment. The mass exchange of cationic surfactants and bromide was determined by measuring the depletion of these compounds in the overlying water column as it mixed with the clean porewater from the bed. Porewater concentration profiles were acquired to monitor the penetration depth of the compounds in the bed. Bromide was used as a conservative tracer to observe the hydraulics of water exchange between the bed and the overlying water. Garnet sand was used as the model sediment because it had heterogeneous properties similar to natural sediments. The net mass exchange with a bed covered with stationary bedforms was greater than the exchange with a flat bed. The mass exchange of the cationic surfactants versus time observed in the flume experiments could not be modeled using linear adsorption; however, linear approximations provided upper and lower limits on the exchange. The total mass transfer of the cationic surfactants to the bed increased with their hydrocarbon chain lengths. The model for the exchange of nonlinearly adsorbing compounds solves the advection equation to track the transport of the compounds within the bed and computes the net mass flux through the bed surface. Nonlinear adsorption was modeled by the means of four different isotherm equations fitted to the batch adsorption data. The effect of the choice of isotherm on the exchange models for the flume experiments was found to be very small. The model generally predicted the flume results well without calibration. Additional model simulations were performed to provide a sensitivity analysis for the model inputs.

No.: 58
ID: CaltechKHR:KH-R-58

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Abstract: Laboratory experiments were conducted to determine the influence of stream bed shear stress and water chemistry on the sediment transport rate for silt-sized particles near the critical threshold for motion. Experiments were conducted in two large recirculating laboratory flumes, 40 m and 12 m long, with a small sediment bed 40 cm long. The sediment transport rate was determined from the volume of sediment eroded from this sediment bed per unit time. The smaller flume was filled with deionized water, to which specific electrolytes were added to vary the water chemistry. Dimensional analysis predicted the sediment transport rate of non-cohesive material can be described by two dimensionless groups, one for transport and one for bed shear stress. A new transport model was developed on physical considerations for particles smaller than the thickness of the viscous sublayer, and supported this conclusion. Sediment transport rates were measured in experiments using carefully cleaned glass beads (15 μm to 69 μm) in low ionic strength (10^-4 M) solution by measuring the elevation of the sediment bed along transects with a laser displacement meter every 10 to 30 minutes. The results supported the prediction that the dimensionless transport rate is solely a function of the dimensionless shear stress (Shields parameter) and the water composition, and not of the bed Reynolds number, when the latter is less than one. Experiments were conducted with NaCl and CaCl2 electrolytes at differing concentrations up to 10^-2 M, which reduced the transport rate by up to 2 to 3 orders of magnitude for the finest particles. Calcium was more effective at reducing the sediment transport rate than sodium. These trends were captured by the transport model, but additional work is required in estimating the inter-particle forces. A new criterion for initiation of motion is proposed based on a small dimensionless transport rate qs* = 0.01, corresponding to about 2% of the surface grains in motion. For bed Reynolds numbers u*d/v < 1, the equivalent Shields parameter for critical shear becomes [Greek tau]* = 0.075 for non-cohesive sediment. With cohesion, a new model is used to predict the change in the Shields curve for various dimensionless interparticle forces.

No.: 59
ID: CaltechKHR:KH-R-59

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Abstract: The transport of adsorbing metal ions (copper, zinc, calcium and magnesium) between the water column and the sand bed in a 5 meter long recirculating laboratory flume with bottom bedforms has been investigated. A non-adsorbing tracer, lithium, was used simultaneously to observe the exchange of water between bed and water column. The presence of bedforms and associated pumping increases the exchange rate by several orders of magnitude over molecular processes. The concentrations of initially added metal ions were monitored both in the circulating overlying water and in the pore-water of the sediment bed. The sand used for the bed was composed of over 99% silica, with geometric means of 500 [microns] and 195 [microns]. Before each run, the sand was acid-washed at pH 3.5 to provide reproducible experimental conditions. The chemical composition of the recirculating water was controlled and steady flow conditions were maintained in the experiments. Batch experiments were performed to investigate the chemical partitioning of the selected metal ions to the sand grain surfaces. The adsorption of zinc onto silica was modeled in detail and binding constants were determined. The observed adsorption of the metal ions in the flume experiments compared well with batch adsorption data. The transfer of metal ions into and out of a bed covered with stationary bedforms is dominated by advective pumping caused by pressure fluctuations over the bed. A residence-time model based on pressure-driven advective flow and linear equilibrium partitioning of the pollutant to the sediment was developed and describes the observed metal ion exchange between sediment and water column well. Increased partitioning of the metal ion onto the sediment leads to an increase of the amount of tracer stored within the sediment bed. Furthermore, the concentrations of metal ions released from the bed after passing of an initial pulse in the overlying water will be lower, but longer lasting for stronger partitioning, leading to tailing in the water column for long times. For a bed with moving bedforms, the main mechanism for mass exchange is the trapping and release of overlying water by the traveling bedform. The transport of metal ions can be approximately described for the initial phase of the experiment, but large deviations from the model occur for long times. The models do not require calibration since the parameters for transport into and out of the bed can be derived from flow conditions, sediment parameters, bedform dimensions and adsorption characteristics of the tracer on the sand. Criteria for the applicability of the models and appropriate scaling variables are identified. The experimental results are presented in nondimensional form.

No.: 56
ID: CaltechKHR:KH-R-56

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Abstract: This study investigates the interaction of breaking waves with a bed of loose angular material with a median grain size of 4.8 mm. It is motivated by the engineering problem of determining rock sizes for revetments used as protection for structures in the coastal zone and by the need for an understanding of the mechanics of material movement under waves. Both the effect of the bed on the velocities and accelerations in breaking and non-breaking waves, and the effect of breaking waves on the movement of bed material is measured. Velocities in breaking waves are measured at elevations approaching the bottom boundary, both for the case of a level bed of graded angular material and for a flat plate at the same location. By changing the water depth and the initial conditions of the incident wave, the relative size of the rock with respect to the breaking wave height is varied. Material movement resulting from the wave passage is measured and compared to the breaking wave height and to the turbulent shear determined near the bed. Using velocity and acceleration records near the rock bed together with observations of rock motion, the mechanics of material movement under waves are investigated. The roughness elements in the bed are found to have a large effect on both the mean and fluctuating velocities in the wave near the bottom. Evidence is shown of the existence of an inner layer where individual pieces of bed material influence the flow over the bed. A method for determining the maximum mean shear under a single wave is presented. Mean vertical velocities are measured to be not negligible near the bed and are shown to produce convective accelerations of the same order as the accelerations due to turbulent fluctuations. The movement of bed material is compared with the calculated shear on the bed and with local velocities and accelerations measured very close to the individual rocks. The mean size of the material moved in the bed is found to vary with the amount of shear on the bed. When adjusted for the mean size of the moved material, the calculated shears correspond well with the criterion for critical shear from the Shields curve used in steady flow. From the observed movement of particles during the passage of a wave and the measured velocities and accelerations in the wave, inertial forces are found to contribute to particle movement, especially in the regions before and after wave crest passage.

No.: 55
ID: CaltechKHR:KH-R-55

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Abstract: The major objective of this study has been to investigate experimentally the forces and overturning moments produced by tsunamis on vertical walls. The experimental results are compared with several analytical and numerical models. Several types of waves were used in a horizontal tank including solitary waves, undular bores, turbulent bores, and surges on a dry bed. Bores produced from breaking solitary waves in a tilting wave tank were also investigated. Various measurements were made, including the incident wave celerity, the wave profile, the runup, force, overturning moment, and pressure time histories. The impact process of the bores in the tilting wave tank were recorded with high-speed movies. The wave profiles in the horizontal tank were defined using a laser induced-fluorescence system (LIF) which allows the free surface on a two-dimensional plane in the center of the wave tank to be recorded. This method was developed to measure accurately the surface elevation profile of turbulent high-speed flows which is difficult to measure reliably either with conventional flow visualization techniques or intrusive devices such as wave gages. The LIF method was also used to determine the runup on the wall. Strong vertical accelerations were shown to occur during the reflection of bores and steep solitary waves at a vertical wall. These reduced the force on the wall relative to a hydrostatic force computed from the maximum runup height on the wall. The accelerations also cause the maximum force to occur before and after the maximum runup for steep solitary waves and bores, respectively. For these cases, the maximum measured force and overturning moment were always less than computed from the maximum measured runup on the wall using hydrostatic considerations. The maximum force due to surges on a dry bed was also less than the hydrostatic force calculated from the maximum runup height on the wall. For all the dry bed cases studied, the maximum runup height on the wall was between 1.46 and 1.62 times the velocity head computed from the celerity of the incident surge. For the entire range of wave conditions of this study, the maximum relative runup occurred for a bore with a relative wave height of 1.23, and produced a runup equal to 3.8 times the velocity head computed from the wave celerity. The maximum measured water surface slopes along the front of long waves, bores, and dry bed surges were computed from the measured wave profiles. At the transition from undular bores to turbulent bores, there was a discontinuity in the maximum water surface slope where the slope increased by a factor of 2.5 to three for turbulent bores. This discontinuity corresponded with a rapid increase in the measured runup, force, and moment on the wall. The properly normalized force on a vertical wall due to the impingement of a bore on a mildly sloping beach is shown to be equivalent to the force produced by a bore of constant volume on a horizontal bed. This implies the results from the horizontal wave tank experiments can be used to estimate the loads expected from bores propagating on mild beaches with slopes ranging up to 0.02m/m. Two numerical models were compared with the experimental results. A boundary integral element model, which solves the potential flow problem subject to the full nonlinear free surface boundary conditions, predicted the loads imposed on the wall due to steep solitary waves quite well. A finite difference model of the Navier-Stokes equations was also used to simulate the reflection of solitary waves and mild turbulent bores at a vertical wall. This finite difference model predicted the solitary wave loads quite well; however, it over-predicted the steepness of the incident bore profiles and produced a force-time history with a high amplitude and short-duration peak, which was not observed in the measurements. Except for this sharp peak, the agreement of the finite difference model with the experimental results was quite reasonable.

No.: 54
ID: CaltechKHR:KH-R-54

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Abstract: A theoretical and experimental investigation of the transport parameters of particles flowing through porous media has been made. These parameters are the particle advective velocity, longitudinal dispersion coefficient, and filter coefficient. Both theoretical and experimental results are limited to flows with low Reynolds number (linear, laminar flow) and high Peclet number (advection dominates diffusion). The theoretical development used dimensionless numbers to define the transport parameters and incorporated them into an advective-dispersion equation describing particle transport. A relationship for unfavorable filtration due to repulsive double layer interactions is proposed. A solution to the complete advective-dispersion equation for particle transport was derived for the case of a constant filter coefficient. This solution when compared to a similar solution previously derived for solute transport, showed that for small filtration the solutions were identical except for the exponential decay factor due to filtration. A numerical model was developed for the case of a variable filter coefficient. Flow experiments were conducted in a 1.5 m vertical column with sand (geo. mean diameter = 381 micron), with suspensions of polystyrene latex particles (three cases, mean diameter = 0.1, 1.4 and 2.8 micron), and with NaCl as the electrolyte (0.4 mM < Ionic strength < 2.1 mM). The range of Peclet number studied was 1.26 x 10^4 to 2.00 x 10^6. The measurement of the particle concentrations during passage of a displacement front provided the necessary data to determine the particle transport parameters. The particle advective velocities for the three different sized particles was found to range approximately from 0 to 5.4% greater than the solute velocity, and these values were within a few percent of predictions based on particle and pore radii. The longitudinal dispersion coefficient for the three different sized particles was found to be a function of only the advective velocity of the particles and grain diameter of the porous bed which confirmed the dimensional analysis argument and closely matched previous solute work. A dimensional analysis argument for the relationship between the favorable and unfavorable filter coefficient was proposed to be a function of the ratio of the particle diffusion length of an advecting particle and the double layer thickness (which in turn depends on the ionic strength of the water). A wide range of filtration data (Brownian to advective particles) was empirically fitted using this dimensionless number. The effects of ionic strength on particle transport were found to be either minimal or separable from the hydraulic variables. For advection, effects of changing ionic strength were analyzed as changes in the effective particle radius and calculations made using this apparent particle radius matched experimental results. For dispersion, an increase of a factor of 6 in the ionic strength increased the longitudinal dispersion by a factor of 1.2.

No.: 53
ID: CaltechKHR:KH-R-53

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Abstract: Laboratory experiments were conducted to determine the mechanisms and rates of bed/stream exchange of non-reactive solutes for beds of medium and fine sand. Experiments were conducted under steady flow conditions with and without sediment transport in a recirculating flume. Flat beds and beds covered with ripples or triangular bedforms were studied. The net mass exchange was determined by measuring concentration changes in the main flow. The penetration of the solute (fluorescent dye) into the bed was also observed visually. Two key exchange mechanisms, 'pumping' and 'turnover', were identified. Pumping is the movement of pore water into and out of the bed due to flows induced by pressure variations over bedforms (ripples and dunes). Turnover occurs as moving bedforms trap and release interstitial fluid. Predictive models based on the details of the exchange processes were developed. A residence time distribution approach was used. The models do not require calibration. Appropriate scaling variables were identified. With stationary bedforms the exchange is strongly influenced by pumping. The predictions of net mass exchange based on models of pumping with periodic bedforms show good agreement with the measured exchange in the initial stages of the experiments (hours to days). The models under-predict the exchange later in the experiments. The deviation is associated with the large-scale and somewhat random features in the penetration of the dye cloud. Such features are expected to influence the net exchange for large time in natural streams. When the bedforms move slowly in relation to the characteristic pore water velocity, turnover can be neglected and pumping dominates. A model based on a random distribution of bedform sizes provides a good prediction of the mass exchange with slowly-moving bedforms. With rapidly-moving bedforms, turnover dominates the exchange at the start of the experiments, when the solute penetration is limited to the maximum bedform scour depth. The scour depth can be predicted well. Later the depth of penetration is greater than the scour depth and the model predictions.

No.: 52
ID: CaltechKHR:KH-R-52

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Abstract: The behavior of thermal plumes discharged from staged diffusers has been investigated experimentally. A staged diffuser is a type of submerged multiport diffuser characterized by an offshore orientation of the individual nozzles. It is commonly employed for the discharge of heated water from coastal power plants into the ocean because of its effective mixing capability, which does not depend on the prevailing longshore-current directions. Experiments have been performed to measure the temperature distribution of the plume in quiescent receiving water. The three-dimensional thermal field is reconstructed from the results of two groups of measurements, the centerline experiments in which the temperature in the vertical plane along the diffuser axis is measured, and the scanning experiments in which the lateral temperature profiles are measured. The emphasis is on a homogeneous ambient receiving water, but a few illustrative experiments with ambient stratification have been carried out. The number of variables associated with the problem is very large, making it difficult to perform a generic study. Nevertheless, five of the variables (the number of ports, n, the initial jet diameter, D[sub]0, the horizontal orientation of the jet, [Greek alpha], the total discharge flow rate, Q[sub]T0, and the water depth, H) have been examined. Experimental observations support the hypothesis of a near field dominated by momentum jet mixing, and an intermediate field dominated initially by turbulent mixing and eventually by gravitational spreading. H, n and D[sub]0 are the governing parameters in both the near field and the intermediate field. By coupling dimensional analysis with experimental results, several empirical relationships have been established to give a first-order approximation relating the mean characteristics of the plume to the governing parameters. It is found that the near-field dilution can be described adequately by the simple jet model with an adjustment factor based on n. The dilution in the intermediate field, however, s relatively insensitive to n. It is also concluded that the horizontal orientation of the jet +-25[degrees] to the diffuser axis, helps to spread the plume over a wider extent, thereby reducing the maximum temperature rise. Results from stratified experiments indicate that for weak stratification, the dynamics of the plume are not significantly modified.

No.: 51
ID: CaltechKHR:KH-R-51

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Abstract: The interaction of normally incident time-periodic water waves with a density-stratified fluid in a rectangular trench is studied experimentally and theoretically; the fluid outside the trench is homogeneous. This investigation has focused on the excitation of internal waves in the trench by surface waves, and the effects of the internal oscillations on the waves on the free surface. The study shows that, when the frequency of the incoming surface waves corresponds to the natural frequency of oscillation of the internal waves in the trench, the amplitude of the internal waves becomes large compared to the amplitude of the surface waves. The effects of the internal waves on the surface waves were very small in the experiments. A two-layer model and a three-layer model are developed and applied to a particular constant-depth channel and trench configuration used in the experiments. The two-layer model is also applied to a rectangular trench in an infinite region. These models treat steady-state wave motions of infinitesimal amplitude for all ranges of fluid depth relative to the wavelength of the surface waves, and include a vigorous treatment of the effects of energy dissipation in the laminar boundary layers adjacent to the solid surfaces and at the density interface. In the two-layer model the stratified fluid in the trench is represented by two homogeneous fluids of different densities; in the three-layer model these two fluids are separated in between by a transition region of linear density variation. Fresh water and salt water were used to model density stratification in the experiments. The effects of surface wave amplitude and density distribution on the internal motion in the trench were investigated for small density differences compared to the density of water. A new technique using a scanning laser beam and detect or system was developed to measure internal wave amplitudes. Satisfactory agreement with the theoretical predictions was obtained. The effects of nonlinearity and viscous dissipation on the internal motions were more pronounced when the depth of the heavier fluid was small compared to the wavelength of the internal waves in the trench. For a trench in an infinite region, the two-layer model also predicts that large surface wave reflections occur when the trench is "at internal resonance," and a significant portion of the incident wave energy can be dissipated within the trench. The investigation has provided insight with regard to both the dynamics of wave-trench interaction and the design of navigation channels in density-stratified fluids for reducing the potential of wave-induced internal resonance.

No.: 50
ID: CaltechKHR:KH-R-50

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Abstract: Particles in the colloidal size range, i.e. smaller than 10^(-6) meter, are of interest in environmental science and many other fields of science and engineering. Since aqueous oxide particles have high specific surface areas they adsorb ions and molecules from water, and may remain stable in the aqueous phase with respect to coagulation. Submicron particles collide as a result of their thermal energy, and the effective collision rate is slowed by electric repulsion forces. A key to understanding particle stability and coagulation is the role of simple chemical changes in the water altering the electrostatic repulsion forces between particles.
Experiments using hematite particles (α-Fe_2O_3, 70nm in diameter) reveal important features of coagulation dynamics. Three experimental techniques are employed: (1) Light scattering measurements to yield quantitative information on the rate of the initial coagulation process; (2) electrokinetic measurements to provide information about the sign and magnitude of the electrical charge on the aqueous oxide particles; (3) acid-base titration and equilibrium adsorption to obtain the intrinsic equilibrium constants for surface species.
The acid-base titration data indicate that the pH_(zpc) of the synthesized hematite colloid is 8.5. This is also supported by the electrophoretic mobility measurements. In the presence of non-specific adsorbing ions (such as Na^+ and Ca^(2+), etc.), the coagulation of a hematite colloid is achieved mainly by compression of the diffuse layer and Schulze-Hardy Rule is exhibited for non-specific electrolytes. Specifically adsorbed counter ions (such as phosphate) are able to reduce the surface charge of aqueous oxide particles, and the critical coagulation concentrations are dependent on the value of the pH, and are much less than those predicted by DLVO theory. In inorganic media, we found that the order of the effectiveness in causing hematite particles to coagulate is:
phosphate>sulfate>chloride at pH

ID: CaltechKHR:AC-5-88

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Abstract: Wave breaking is investigated experimentally by use of laser doppler velocimetry for two cases: a plunging breaker and a spilling breaker. Specifically, emphasis is given to the kinematics at breaking, the early breaking phase, and the turbulent wake generated from wave breaking. A significant contribution is provided on the amplitude behavior for a solitary wave on a beach, as it is the solitary wave that is used to conduct this study. Associated with the use of the solitary wave, a technique of flow field construction by repeated measurement with an LDV is presented. Four well defined regions of the shoaling-through-breaking solitary wave on a beach are identified and termed according to the wave amplitude behavior within each region. They are: the zone of gradual shoaling, the zone of rapid shoaling, the zone of rapid decay and the zone of gradual decay. The plunging wave case studied exhibited a definite transitional zone, between the previously known -1/4 and -1 power laws, following a power law of -3/5. Velocity fields for a plunger and a spiller at the point of breaking are measured and the corresponding acceleration fields are computed for each. The results show good qualitative comparison to those obtained by theoretical approaches, however, no clear mechanism is demonstrated to initiate breaking for the spilling breaker studied. The existence of counter-rotating vortices, generated from breaking, is established from velocity measurements of the flow taken during the early breaking phase and within the turbulent wake of the plunging breaker studied. The measurements indicate that the size of the vortices are roughly the same as the undisturbed depth at the point of breaking. Turbulent intensities determined within the wake of the plunging breaker illustrate its character and show that level of turbulent intensity does not progressively decrease behind the turbulent source.

ID: CaltechKHR:KH-R-48

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Abstract: Some aspects of turbulence in sediment-laden open-channel flows are examined. A conceptual model based on similarity hypotheses rather than the traditional mixing-length closures is proposed. It is argued that, over a wide range of laboratory conditions, the main effect of the suspended sediment on the flow is confined to a layer near the bed. If such a distinct layer can be discerned, then this is separated from the outer flow by an inertial subregion in which the mean-velocity profile is approximately logarithmic, with an associated von Kàrman constant of ≈ 0.4, i.e., the same value as in single-phase flows. It is further shown that power-law profiles may be derived from general similarity arguments and asymptotic matching. These implications contrast with those of previous models in which changes in the mean-velocity profile are supposed to occur throughout the flow or primarily in the flow far from the bed. Length and concentration scales appropriate to sediment-laden flows are suggested. An experimental study was also undertaken. Both the saturated case, in which a sand bed was present, and the unsaturated case, in which a sand bed was absent, were investigated. The study was restricted to nominally flat beds, composed of three well sorted sands (median grain diameters ranged from 0.15 mm to 0.24 mm). A two-component laser-Doppler-velocimetry system was used for velocity measurements. Suction sampling was used to measure local mean concentrations. The major points of the conceptual model are supported by the experimental results. Higher-order statistics of the velocity field were found to exhibit little evidence of any effect on the outer flow, supporting the view that the effect of the suspended sediment is felt primarily in the inner region. This contrasts with the predictions of recent models that propose an analogy between sediment-laden flows and weakly stable density-stratified flows.

ID: CaltechKHR:KH-R-49

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Abstract: The influence of sloping boundaries on long wave response of bays and harbours is studies in this work. Laboratory experiments are performed to help validate the theoretical analysis which is applicable to nonbreaking waves. A set of long wave equations in the Langrangian description is derived which includes terms to account for nonlinear, dispersive, and dissipative processes for wave propagation in two horizontal coordinates. A finite element model is developed based on these equations which is capable of treating arbitrary geometry and the runup of nonbreaking waves on a beach. An analytical harbour response model, capable of treating narrow rectangular harbours with variable bathymetry and sidewall geometry, is developed and applied to several simple geometries. The model shows that for a given harbour length and entrance width, the resonant frequencies and the response of a harbour are very dependent on the harbour sidewall geometry and bathymetry. Some of the nonlinear effects of the runup of nonbreaking waves on a plane beach are discussed. In particular, the time average of the water surface time history at a fixed spatial location is negative and the wave crests are smaller than the troughs. Nonlinear effects do not alter the runup maxima or minima and the maximum fluid acceleration occurs at the point of maximum rundown of the wave. Laboratory experiments were performed to determine the long wave response of a narrow rectangular harbour whose still water depth decreases linearly between the harbour entrance and the shoreline. Good agreement with the finite element model was obtained, including the prediction of the depression of the mean water level within the harbour. A three-dimensional application of the finite element model treats the runup of solitary waves on a coastline with variable bottom topography and a curved shoreline. The results indicate the model can predict the trapping of wave energy along a sloping coastal margin, a process of fundamental importance for predicting potential tsunami damage.

No.: 47
ID: CaltechKHR:KH-R-47

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Abstract: The use of optical methods such as Laser Doppler Velocimetry (LDV) and laser induced fluorescence techniques (LIF) in experimental fluid mechanics is becoming very common. The greatest advantage of such methods is that measurements are made without disturbing the flow. A major impediment to using optical methods to study density stratified flows is the variation of the refractive index within the flow field. McDougall (1979a) has proposed a method for the reduction of refractive index variations while maintaining a density difference. The method relies on the fact that various solutes in, say, water can contribute to the density and to the refractive index of the solution in different proportions. A new pair of solutes (ethanol and NaCl) were found to be suitable for use in LDV and LIF studies of stratified flows. In some circumstances the new pair is more useful than that described by McDougall (1979a).

ID: CaltechKHR:KH-TM-85-1

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Abstract: Chrysotile asbestos fibers enter California waters from physical weathering of magnesium-silicate, serpentine rocks in mountains of the northern and central portions of the state. Chrysotile particles, initially positively charged below pH 8.9 because of their magnesium-hydroxide surface, become negatively charged due to dissolution and adsorption of organic matter. Chrysotile suspended in 0.1 M inorganic electrolyte at pH 7-10 for up to five days dissolves with magnesium being released in excess of the 3:2 Mg:Si to silica molar ratio in the solid. The rate of magnesium release exhibits a fractional dependence on hydrogen-ion concentration: r = k_1'[H^+]^(0.24) The observed rate constant, k_l', depends on dissolution mechanism, specific surface area of the solid and charge-potential relation at the surface. Interpreted in terms of a site-binding model for adsorption and desorption of protons on the surface, the fractional dependence implies that dissolution is limited by a chemical reaction involving an average of less than one adsorbed proton per magnesium ion released into solution. Silica release from chrysotile shows no clear pH dependence. The rate of magnesium release is independent of the anions NO^(3-), Cl^- , SO_4^(2-), HCO_3^-, oxalate or catechol. Oxalate inhibited and catechol slightly enhanced silica release over the pH range 7.5-8.5; other anions had no systematic effect. Chrysotile's dissolution rate (10^(-15.7) mol/cm^2·s at pH 8) is consistent with observations on other magnesium silicates and brucite. Catechol adsorption onto chrysotile or aluminum oxide (pH 7.5-8.5) does not reach equilibrium but increases over five days. After one day the maximum adsorption density (Langmuir adsorption equation) on chrysotile is 0.7 x 10^(-9) mol/cm^2 (50 x 10^(-6) mg C/cm^2), approximately one-third of the estimated number of surface sites available for proton exchange. The maximum adsorption density for natural organic matter was near 30 x 10^(-6) mg C/cm^2 on both chrysotile and aluminum oxide. Chrysotile adsorbs sufficient catechol, oxalate, phthalate or natural organic matter within one day to reverse its surface charge. The extent of reversal is larger than observed for adsorption of the same organics on aluminum oxide, because of selective dissolution of chrysoti1e's outer magnesium-hydroxide layer. In reservoirs, submicron-sized chrysoti1e particles coagulate with larger (>2 μm), negatively-charged particles that subsequently settle out. The rate at which freshly-suspended, positively-charged chrysotile fibers coagulate is at least ten-fold greater than the rate for aged, negatively-charged fibers coagulate. Removal of chrysotile particles in water treatment occurs by deposition of fibers onto sand grains in filtration. Capture efficiency for single fibers is low; removal is enhanced 10-fold or more by incorporating fibers into larger flocs. Removal of chrysotile fibers in water filtration to levels near detection limits (typically 10^5-10^6 fibers/L) is possible; consistent achievement of this level will require a higher removal efficiency than is routinely achieved in treatment plants receiving water from the California aqueduct.

ID: CaltechKHR:AC-8-84

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Abstract: A theoretical and experimental investigation has been made of the longitudinal dispersion of chemically and dynamically passive solutes during flow through nonuniform, isotropic porous media. Both theoretical and experimental results are limited to the high Peclet number, low Reynolds number flow regime. The goal of the theoretical investigation is to provide a quantitative method for calculating the coefficient of longitudinal dispersion using only measurable structural features of the porous medium and the characteristics of the carrying fluid and solute. A nonuniform porous medium contains variations in grain scale pore structure, but is homogeneous at the macroscopic level for quantities such as the permeability or porosity. A random capillary tube network model of nonuniform porous media is developed which uses a pore radius distribution and pore length distribution to characterize the grain scale structure of porous media. The analysis gives the asymptotic longitudinal dispersion coefficient in terms of integrals of kinematic properties of solute particles flowing through individual, random capillary tubes. However, shear dispersion within individual capillary tubes is found to have negligible impact on the overall longitudinal dispersion in porous media. The dispersion integrals are evaluated using a Monte Carlo integration technique. An analysis of the permeability in nonuniform porous media is used to establish a proper flow field for the analysis of longitudinal dispersion. The experimental investigation of longitudinal dispersion is carried out by measuring (with conductivity probes) the development of an initially sharp miscible displacement interface. The experimentally determined longitudinal dispersion coefficients are found to be greater in nonuniform media than in uniform media when compared using Peclet numbers based on the geometric mean grain diameter. The experimental breakthrough curves also display highly asymmetrical shapes, in which the "tail" of the breakthrough is longer than would be expected from advection-diffusion theory. Although the theoretical model does not predict the tailing behavior, it is found that the leading portion of the breakthrough curve is described by advection-diffusion theory. The theoretically determined longitudinal dispersion coefficients lie roughly within a factor of 1.35 of the measured values. The material presented in this report is essentially the same as the thesis submitted by the author in partial fulfillment of the requirements for the degree of Doctor of Philosophy.

ID: CaltechKHR:KH-R-45

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Abstract: The entrainment and mixing processes in an axisymmetric vertical turbulent buoyant jet and its transition from a jet to a plume have been studied. The ambient fluid is of uniform density and calm except for the flow induced by the jet, and the density variations are assumed small. A systematic set of experiments was carried out to examine turbulent buoyant jet behavior over a wide range of initial jet Richardson numbers. All experiments were performed in a glass wall tank with dimensions 1.15m x 1.15m x 3.30m deep, equipped with a jet flow source and an instrument carriage to enable the velocity and concentration measurements in the entire jet flow field. The axial and radial velocity components and the concentration of a Rhodamine 6G dye were measured simultaneously at the same point of the jet flow field using a two-reference beam laser-Doppler velocimeter combined with a laser induced fluorescence measuring device. From the time signals of the axial and radial velocity components (w) and (u) and the concentration (c) of the Rhodamine 6G dye, information was obtained concerning the mean values, turbulent fluctuations and correlations between w, u and c, up to 100 jet and 80 plume diameters downstream of the jet exit. More specifically, the mean flow (including the spread rate of the mean velocity and tracer concentration profiles and distribution along the jet axis) and the turbulent structure (including the profile of turbulence intensity, turbulent mass flux of a tracer and turbulent momentum flux) were investigated as a function of distance from jet origin made dimensionless by a characteristic length scale based on jet buoyancy and momentum fluxes. The results from a detailed dimensional analysis were verified experimentally. It was determined that the turbulent flux of a tracer (or buoyancy) varied from 6-10% for jets and was 15-20% of the total for plumes. The turbulent momentum flux was found to be 15% of the local momentum flux transported by the mean flow. While the profiles of w and c and the turbulent velocity profiles are found to be much the same for both jets and plumes, the turbulence intensity profiles of the concentration take higher values in plumes than in jets. More rapid dilutions were obtained in buoyancy driven plumes than in momentum driven jets. Useful information concerning engineering applications is provided from the experimental constants derived.

ID: CaltechKHR:KH-R-46

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Abstract: Coagulation, in the physical context, is looked upon here first from the fundamental perspective of collision and coalescence of individual particles. A Monte Carlo technique is used to investigate the particle size distribution in a suspension of coagulating particles when one or more collision mechanisms operate. The effect of interparticle forces - hydrodynamic, van der Waals' and electrostatic - on the collision probability of the particles is examined. The results obtained are used to evaluate the well-known dynamic equilibrium hypothesis according to which an equilibrium particle size distribution is assumed to exist under the action of a given collision mechanism. It is shown that dimensional analysis cannot, in general, be used to predict steady state particle size distributions, mainly because of the strong dependence of the interparticle forces on the sizes of the interacting particles. The insight into particle kinetics thus gained from the Monte Carlo simulation of collision processes is used to develop a numerical simulation of a rectangular settling basin. The computer model follows the spatial and temporal development of the influent particle size distribution towards the outlet of the tank, accounting for all of the basic kinetics of particle collision and coalescence processes and including transport processes such as particle settling, advection, resuspension and turbulent mixing. The influence of the particle size-density relationship and floc deaggregation by turbulent shearing are also modeled. Of necessity, modeling of some of these processes has been somewhat empirical since the physical and biochemical nature of the flocs are unique to a particular suspension and their determination requires experimental work. The results of the simulations performed indicate that the particle size-density relationship, the collision efficiencies between flocs and the influent particle size distribution are of major importance to the performance of the sedimentation basin. Clearly, further modifications, Improvements and trials are needed in order to use the model for the design of new facilities. Nevertheless, the computer model may serve as a guide for selection of several design and operation variables for the successful treatment of a particular waste or the selective removal of pollutants whose concentration depends on the shape of the effluent particle size distribution.

ID: CaltechKHR:KH-R-44

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Abstract: Although it is known that manganese oxides are solubilized by reduction in anoxic waters, the chemical processes are poorly understood. A study of the reduction and dissolution of manganese oxide suspensions by twenty-seven organic substrates that have chemical structures similar to those of natural organics was undertaken to determine the rates and mechanisms of the solubilization reactions. Dissolution of suspensions by hydroquinone in the pH range 6.5 < pH < 8.5 is described by the following experimental rate law: d[Mn^(2+)]/dt = k_l{H^+}^(0. 46) [HQ]^(1.0) (Mn_T - [Mn^(2+)]) where [Mn^(2+)] is the amount of dissolved manganese, [HQ] is the hydroquinone concentration, and Mn_T is the initial amount of manganese oxide. The apparent activation energy of the reaction was found to be +37 kJ/mole. The Mn(III,IV) oxide suspension was prepared by oxidizing a Mn(OH)_2(s.) suspension with oxygen, and has a composition characterized by MnO_(1.66). Suspension particles were between 0.2 and 1.0 microns in diameter. Calcium and phosphate were found to inhibit the dissolution reaction, by adsorbing on the oxide surface. Dihydroxybenzenes and methoxyphenols dissolved the suspensions at appreciable rates. Of the aliphatic substrates examined, only ascorbate, oxalate, and pyruvate dissolved the oxide. Dissolution by marine fulvic acid was found to be photocatalyzed. A model was developed to explain the observed rate dependence and the relative reactivity of different organic substrates. The model assumes that complexes between substrate and surface sites form prior to electron transfer and dissolution. The pH dependence is not explained by this model; involvement of H^+ in the dissolution of reduced surface sites may be responsible for the observed fractional order with respect to H^+.

ID: CaltechKHR:AC-1-83

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Abstract: In recent years, attempts have been made to develop numerical models for unsteady flows in channels with sediment transport. The work presented in Reports KH-R-43A and KH-R-43B was conducted to analyze two essential ingredients of any numerical model: the relationship between the hydraulic variables (slope, depth, and velocity), and the predictor of sediment concentration. Report KH-R-43A presents a detailed analysis of the two components and examines their role in numerical modeling. Six hydraulic relationships and 13 sediment concentration predictors are examined and compared. New relationships are then developed which appear to be more accurate than the existing techniques. Finally, the new relationships are utilized in a numerical unsteady flow, moveable bed model which uses a four-point implicit finite difference solution scheme. The data base utilized in the first report is presented in Report KH-R-43B. The data base contains 7,027 records (5,263 laboratory records and 1,764 field records), in 77 data files. Not all records were used in the final analyses, but they have been included in an attempt to provide a historically complete set of alluvial channel observations. The material presented in these reports is essentially the same as the thesis submitted by the author in partial fulfillment of the requirements for the degree of Doctor of Philosophy. A common list of references, with data sources separated from other references, has been included in both reports.

No.: 43A
ID: CaltechKHR:KH-R-43A

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Abstract: The laser-Doppler velocimetry technique was adapted for use in sediment-laden flows. The developed instrumentation was used to make one-dimensional, instantaneous measurements of both fluid and sediment grain velocities throughout the water column in such a flow. The velocimetry results were obtained in a steady, uniform flow over a natural sediment bed in the high-transport, flat bed regime. Laser-Doppler velocimetry is particularly attractive for use in sediment-laden flows as no calibration is required and no probe is introduced into the flow field. Measurements of the fluid velocity and the occurrence and velocity of individual sediment grains are possible with the instrumentation developed in this study. The major difficulties encountered are the possible conditional sampling, hence possible biasing, of the fluid velocity data and the failure of the instrumentation to record or resolve individual sediment grains at higher sediment transport rates. The instrumentation employed in this study is still in the developmental stages and suggestions for its improvement are given. Despite the difficulties encountered, the data obtained in this study give some insights into the mechanics of suspension and entrainment of sediment during transport by water. The longitudinal turbulence intensity does not seem to be significantly affected by the presence of suspended sediment; the turbulence intensities observed in the sediment-laden flow of this study do not differ greatly from the values reported by previous investigators for clear fluid flows. The mean and standard deviation of the sediment grain velocity were observed to be less than those for the fluid velocity in the lower portion of the flow, but respectively greater near the water surface. The data demonstrate the shortcoming of the continuum approach to the mechanics of the suspension on sediment. The length (or time) scales of the fluid turbulence are smaller than the length (or time) scale of a set of sediment grains required to define suspended sediment concentration. Near the water surface, where the velocimeter acts as a grain counter, the probability density functions of the sediment grain inter-arrival times, the time between the detection of successive sediment grains, were observed to be negative exponentials. The transport of individual sediment grains might be modeled as a Poisson process. This work is the foundation of an ongoing experimental program of direct measurements of the fine-scale, time-fluctuating characteristics of sediment-laden flows. This study developed and implemented instrumentation capable of making such measurements and established a conceptual framework for the subsequent interpretation of the data obtained. Two-dimensional measurements, with improved instrumentation, will give additional insights into the mechanics of sediment transport.

No.: 42
ID: CaltechKHR:KH-R-42

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Abstract: In recent years, attempts have been made to develop numerical models for unsteady flows in channels with sediment transport. The work presented in Reports KH-R-43A and KH-R-43B was conducted to analyze two essential ingredients of any numerical model: the relationship between the hydraulic variables (slope, depth, and velocity), and the predictor of sediment concentration. Report KH-R-43A presents a detailed analysis of the two components and examines their role in numerical modeling. Six hydraulic relationships and 13 sediment concentration predictors are examined and compared. New relationships are then developed which appear to be more accurate than the existing techniques. Finally, the new relationships are utilized in a numerical unsteady flow, moveable bed model which uses a four-point implicit finite difference solution scheme. The data base utilized in the first report is presented in Report KH-R-43B. The data base contains 7,027 records (5,263 laboratory records and 1,764 field records), in 77 data files. Not all records were used in the final analyses, but they have been included in an attempt to provide a historically complete set of alluvial channel observations. The material presented in these reports is essentially the same as the thesis submitted by the author in partial fulfillment of the requirements for the degree of Doctor of Philosophy. A common list of references, with data sources separated from other references, has been included in both reports.

No.: 43B
ID: CaltechKHR:KH-R-43B

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Abstract: This widely referenced, but seldom seen report is of both historic and engineering interest. While much of the work presented has since been eclipsed by more recent work, the velocity equation for open channels (Eq. 37) is still in use. It is interesting to learn how this equation came into being, particularly in light of the fact that it predates the well known von Karman-Prandtl logarithmic velocity distribution equation. Also of interest, is the plethora of velocity equations for open channels and pipes, which existed over sixty years ago (particularly when one considers that the search for a satisfactory equation continues to this day). A final benefit of this translation is that the extensive tabulations of data have been preserved for a new constituency. Every attempt has been made to translate as literally as possible, to preserve the flavor of the original report. Therefore, certain phrases may seem somewhat awkward. A few archaic German idioms required a somewhat looser translation. The data in Tables 1 through 14 have been reproduced directly from the original report, with the substitution of captions in English. Therefore, the data entries contain commas which should be replaced by decimal points to convert to the North American convention. The preparation of this translation was supported by the National Science Foundation, under Grant CME 79-20311. Special thanks to Joan Mathews and Melinda Hendrix-Werts for their excellent typing and to Theresa Fall, for preparation of the tables and figures.

No.: T-10
ID: CaltechAUTHORS:20120202-142837599

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Abstract: Previous investigations of Fe(II) oxygenation had resulted in a wide range in the reported rate constant(s). While Fe(II) oxygenation rates are fast in simple laboratory systems (seconds to minutes when pH > 7), actual rates observed in natural waters can be orders of magnitude lower. Conversely, while Mn(II) oxygenation rates are slow in laboratory systems (days when pH < 9), much faster rates are observed in natural waters or implicated in model studies. The influences of ionic strength, temperature and anions on the Fe(II) homogeneous oxygenation rates were examined in this study. Other rate constants from the literature were successfully incorporated into this framework. Complexation by major anions (e.g., SO_4^(2-) and Cl^-) and ionic strength effects were sufficient to account for the retardation of Fe(II) oxygenation in seawater. Autocatalysis of Fe(II) oxygenation was observed for pH > 7. A general integrated autocatalytic rate expression suitable for Fe(II) or Mn(II) oxygenation was used to interpret laboratory-obtained kinetic data. Oxidation of Fe(II) in various laboratory systems with characteristics like those of natural water was shown to form the allotrope γ-FeOOH. The γ-FeOOH surface was shown to be an excellent catalyst for Fe(II) and Mn(II) oxygenation. The γ-FeOOH surface obtained by oxidizing milli-molar levels of Fe(II) in 0.7 M NaCl was studied in the following ways: surface charge characteristics by acid/base titration; adsorption of Mn(II) and surface oxidation of Mn(II). A rate law was formulated to account for the effects of pH and the amount of surface on the surface oxidation rate of Mn(II). The presence of milli-molar levels of γ-FeOOH was shown to reduce significantly the half-life of Mn(II) in 0.7 M NaCl from hundreds of hours to hours. The γ-FeOOH surface was shown to be as effective as colloidal MnO_2 in catalysing Mn(II) oxygenation.

ID: CaltechKHR:AC-12-80

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Abstract: The process of excitation of harbors and bays by transient nonlinear long waves is investigated theoretically and experimentally. In addition, nonlinear shallow water waves generated in a closed rectangular basin by the motion of the basin are also examined. Two numerical methods based on finite element techniques are used to solve the weakly nonlinear-dispersive-dissipative equations of motion and are applied to the basin excitation problem and the transient harbor oscillation problem, respectively. In the latter case, the open sea conditions are simulated by including a radiative boundary condition in time at a finite distance from the harbor entrance. Various dissipative effects are also included. In addition to the numerical results, analytical solutions are presented to investigate certain particular aspects of basin and harbor oscillations (e.g., the effects of viscous dissipation in a harbor with simple geometry). Experiments conducted in the closed rectangular basin indicate that for a continuous excitation at or near a resonant mode of oscillation the linear theory becomes inadequate and the nonlinear-dispersive-dissipative theory must be used. For a transient excitation the validity of the linear theory depends on the value of the Stokes parameter. Indeed, some features not predicted by the linear theory can be directly inferred from the magnitude of this parameter. Experiments on the continuous wave induced oscillations of a narrow rectangular harbor with constant depth show that at the first resonant mode convective nonlinearities can be neglected and a linear dissipative solution is sufficient to describe the waves inside the harbor. At the second resonant mode which corresponds to a longer harbor relative to the length of the incident wave, nonlinear convective effects become important and must be incorporated into the numerical model. Also the characteristics of various sources of dissipation which reduce resonance in the harbor are investigated experimentally. The sources considered include, among others, laminar boundary friction, leakage losses underneath the harbor walls, and energy dissipation due to flow separation at the entrance of the harbor. The good agreement obtained between the experiments and the nonlinear numerical model developed in this study suggests that this model could be used with some confidence to predict the response characteristics of prototype harbors. As an example, the results of this study have been applied to the response of Ofunato Bay (Japan) to the tsunami generated by the Tokachi-Oki earthquake of May 16, 1968. The model has been used to investigate the effects of convective nonlinearities on the bay oscillations and also to determine the efficiency of the breakwater which was built to reduce the effects of tsunamis at Ofunato.

No.: 41
ID: CaltechKHR:KH-R-41

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Abstract: Previous theories for particle coagulation are not readily applicable to the continuous particle size distributions encountered in natural waters. By extending concepts developed in the analysis of aerosol dynamics, predictions of continuous particle size distributions were obtained dimensionally for size intervals dominated by Brownian, shear, differential sedimentation coagulation and gravitational settling. A dynamic steady state size distribution was assumed to exist, maintained by a constant flux of particle volume through the distribution. Predictions have been successfully compared with the shapes of particle size distributions measured in oceanic waters. An experimental program was designed to test the predictions with cleaned clay and silica minerals in artificial seawater. A series of batch experiments was conducted at fluid shear rates of 1/2 to 32 sec^(-1) in a rotating cylinder apparatus. During the experiments, total suspended volumes were determined from suspension optical absorbance, and particle size distributions were measured with a Coulter Counter-multichannel analyzer system. The volume flux through the distribution was estimated from the rate of suspended particle volume removal, which was second order in suspended volume and depended on the fluid shear rate. The Brownian and shear coagulation predictions were verified for the kaolinite, illite, and montmorillonite clays. The three clays were significantly different in the regions of Brownian and shear coagulation dominance and in the volume removal rates at low fluid shear rates. At higher shear rates the volume removal rates declined because of aggregate breakup by fluid shear in the rotating cylinder apparatus. Differences in the clay coagulation and breakup characteristics were explained by variations in clay aggregate porosities. Experiments with silica did not agree with predictions because the silica particles were not destabilized in seawater. Predictions for differential sedimentation coagulation and gravitational settling could not be tested because of larger aggregate breakup by the Coulter Counter. The theoretical predictions have direct application to particle coagulation in oceanic waters and possible application to more complex systems, such as estuarine waters and water and wastewater treatment operations.

ID: CaltechKHR:AC-5-80

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Abstract: The objective of this investigation is to examine the buoyancy-driven gravitational spreading currents, especially as applied to ocean disposal of wastewater and the accidental release of hazardous fluids, such as liquefied natural gas. A series of asymptotic solutions are used to describe the displacement of a gravitationally driven spreading front during an inertial phase of motion and the subsequent viscous phase. Solutions are derived by a force scale analysis and a self-similar technique for flows in stagnant, homogeneous, or linearly density-stratified environments. The self-similar solutions for inertial-buoyancy currents are found using an analogy to the well-known shallow-water wave propagation equations and also to those applicable to a blast wave in gasdynamics. For the viscous-buoyancy currents the analogy is to the viscous long wave approximation to a nonlinear diffusive wave, or thermal wave propagation. Other similarity solutions describing the initial stage of motion of the flow formed by the collapse of a finite volume fluid are developed by analogy to the expansion of a gas cloud into a vacuum. For the case of a continuous discharge there is initially a starting jet flow followed by the buoyancy-driven spreading flow. The jet mixing zone in such flows is described using Prandtl's mixing length theory. Dimensional analysis is used to derive the relevant scaling factors describing these flows.

No.: 40
ID: CaltechKHR:KH-R-40

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Abstract: The purpose of the work was to define the extent, degree and pertinent chemical characteristics of acid precipitation in the Los Angeles Basin of Southern California. Precipitation samplers were placed at nine locations: Pasadena, Azusa, Big Bear Lake, Central Los Angeles, Long Beach, Mt. Wilson, Riverside, Westwood and Wrightwood. A total of 533 individual samples were analyzed from the nine locations, and 38 different storms were sampled at one or more of the locations. Increments of precipitation collected during a storm were analyzed for pH, titration acidity, chloride, nitrate, nitrite, sulfate, fluoride, bromide, orthophosphate, total phosphate, bicarbonate, sodium, potassium, calcium, magnesium, ammonium, organic carbon and suspended solids. The mean acidity in the Fall-Spring 1978-79 period ranged from a high of 38.4 μequiva1ents/1iter at Pasadena to a low of 2.45 μequiva1ents/liter at Big Bear Lake, with corresponding mean pH's of 4.41 at Pasadena and 5.42 at Big Bear Lake. At Pasadena, individual sample (0.25 inch increments of precipitation) acidities ranged from 1600 μequiva1ents/1iter to -8.1 μequivalents/liter, and individual sample pH's ranged from 2.89 to 6.24. Incremental sampling during storms revealed significant changes in pH and chemical composition with time, with early stages of precipitation generally showing low pH and high nitrate and sulfate concentrations. For the Fall-Spring 1978-79 period the mean ratio of nitrate to non-sea salt sulfate in precipitation varied from 0.4 at Long Beach to 2.8 at Big Bear Lake. The mean ratio at Pasadena was 0.9. Data on chemical composition of precipitation indicate that the observed net acidity is the result of partial neutralization of the strong acids H_2SO_4 and HNO_3 by basic NH_3 and metal carbonates and oxides from soil dust. The relative extent of mixing of acids and bases varies considerably with location in the Basin. At Pasadena, mean Fall-Spring 1978-79 concentrations suggest that the net acidity, 38.5 μeq/l, results from mixing of 31.4 μeq/l of HNO_3, 35.6 μeq/l, of H_2SO_4, 21.1 μeq/l, of NH3, and 7.4 μeq/l, of alkalinity from soil dust. Nitrate and nitrite in rainfall at Pasadena are correlated significantly with rainfall intensity, atmospheric ozone concentration and atmospheric nitric oxide concentrations. The same correlation is found for sulfate in rainfall. Inverse correlation of nitrates and sulfate with rainfall intensity is taken to reflect a rainfall dilution effect. For both nitrate and sulfate in rainfall a correlation is observed with Pb aerosol and total aerosol particulate matter.

ID: CaltechKHR:AC-2-80

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Abstract: The objective of this study was to examine in a fundamental way the mixing processes in a stably-stratified shear flow. The results of the experimental program have yielded information on the nature of turbulence and mixing in density-stratified fluids. The results can be applied to such problems as the determination of the spreading and mixing rates of heated effluents discharged to lakes or the ocean, as well as to many geophysical problems. An experimental investigation was made to measure the mixing in a two-layered density-stratified shear flow in a flume 40-meters long, with a cross-section of 110 cm wide by 60 cm deep. Both mean temperatures and the mean velocities of the two layers could be independently controlled, and steps were taken to ensure that the temperatures and velocities of the two layers remained nearly constant at the inlet. The relative density difference between the layers was 10^-3 or less. A laser-Doppler velocimeter, designed for this study, allowed measurements of two components of velocity simultaneously, while a sensitive thermistor was used to measure the temperature. The temperature and velocity measurements were recorded and later analyzed. The initial mixing layer which developed at the inlet was found to be dominated by large, two-dimensional vortex structures. When the flow was sufficiently stratified, these structures would collapse in a short distance and the flow would develop a laminar shear layer at the interface. It was found that the bulk-Richardson number , where is the maximum-slope thickness of the temperature profile, attained a maximum value of between 0.25 and 0.3 when the mixing layer collapsed. Downstream, much less turbulent mixing took place in the stratified flows than homogeneous flows. The depth-averaged turbulent diffusivities for heat and momentum were often 30 to 100 times smaller in stratified flows than in homogeneous flows. The turbulence downstream was found to be dominated by large turbulent bursts, during which the vertical turbulent transport of momentum, heat and turbulent kinetic energy are many times larger than their mean values. It was found these bursts were responsible for most of the total turbulent transport of momentum, heat and turbulent kinetic energy, even though the bursts were found only intermittently. The flux Richardson number, Rf, in the flow was examined and found to be related to the local mean-Richardson number in many cases. When production of turbulent kinetic energy from the mean shear, , was the largest source of turbulent kinetic energy, it was found that Rf < 0.3, and when the flow was strongly stratified, then Rf < 0.2. If the diffusion of turbulent kinetic energy was the largest source of turbulent kinetic energy, then the flux-Richardson number often attained large values, and the quantity was found to be a more useful parameter than Rf. It was found that, in almost all cases, the rate at which the potential energy of the fluid increased due to turbulent mixing was much less than the estimated rate of viscous dissipation of turbulent kinetic energy.

No.: 39
ID: CaltechKHR:KH-R-39

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Abstract: The work was to be carried out as part of WMO's participation in the United Nations Development Project (UNDP) on Hydrology and Climatology of the Brazilian Amazon River Basin under the direction of Eduardo Basso, Project Manager. This project is carried out in cooperation with The General Directorate for Amazon Development of the Brazilian Government (SUDAM).

ID: CaltechKHR:KH-P-168

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Abstract: The various aspects of the propagation of long waves onto a shelf (i.e., reflection, transmission and propagation on the shelf) are examined experimentally and theoretically. The results are applied to tsunamis propagating onto the continental shelf. A numerical method of solving the one-dimensional Boussinesq equations for constant depth using finite element techniques is presented. The method is extended to the case of an arbitrary variation in depth (i.e., gradually to abruptly varying depth) in the dirlection of wave propagation. The scheme is applied to the propagation of solitary waves over a slope onto a shelf and is confirmed by experiments. A theory is developed for the generation in the laboratory of long waves of permanent form, i.e., solitary and cnoidal waves. The theory, which incorporates the nonlinear aspects of the problem, applies to wave generators which consist of a vertical plate which moves horizontally. Experiments have been conducted and the results agree well with the generation theory. In addition, these results are used to compare the shape, celerity and damping characteristics of the generated waves with the long wave theories. The solution of the linear nondispersive theory for harmonic waves of a single frequency propagating over a slope onto a shelf is extended to the case of solitary waves. Comparisons of this analysis with the nonlinear dispersive theory and experiments are presented. Comparisons of experiments with solitary and cnoidal waves with the predictions of the various theories indicate that, apart from propagation, the reflection of waves from a change in depth is a linear process except in extreme cases. However, the transmission and the propagation of both the transmitted and the reflected waves in general are nonlinear processes. Exceptions are waves with heights which are very small compared to the depth. For these waves, the entire process of propagation onto a shelf in the vicinity of the shelf is linear . Tsunamis propagating from the deep ocean onto the continental shelf probably fall in this class.

No.: 38
ID: CaltechKHR:KH-R-38

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Abstract: A mathematical model is developed resulting in a computer program for the prediction of the behavior of plumes from multiple cooling towers with multiple cells. A general integral method based on the conservation of mass, momentum, energy (heat), and moisture fluxes (before and after plume merging), were employed in the prediction scheme. The effects of ambient stratifications of temperature, moisture, and wind are incorporated in the model. An axisymmetric round plume is assumed to be emitted from each individual cell before interference with neighboring plumes. A finite length slot plume in the central part and two half round plumes at both ends of the merged plume were used to approximate the plume after merging. The entrainment and drag functions are calculated based on the modified merged plume shape. The computer output provides the predicted plume properties such as excess plume temperature, humidity and liquid phase moisture (water droplet), plume trajectory, width, and dilution at the merging locations and the beginning and ending points of the visible part of the plumes. Detailed printout and contour plots of excess temperature and moisture distribution can also be obtained if desired. Based on comparison with laboratory data this model gives good predictions for the case of dry plumes (no moisture involved). It should be noted that several empirical coefficients are as yet not accurately known. Verification of this model for the wet plume (such as for prototype cooling tower plumes) and the determination of the values for these empirical coefficients to be used in prototype applications must await detailed comparison with field data.

ID: CaltechKHR:KH-R-37

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Abstract: This investigation considers a round, turbulent buoyant jet in an ambient crossflow that is either of uniform density or with a linear density stratification. The primary emphasis is the development of a fundamental understanding of the jet properties that are of interest in engineering design problems. These include jet trajectories, characteristic dilutions, and in the case of a stratified crossflow, the maximum and equilibrium heights of rise. Most previous studies of similar buoyant jet flows have used the integral method to solve for the jet characteristics. This approach requires an assumed relation for the rate of entrainment of ambient fluid by the jet, and also depends upon experimental evidence to estimate values for the coefficients in the assumed relation. Most previous experimental studies have been directed toward evaluating entrainment coefficients and have not considered a systematic investigation of the effects of the various jet and ambient flow parameters. A major objective of this investigation is to provide a basis for the interpretation and extension of the results from previous theoretical and experimental investigations. A systematic dimensional analysis is performed to define the basic problem and to provide approximate solutions without using the integral equations. The analysis indicates the types of experiments necessary to adequately describe general buoyant jet behavior and also provides a framework for the presentation of experimental data. The approximate solutions for the jet characteristics were derived from the dimensional analysis by considering asymptotic descriptions of a general buoyant jet as different effects become predominant in determining the flow behavior. The limiting cases considered are for the jet behavior controlled by either its initial momentum or by its buoyancy for situations where the ambient velocity either is relatively large or approaches zero. Combinations of these four asymptotic descriptions can be used to approximately describe a general buoyant jet. Several different types of flow behavior can be expected, depending upon the relative magnitudes of various characteristic length scales associated with these buoyant jet flows. These different types of flow can be compared to the theoretical solutions proposed by other researchers, providing a basis for better understanding previous research. Experiments were performed to confirm the asymptotic relations developed in the analysis, to evaluate the coefficients in the relations, and to determine the limits of their applicability. The experimental configuration was a salt water jet discharged downward into a tank of less dense fluid with either uniform density or linear density stratification. The Boussinesq approximation implies that these results will be comparable to a buoyant jet rising in a less dense ambient fluid. The crossflow was simulated by towing the jet source along the water surface in the tank. Jet trajectories and dilutions were measured for the experiments with an unstratified crossflow. For the experiments performed with the tank stratified, maximum and equilibrium heights of rise, a few trajectories, and jet dilutions were measured. The results of these various experimental measurements are presented in a unified manner to facilitate the application to design problems. The experimental evidence indicated that the coefficients in the asymptotic relations were somewhat dependent upon the initial jet volume flux, an observation that has not been previously noted by other researchers. This variation can be expected from the dimensional analysis and is shown to be significant in some instances.

No.: 36
ID: CaltechKHR:KH-R-36

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Abstract: The three-dimensional flow field created by a simple line plume of finite length in a steady current of uniform density was investigated in a laboratory basin. The results can be used to aid in the prediction of dispersion of buoyant waste water released from line diffusers, particularly sewage discharges into the ocean. The experimental results for minimum surface dilution, S_m, were found to be independent of L/H, in the range 3.7 < L/H < 30 where L is the diffuser length and H the water depth, and independent of Reynolds number, Re = 4uH/ν, in the range 1190 < Re < 12,900 where u is the current velocity. The results are expressed graphically in the form: (S_(m)q)/uH = f(F,θ), where q is the volume flux per unit length, and θ the orientation of the line diffuser to the current. F is a type of Froude number defined by F = u^(3)/b, where b is the buoyancy flux per unit length. The initial momentum flux is assumed to be small. For a current perpendicular to the diffuser, and F > 0.2, the effluent mixes over the receiving water depth due to self-induced turbulence. When the diffuser is of finite length, the diluted effluent separates from the bottom at some point downstream and forms a two-layer flow. However, currents parallel to the diffuser do not produce mixing over the depth, and the flow forms a two-layer system immediately, even for Froude numbers as high as 100. For F < 0.1, dilution is independent of current speed and direction. For F > 0.1, dilutions when the current is perpendicular to the diffuser are proportional to the current speed. For 0.1 < F < 100 this dilution is about 60% of that predicted assuming uniform mixing of the effluent over the receiving water depth. This is due to the development of a vertically stable density profile. For F > 0.1, a diffuser placed perpendicular to the current will result in greater dilutions than if parallel. The ratio of minimum surface dilution when the current is perpendicular to that when the current is parallel increases with F, and is equal to about 4 at F = 100. Horizontal spreading of the waste field is governed by buoyancy forces rather than ambient turbulence. For F ≥ 1 the initial surface plume spreading is found to be linear, and independent of L/H and Re for 3.7 < L/H < 15, and 2,900 < Re < 13,000. Beyond this initial linear spreading zone the rate of plume growth decreases. It is speculated that regimes may exist where the surface width grows as the 2/3 or 1/5 power of downstream distance; the results are not adequate to confirm these growth laws. It is believed that ambient turbulence has no significant effect on diluting the waste within several diffuser lengths from the source. The results have been presented in a manner which makes them immediately applicable for improving outfall designs, and demonstrates the error frequently made in assuming two-dimensional flow fields. This assumption is incorrect even if the diffuser length is an order of magnitude greater than the water depth.

No.: 35
ID: CaltechAUTHORS:20160505-112155687

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Abstract: An empirical relationship is presented for the incipient motion of bottom material under solitary waves. Two special cases of bottom material are considered: particles of arbitrary shape, and isolated sphere resting on top of a bed of tightly packed spheres. The amount of motion in the bed of particles of arbitrary shape is shown to depend on a dimensionless shear stress, similar to the Shields parameter. The mean resistance coefficient used in estimating this parameter is derived from considerations of energy dissipation, and is obtained from measurements of the attenuation of waves along a channel. A theoretical expression for the mean resistance coefficient is developed for the case of laminar flow from the linearized boundary layer equations and is verified by experiments. For the case of a single sphere resting on top of a bed of spheres, the analysis is based on the hypothesis that at incipient motion the hydrodynamic moments which tend to remove the sphere are equal to the restoring moment due to gravity which tends to keep it in its place. It is shown that the estimation of the hydrodynamic forces, based on an approach similar to the so-called "Morison's formula", in which the drag, lift, and inertia coefficients are independent of each other, is inaccurate. Alternatively, a single coefficient incorporating both drag, inertia, and lift effects is employed. Approximate values of this coefficient are described by an empirical relationship which is obtained from the experimental results. A review of existing theories of the solitary wave is presented and an experimental study is conducted in order to determine which theory should be used in the theoretical analysis of the incipient motion of bottom material. Experiments were conducted in the laboratory in order to determine the mean resistance coefficient of the bottom under solitary waves, and in order to obtain a relationship defining the incipient motion of bottom material. All the experiments were conducted in a wave tank 40 m long, 110 cm wide with water depths varying from 7 cm to 42 cm. The mean resistance coefficient was obtained from measurements of the attenuation of waves along an 18 m section of the wave tank. Experiments were conducted with a smooth bottom and with the bottom roughened with a layer of rock. The incipient motion of particles of arbitrary shape was studied by measuring the amount of motion in a 91 cm x 50 cm section covered with a 15.9 mm thick layer of material. The materials used had different densities and mean diameters. The incipient motion of spheres was observed for spheres of different diameters and densities placed on a bed of tightly packed spheres. The experiments were conducted with various water depths, and with wave height-to-water depth ratios varying from small values up to that for breaking of the wave. It was found that: (a) The theories of Boussinesq (1872) and McCowan (1891) describe the solitary wave fairly accurately. However, the differences between these theories are large when used to predict the forces which are exerted on objects on the bottom, and it was not established which theory describes these forces better. (b) The mean resistance coefficient for a rough turbulent flow under solitary waves can be described as a function of D_s, h, and H, where D_s is the mean diameter of the roughness particles, h is the water depth, and H is the wave height. (c) Small errors in the determination of the dimensionless shear stress for incipient motion of rocks result in large errors in the evaluation of the diameter of the rock required for incipient motion. However, it was found that the empirical relationship for the incipient motion of spheres can be used to determine the size of rock of arbitrary shape for incipient motion under a given wave, provided the angle of friction of the rock can be determined accurately.

ID: CaltechKHR:KH-R-34

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Abstract: The classical concept that mean bed elevation over an entire stream reach is lowered by scour during flood-wave passage and is restored by deposition in the waning flood phase (mean-bed scour and fill) can be challenged. The alternative that both scour and fill occur concurrently at different migrating loci within a reach (local scour and fill) is more consistent with published field data. The field and laboratory investigations reported herein suggest that mean-bed scour and fill in a uniform channel is minor compared to local scour and fill caused by bedform migration, and that maximum local scour and fill may occur on the waning flood in some instances. The field experiment, utilizing a rectilinear array of buried maximum-scour indicators (scour-cords), produced data for contouring of maximum scour and fill in an ephemeral streambed during two floods. In the first flood, 24 em of scour and fill was measured for a bankfull flow depth of 23 cm. In the second, maximum scour and fill was at least 66 cm for a bankfull flow depth of 34 cm. Estimates of antidune amplitudes for the two floods, based on theoretical models and laboratory and field observations, are 28 to 64 cm and 48 to 97 cm, respectively. This indicates that all scour and fill measured by the scour-cord array could have been caused by antidune migration. Laboratory experiments were conducted in an 18 m-long open-circuit flume with automated sediment and water input-rate controls. A series of experiments in a 26.7 cm-wide sand-bed channel with rigid walls, at grade for a simulated flood patterned after those typical of ephemeral streams, showed that mean-bed scour and fill was less than 3 percent of local scour and fill. For these experiments, mean sand size was 0.3 mm, channel slope was .009, maximum water depth was 40 mm, maximum local scour and fill was 22 mm, and maximum mean-bed scour and fill was 0.6 mm. Maximum mean bed elevation variation was thus only two sand-grain diameters. Fill occurred at peak flow followed by scour to the pre-flood mean bed elevation on the waning flood. Maximum local scour and fill took place near the end of the simulated floods, when bedform amplitudes were the greatest. A series of simulated-flood experiments in a sand-bed channel with erodible sand banks showed scour and fill behavior qualitatively similar to that of the rigid-wall channel. Bank erosion, channel meandering, and braiding prevented quantitative scour and fill measurements in these alluvial-bank experiments. Measured flow and bedform parameters and scour and fill data derived from small laboratory scour-chains were compatible with those estimated from the theoretical model used in the field experiment.

ID: CaltechKHR:KH-R-33

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Abstract: The entrainment and mixing processes in a two-dimensional vertical turbulent buoyant (heated) jet in its transition state from a pure jet to a pure plume have been studied. The ambient fluid is of uniform density and non-flowing except for the flow induced by the jet. Density variations are assumed small. The equations of motion integrated across the jet have been carefully examined and it has been found that the kinematic buoyancy flux of a heated plume and the kinematic momentum flux of a pure jet are not in general conserved. It has been proven that the flow in a two-dimensional pure jet is not self-preserving. A systematic set of experiments was carried out to examine turbulent buoyant jet behavior for a wide range of initial Richardson numbers (or densimetric Froude numbers). Values of the Richardson number, which describes the relative importance of buoyancy in a jet, extended from the value appropriate for a pure jet (zero) to that appropriate for a plume (approximately 0.6). The buoyant jet temperature and velocity fields were measured using calibrated fast response thermistors and a laser Doppler velocimeter respectively. The velocity and temperature data obtained were recorded magnetically in digital form and subsequently processed to extract both mean and fluctuating values of temperature and velocity. The structure of the mean flow (including the spreading rate of the mean velocity and temperature profiles, velocity and temperature distribution along jet axis, and the heat flux profile), the turbulence structure (including the profile of turbulence intensity and turbulent heat transfer, probability density distribution of temperature and velocity, skewness and flatness factor of temperature fluctuations) and the large scale motions (intermittency, profile of maximum and minimum temperature, frequency of crossing of hot/cold, cold/hot interface) of a buoyant jet were investigated as a function of the jet Richardson number. It was determined that the turbulent heat transfer and the turbulent intensity increase with increasing the Richardson number. The spreading rate of the transverse mean velocity and temperature profiles were found to be independent of the Richardson number. The turbulent buoyancy flux in a fully developed buoyant jet has been found to be a significant fraction (38%) of the axial buoyancy flux.

ID: CaltechKHR:KH-R-32

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Abstract: For thousands of years breakwaters have been built at or near the coast to protect harbors or coastlines from wave attack. One of the earliest known harbor protection schemes was devised in about 2000 B.C. for the Port of Pharos on the open coast of Egypt; it had a rubble-mound breakwater approximately 8500 ft long composed of large blocks of stone with smaller stone filling the spaces between blocks (Savile 1940). Until the development of experimental laboratory techniques to investigate the effect of waves on breakwaters, these structures were designed primarily from experience gained from other similar structures. It is the purpose of this review to discuss various aspects of the hydrodynamics of wave attack on such structures and the relation of certain analytic considerations and experimental results to the design of a rubble-mound. A breakwater built as a rubble-mound is constructed by placing material of various sizes layer by layer (or unit by unit) until the desired cross-section shape is achieved. Generally, the units are not structurally connected, so that the integrity of the rubble-mound depends on features such as the weight of the material, the interlocking nature of the material, and the cross section of the structure. Usually the structure is built with material graded from smaller sizes in the core to larger material armoring the face against wave attack. The armor layer may be composed of quarry-stone, if it is available in the required sizes and is economically feasible to use. When these conditions are not met, specially designed concrete units for armoring the face of the rubble-mound have been developed that tend to interlock better than rock when properly placed; hence, it may be possible to use armor units lighter than the required quarry-stone. Over the years numerous geometric shapes have been developed for such armor units, with each shape generally introduced in an attempt to improve on the interlocking characteristics of its predecessors. To mention only a few, various names used for different units are: tribars, tetrapods, quadripods, and dolosse. A brief description of two of these is presented; for a more detailed discussion of shape along with drawings of the units the interested reader is directed to CERC (1966) and Hudson(1974). Tribars, which consist basically of three circular cylinders connected by a yoke of three cylinders, are usually placed in a uniform geometric pattern on the face of the rubble-mound. Dolosse are shaped like the letter "H" with the vertical legs rotated 90° to each other, and are generally placed randomly on a rubble-mound face. It is the effective interlocking of dolosse that leads to the use of random placement techniques. Obviously an important aspect in the design of a rubble-mound is its stability under wave attack. This subject is discussed in detail, along with descriptions of the basis for certain design approaches currently used. The support of these design criteria as well as their limitations are discussed with reference to available experimental data. Three other aspects of the effect of waves on rubble-mounds are treated in this review: wave run-up, transmission, and overtopping. Run-up is defined as the vertical height above still water level to which waves incident upon a structure can be expected to travel up the face of the structure. Wave run-up is important in defining both the amount of wave energy transmitted over and through permeable rubble-mounds and also the quantity of water that may be expected to overtop the structure. In each of the following sections the discussion is directed toward understanding the fluid-mechanic aspects of the various problems and the features and the shortcomings of analytical and experimental models used in connection with the design of breakwaters constructed as rubble-mounds.

Publication: Annual Review of Fluid Mechanics Vol.: 7ISSN: 0066-4189

ID: CaltechAUTHORS:RAIarfm75

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Abstract: This report presents and interpretation of results obtained during the hydraulic model study previously documented in "Hydraulic Modeling of Thermal Outfall Diffusers for the San Onofre Nuclear Power Plant" which described the hydraulic laboratory studies conducted to investigate outfall configurations for the thermal discharge from proposed Units 2 and 3 at the San Onofre Nuclear Generating Station, jointly owned by the Southern California Edison Company and San Diego Gas and Electric Company. A number of different experimental investigations were performed to develop the conceptual design for the new Units 2 and 3 discharge diffusers. The primary reason for the investigations was the new California thermal standards (essentially ambient temperature increment less than 4°F), which in effect precluded the use of shoreline or single outlet discharges for new units and necessitated the use of multiport diffusers. The result of the investigations of different diffuser concepts was the establishment of a preliminary design for the discharge structures for Units 2 and 3, each consisting of a diffuser 2500 ft long containing 76 discharge nozzles with a nominal discharge velocity of 13 ft/sec. This preliminary design was later modified somewhat by the engineers of the Southern California Edison Company (SCE) in consideration of other factors such as structural requirements, cost, construction problems, and more accurate bathymetric details at the site. As a result the final design for each diffuser contains 63 discharge ports of diameters varying from 21.85 to 23.9 inches. The discharge ports are nozzle-riser assemblies at alternate angles of ±25° with respect to the longitudinal axis of the diffuser and 20° up from horizontal. The nozzles are positioned approximately 6 ft from the ocean bottom. The diffusers are aligned perpendicular to shore and extend from approximately 3500 ft to 8500 ft offshore. The performance of the final diffuser design was evaluated in a series of confirming tests. The major results will be summarized and discussed in section 3 of this report. Sections 3 and 4 will also include projections and elaborations on several aspects of the diffuser performance to be expected in the prototype. The possible interactions of the proposed diffuser operation with existing site factors such as ocean currents, water temperature, heat losses, and the existing power plant (Unit 1) will also be discussed in section 4.

ID: CaltechKHR:KH-R-31

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Abstract: Various hydraulic model tests were performed in connection with the design and performance of the offshore thermal outfalls for the San Onofre Nuclear Generating Station (jointly owned by the Southern California Edison Company and the San Diego Gas and Electric Company)near San Clemente, California. These include model investigations of: (i) the multiple port discharges for the proposed Units 2 and 3, (ii) the existing submerged single outlet from Unit 1, (iii) the discharge of heated water from the Units 2 and 3 intakes during heat treatment, and (iv) hydraulic characteristics of discharge ports. On the basis of these investigations, the diffusion structure for each of the proposed new units was designed to be 2500 feet long aligned perpendicular to shore. The diffuser for Unit 3 will extend from 3500 to 6000 feet from shore, and that for Unit 2 from 6000 to 8500 feet from shore. Each diffuser will have 63 discharge nozzles aimed offshore (±25° from the pipe axis, 20° above horizontal). The momentum of the discharge produces and offshore drift of the diluted warm-water plume. The maximum temperature rise on the surface caused by the discharge was found to decrease with increasing longshore current speed, and the discharge momentum from the jets was effective in preventing significant re-entrainment in the event of reversing or low currents. Although the California thermal discharge requirements specify a maximum surface temperature increase of 4°F (beyond 1000 feet from the discharge structure), the laboratory target maximum was established at 2.5°F, to account for possible model-prototype differences and unmodeled effects. The hydraulic model studies showed that the proposed outfall design meets the laboratory target value for a variety of possible longshore current conditions; therefore, it is predicted that the prototype outfall operation will meet the California thermal discharge requirements.

ID: CaltechKHR:KH-R-30

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Abstract: This report summarizes the results of a five-year laboratory research project on various flow phenomena of importance to transport and dispersion of pollutants in hydrologic and coastal environments. The results are useful in two general ways: first, to facilitate the prediction of ambient water quality from effluent characteristics in various water environments; and secondly, to provide the basis for design of systems (like outfalls) required to meet given ambient water quality requirements. The results for buoyant jets may be used for the design of waste-water outfalls in oceans, reservoirs, lakes, and large estuaries. Particular emphasis is given to line sources (or slot jets) which represent long multiple-outlet diffusers, which are necessary for all large discharges to get high dilutions. For reservoirs which are density stratified, the results include formulations for prediction of selective withdrawal, and a simulation procedure for predicting reservoir mixing by systems which pump water from one level to the other. For application to rivers and estuaries, laboratory flume experiments were made to measure transverse mixing of buoyant or heavy tracer flows, as well as for neutral-density flows. Abstracts for all publications and reports resulting from the project are given as an appendix to the report.

ID: CaltechKHR:KH-R-29

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Abstract: A general solution is presented for water waves generated by an arbitrary movement of the bed (in space and time) in a two-dimensional fluid domain with a uniform depth. The integral solution which is developed is based on a linearized approximation to the complete (nonlinear) set of governing equations. The general solution is evaluated for the {specific case of a uniform upthrust or downthrow of a block section of the bed; two time-displacement histories of the bed movement are considered. An integral solution (based on a linear theory) is also developed for a three-dimensional fluid domain of uniform depth for a class of bed movements which are axially symmetric. The integral solution is evaluated for the specific case of a block upthrust or downthrow of a section of the bed, circular in planform, with a time-displacement history identical to one of the motions used in the two-dimensional model. Since the linear solutions are developed from a linearized approximation of the complete nonlinear description of wave behavior, the applicability of these solutions is investigated. Two types of nonlinear effects are found which limit the applicability of the linear theory: (1) large nonlinear effects which occur in the region of generation during the bed movement, and (2) the gradual growth of nonlinear effects during wave propagation. A model of wave behavior, which includes, in an approximate manner, both linear and nonlinear effects is presented for computing wave profiles after the linear theory has become invalid due to the growth of nonlinearities during wave propagation. An experimental program has been conducted to confirm both the linear model for the two-dimensional fluid domain and the strategy suggested for determining wave profiles during propagation after the linear theory becomes invalid. The effect of a more general time-displacement history of the moving bed than those employed in the theoretical models is also investigated experimentally. The linear theory is found to accurately approximate the wave behavior in the region of generation whenever the total displacement of the bed is much less than the water depth. Curves are developed and confirmed by the experiments which predict gross features of the lead wave propagating from the region of generation once the values of certain nondimensional parameters (which characterize the generation process) are known. For example, the maximum amplitude of the lead wave propagating from the region of generation has been found to never exceed approximately one-half of the total bed displacement. The gross features of the tsunami resulting from the Alaskan earthquake of 27 March 1964 can be estimated from the results of this study.

No.: 28
ID: CaltechKHR:KH-R-28

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Abstract: A laboratory investigation was conducted to determine the effects of water temperature on sediment discharge close to the bed (bed-load discharge), and on bed roughness and geometry in alluvial, open-channel flows. Three types of experiments were made: 1) Low-transport, flat-bed experiments in which all of the sediment discharged moved as bed load; 2) high-transport, flat-bed experiments with fine sands wherein there was considerable suspended sediment discharge; and 3) a series of experiments where the discharge was kept constant and the velocity varied to produce ripple, dune, and flat-bed configurations. The experiments were made in pairs. In each pair the velocity and depth were the same or nearly the same, but in one experiment the water temperature was from 15°C to 20°C higher than in the other. It was found that in low-transport, flat-bed flows where particle transport is by rolling and sliding along the bed, a 15°C to 20°C increase in water temperature can produce a relatively large change in sediment discharge. The nature of this change depends on the flow condition at the bed. With hydrodynamically smooth flow there is an increase in sediment discharge with increase in water temperature; whereas in transition from smooth to rough an increase in water temperature effects a reduction in sediment discharge. With fully-rough flow which obtains at boundary Reynolds numbers larger than approximately 200, sediment discharge does not depend on water temperature. A phenomenological explanation has been presented for these observed temperature effects on sediment discharge. In high-transport, flat-bed flows with suspended sediment transport, it was observed that the temperature effects on bed-load discharge are qualitatively the same as those which obtain in low-transport, flat-bed flows of approximately the same boundary Reynolds numbers. It was also found that under certain flow conditions a change in water temperature alone can cause a change in bed form. The nature of this change in bed form seems to be related to the boundary Reynolds numbers R'_(*b) of the flows. For R'_(*b) less than a value near 8 bed form transitions were accomplished at lower velocities in a warm water flow than in a cold water flow at the same discharge; whereas for larger values of R'_(*b) contrary temperature effects on bed form transitions have been observed.

ID: CaltechKHR:KH-R-27

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Abstract: A linear, inviscid theory, termed the coupled basins theory, has been developed to analyze the response to periodic incident waves of an arbitrary shape harbor containing several interconnected basins. The region of consideration is divided into an open-sea region and several inner-basin regions (the number depending on the harbor geometry). The solution in each region is formulated as an integral equation in terms of the normal velocity at the entrance and/or at the common boundaries between regions. An approximate method is used to solve the integral equation by converting it to a matrix equation. The initially unknown boundary condition at the entrance is determined by matching the wave amplitudes and their normal derivatives at the harbor entrance and at all the common boundaries. The solution for the response and the amplitude distribution within the complete harbor can then be obtained. It has been found that the coupled-basins theory gives results which agree well with experiments both for an irregular shape harbor as well as for a harbor composed of two connected circular basins. Various aspects of the response of harbors composed of several types of circular connected basins as well as circular harbors with rectangular entrance channels have been investigated. It is found that to a first approximation the response of a coupled harbor system can be constructed by superposing the response of the individual harbors Certain aspects of the effect of viscous dissipation on harbor resonance are discussed. Some attention is given to problems of scaling model results to the prototype harbor.

No.: 26
ID: CaltechKHR:KH-R-26

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Abstract: The diffusion following the release of a buoyant slot jet into a confined, uniformly flowing environment has been studied. A dimensionless analysis reveals the complexity of the problem; there are in general four governing dimensionless numbers. However, if the overall mixing and not the details of the process of diffusion is of importance, we can define basic flow regimes using a reduced number of parameters. Experiments were conducted first with a horizontal, buoyant slot jet into stagnant, ambient fluid. Observed trajectories and centerline dilutions were in good agreement with existing theories. In addition, two sets of experiments were perform ed with a vertical and a horizontal buoyant slot jet issuing into a uniformly flowing stream. A two-layer flow analysis provided the rationale for a classification of flow regimes. It was found that the mechanism of upstream intrusion of jet effluent is characterized primarily by a gross densimetric Froude number based on the ambient flow velocity and the buoyancy flux from the source. However, the formation of an upstream wedge may be hampered due to the effect of initial flux of momentum in the downstream direction. When the buoyant slot jet cannot entrain all the oncoming flow, while maintaining the typical jet or plume behavior, then the jet flow pattern breaks up and there is efficient mixing close to the source.

No.: 25
ID: CaltechKHR:KH-R-25

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Abstract: The transverse spreading of a plume generated by a point source in a uniform open-channel flow is investigated. A neutrally-buoyant tracer was injected continuously at ambient velocity through a small round source at a point within the flow. Tracer concentration was measured in situ at several points downstream of the source using conductivity probes. Tracer concentration was analyzed in two phases. In Phase I, time-averaged concentration was evaluated, its distribution within the plume determined, and characteristic coefficients of transverse mixing calculated. It was shown that the transverse mixing coefficient varied with the flow level and was highest near the water surface where flow velocity was greatest. In contrast to previous speculation, the ratio of the depth-averaged coefficient of transverse mixing D-_z to the product of the (bed) shear velocity u_* and the flow depth d was not a constant but depended on the aspect ratio γ = d/W, where W = flume width. For laboratory experiments D-_z/u_*d decreased from .024 to 0.093 as γ increased from 0.015 to 0.200. In Phase II, the temporal fluctuation of tracer concentration was studied in three sections. In the first, the intermittency factor technique was used to delineate three regions of the plume cross section: an inner core where tracer concentration c(t) was always greater than the background C_b; an intermittency region where c(t) was only intermittently greater than C_b; and the outer region where C_b was never exceeded. Dimensional analysis furnished universal curves for prediction of the geometric characteristics of the three regions. In the second section, the entire plume, at a fixed station, was treated as a fluctuating cloud. Variances characterizing the fluctuation of the plume centroid and the variation of the plume width were calculated and compared. In the third section, the intensity and probability density of the concentration fluctuations at fixed points were calculated. The distribution of the peak-to-average ratio was also determined. Finally the results of the two phases of study were interrelated to evaluate their contributions to the transverse spreading of the plume.

ID: CaltechKHR:KH-R-23

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Abstract: The air-bubble plume induced by the steady release of air into water has been analyzed with an integral technique based on the equations for conservation of mass, momentum and buoyancy. This approach has been widely used to study the behavior of submerged turbulent jets and plumes. The case of air-bubble induced flow, however, includes additional features. In this study the compressibility of the air and the differential velocity between the rising air bubbles, and the water are introduced as basic properties of the air-bubble plume in addition to a fundamental coefficient of entrainment and a turbulent Schmidt number characterizing the lateral spreading of the air bubbles. Theoretical solutions for two- and three-dimensional air-bubble systems in homogeneous, stagnant water are presented in both dimensional and normalized form and compared to existing experimental data. The further complication of a stratified environment is briefly discussed since this case is of great practical interest. This paper is to be considered as a progress report, as future experimental verification of various hypotheses is needed.

ID: CaltechKHR:KH-R-24

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Abstract: This study is an investigation of the mixing of density-stratified impoundments by means of buoyant jets created by a pumping system. The deterioration of water quality which often occurs in density-stratified lakes and reservoirs may be counteracted by mixing. The physical aspects of the mixing process are the primary concern of this study, although several implications regarding changes in water quality are indicated. A simulation technique is developed to predict the time-history of changes in the density-depth profiles of an impoundment during mixing. The simulation model considers the impoundment closed to all external influences except those due to the pumping system. The impoundment is treated in a one-dimensional sense, except for the fluid mechanics of the three-dimensional jet and selective withdrawal of pumping system. The numerical solution to the governing equations predicts density profiles at successive time steps during mixing, given the initial density profile, the area-depth relation for the impoundment, the elevations of intake and jet discharge tubes, and the jet discharge and diameter. The changes due to mixing in the profiles of temperature and of a conservative, non-reacting tracer can be predicted also. The results of laboratory experiments and two field mixing experiments in which density-stratified impoundments were mixed using pumping systems show that the simulation technique predicts the response of the impoundment reasonably well. The results of a series of simulated mixing experiments for impoundments which have prismatic shapes and initially linear density profiles are given in dimensionless form. For these special conditions, the efficiency of the pumping system increased as the jet densimetric Froude number decreased, and the time required for complete mixing was a fraction of the characteristic time, T ≤ V-/Q (where V- is the impoundment volume included between intake and jet elevations and Q is the pumped discharge). Recommendations are made for the application of the generalized results and for the use of the simulation technique for lakes and reservoirs which are not closed systems.

ID: CaltechKHR:KH-R-22

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Abstract: This study investigates lateral mixing of tracer fluids in turbulent open-channel flows when the tracer and ambient fluids have different densities. Longitudinal dispersion in flows with longitudinal density gradients is investigated also. Lateral mixing was studied in a laboratory flume by introducing fluid tracers at the ambient flow velocity continuously and uniformly across a fraction of the flume width and over the entire depth of the ambient flow. Fluid samples were taken to obtain concentration distributions in cross-sections at various distances, x, downstream from the tracer source. The data were used to calculate variances of the lateral distributions of the depth-averaged concentration.When there was a difference in density between the tracer and the ambient fluids, lateral mixing close to the source was enhanced by density-induced secondary flows; however, far downstream where the density gradients were small, lateral mixing rates were independent of the initial density difference. A dimensional analysis of the problem and the data show that the normalized variance is a function of only three dimensionless numbers, which represent: (1) the x-coordinate, (2) the source width, and (3) the buoyancy flux from the source. A simplified set of equations of motion for a fluid with a horizontal density gradient was integrated to give an expression for the density-induced velocity distribution. The dispersion coefficient due to this velocity distribution was also obtained. Using this dispersion coefficient in an analysis for predicting lateral mixing rates in the experiments of this investigation gave only qualitative agreement with the data. However, predicted longitudinal salinity distributions in an idealized laboratory estuary agree well with published data.

ID: CaltechKHR:KH-R-21

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Abstract: Theoretical and experimental studies were conducted to investigate the wave induced oscillations in an arbitrary shaped harbor with constant depth which is connected to the open-sea. A theory termed the "arbitrary shaped harbor" theory is developed. The solution of the Helmholtz equation, ∇^2f + k^af = 0, is formulated as an integral equation; an approximate method is employed to solve the integral equation by converting it to a matrix equation. The final solution is obtained by equating, at the harbor entrance, the wave amplitude and its normal derivative obtained from the solutions for the regions outside and inside the harbor. Two special theories called the circular harbor theory and the rectangular harbor theory are also developed. The coordinates inside a circular and a rectangular harbor are separable: therefore, the solution for the region inside these harbors is obtained by the method of separation of variables. For the solution in the open-sea region, the same method is used as that employed for the arbitrary shaped harbor theory. The find solution is also obtained by a matching procedure similar to that used for the arbitrary shaped harbor theory. These two special theories provide a useful analytical check on the arbitrary shaped harbor theory.

No.: 20
ID: CaltechKHR:KH-R-20

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Abstract: The major objective of the study has been to investigate in detail the rapidly-varying peak uplift pressure and the slowly-varying positive and negative uplift pressures that are known to be exerted by waves against the underside of a horizontal pier or platform located above the still water level, but not higher than the crests of the incident waves. In a "two-dimensional" laboratory study conducted in a 100-ft long by 15-in.-wide by 2-ft-deep wave tank with a horizontal smooth bottom, individually generated solitary waves struck a rigid, fixed, horizontal platform extending the width of the tank. Pressure transducers were mounted flush with the smooth soffit, or underside, of the platform. The location of the transducers could be varied. The problem of adequate dynamic and spatial response of the transducers was investigated in detail. It was found that unless the radius of the sensitive area of a pressure transducer is smaller than about one-third of the characteristic width of the pres sure distribution, the peak pressure and the rise-time will not be recorded accurately. A procedure was devised to correct peak pressures and rise-times for this transducer defect. The hydrodynamics of the flow beneath the platform are described qualitatively by a simple analysis, which relates peak pressure and positive slowly-varying pressure to the celerity of the wave front propagating beneath the platform, and relates negative slowly-varying pressure to the process by which fluid recedes from the platform after the wave has passed. As the wave front propagates beneath the platform, its celerity increases to a maximum, then decreases. The peak pressure similarly increases with distance from the seaward edge of the platform, then decreases. Measured peak pressure head, always found to be less than five times the incident wave height above still water level, is an order of magnitude less than reported shock pressures due to waves breaking against vertical walls; the product of peak pressure and rise-time, considered as peak impulse, is of the order of 20% of reported shock impulse due to waves breaking against vertical walls. The maximum measured slowly-varying uplift pressure head is approximately equal to the incident wave height less the soffit clearance above still water level. The normalized magnitude and duration of negative pressure appears to depend principally on the ratio of soffit clearance to still water depth and on the ratio of platform length to still water depth.

No.: 19
ID: CaltechKHR:KH-R-19

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Abstract: Theoretical solutions were obtained for four classes of turbulent buoyant jet problems, namely,
1) an inclined, round buoyant jet in a stagnant, uniform ambient fluid;
2) an inclined, round buoyant jet in a stagnant ambient fluid with linear density-stratification;
3) an inclined, slot buoyant jet in a stagnant, uniform ambient fluid;
4) an inclined, slot buoyant jet in a stagnant ambient fluid with linear density-stratification.
This report is a summary of the numerical simulations on buoyant jets in stagnant environments carried out in connection with previous investigations by Fan (10), Fan and Brooks (12) and Brooks and Koh (8). Using the integral type of analysis, assuming similarity, predictions can be made for jet trajectory, widths, and dilution ratios, in a uniform or density-stratified environment without ambient currents. Numerical solutions have been presented in dimensionless form for a wide range of initial conditions including the effect of the initial angle of discharge.
Problems with __non__-linear density profiles are not readily treated in generalized non-dimensional form. Rather it is more feasible to make case by case calculations using dimensional variables. A program for such calculations for a round jet is available in a technical memorandum by Ditmars (16).
These solutions are useful in the design of disposal systems for sewage effluent into the ocean or cooling water into a lake.

No.: 18
ID: CaltechKHR:KH-R-18

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Abstract: Beginning of bedload transport in channels, whose beds are formed by gravel-sand mixtures, is theoretically and experimentally investigated. In order to make a theoretically approachable treatment to the problem two assumptions are made: 1. the turbulent fluctuations of the bottom shear stress are statistically describable by a Gaussian distribution; 2. a grain starts in motion when the effective (instantaneous) eroding bottom shear stress on a grain exceeds a critical value, which is a function of the grain size and Reynolds number of the grain. On the basis of these assumptions the probability of remaining still (or being eroded) for a certain grain under given hydraulic conditions is calculated (equation 8; this probability is independent of the grain size distribution of the gravel-sand mixture). During the work a feasible way was found to determine the critical shear stress by a basically new method: the average bottom shear stress was defined as equal to the control shear stress, when for the grain in question, the probability for remaining still and being eroded are equal. To supplement and verify the theory, natural armoring of channel bottoms consisting of gravel-sand-mixtures was investigated in the laboratory. On the basis of these experiments the dimension- less critical shear stress can be determined as a function of the Reynolds number of the grains (Fig. 8), and the distribution function of the fluctuation of the bottom shear stress (Fig. 9); in doing so it was confirmed that the distribution function can be approximated by the Gaussian distribution with a standard deviation of σ = 0.57. The laboratory experiments were supplemented by observations in the field.

No.: T-5
ID: CaltechAUTHORS:20200624-114805343

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Abstract: This study was conducted to determine the dynamic characteristics of small boats moored with non-linear-elastic lines in an asymmetrical manner. The motions being considered are surge motions where the moored boat is allowed to move either in the direction of the bow or the stern, but not in other coordinate directions. An analytical model is proposed where the small boat is simulated by a block-body which is moored asymmetrically to a fixed dock. A method is developed from which the non-linear restoring forces and the dynamic response of the boat in surge can be obtained. The restoring force which is associated with the boat displacement is defined by the material, condition, and dimensions of the lines and the mooring geometry. From those results, an approximation to the restoring force is made so that a closed solution to the problem is possible. The periods of free oscillation determined by this method are compared to the results of some experiments conducted on a 26-foot boat with a displaced weight of approximately 7000 lbs. The experiments were performed using this small boat moored under different conditions: all lines taut, 4 inches slack in all lines, and 8 inches slack in all lines. These results compared favorably with the analytical results. The response of seven small boats of various displaced weights were determined analytically to evaluate the range of important wave periods for this sample. The mooring dimensions of these boats were measured in situ and the theoretical approach developed was applied. The results indicate, for the samples considered, that the important range of periods of forced oscillation for excessive motions of these boats in surge was less than 10 secs. If stiff mooring systems had been employed for all of these boats the important wave period range for these motions could probably be reduced further. Due to the different mooring systems used, the response curves for some of the small boats were highly asymmetrical indicating the possibility of much greater motions in one direction than in another under the action of a periodic symmetrical force. A limited series of experiments were conducted to determine the effect of the proximity of flotation chambers which are used on some floating slips on the response of the moored boat. It was found that these chambers, as simulated in the laboratory, did not have a significant effect on the dynamic characteristics of the moored boat. However, they did act as floating breakwaters thereby reducing the transmitted wave energy.

No.: 17
ID: CaltechKHR:KH-R-17

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Abstract: This study is concerned with some of the properties of roll waves that develop naturally from a turbulent uniform flow in a wide rectangular channel on a constant steep slope. The wave properties considered were depth at the wave crest, depth at the wave trough, wave period, and wave velocity. The primary focus was on the mean values and standard deviations of the crest depths and wave periods at a given station and how these quantities varied with distance along the channel. The wave properties were measured in a laboratory channel in which roll waves developed naturally from a uniform flow. The Froude number F (F = u_n/√gh_n, u_n = normal velocity, h_n = normal depth, g = acceleration of gravity) ranged from 3.4 to 6.0 for channel slopes S_0 of .05 and . 12 respectively. In the initial phase of their development the roll waves appeared as small amplitude waves with a continuous water surface profile. These small amplitude waves subsequently developed into large amplitude shock waves. Shock waves were found to overtake and combine with other shock waves with the result that the crest depth of the combined wave was larger than the crest depths before the overtake. Once roll waves began to develop, the mean value of the crest depths h_(max) increased with distance. Once the shock waves began to overtake, the mean wave period T_(av) increased approximately linearly with distance. For a given Froude number and channel slope the observed quantities h_(max)/h_n, T' (T' = S_0 T_(av) √g/h_n), and the standard deviations of h_(max)/h_n and T', could be expressed as unique functions of ℓ /h_n (ℓ= distance from beginning of channel) for the two-fold change in h_n occurring in the observed flows. A given value of h_(max)h_n occurred at smaller values of ℓ/h_n as the Froude number was increased. For a given value of h_(max) /h_n the growth rate ∂h_(max)/∂ℓ of the shock waves increased as the Froude number was increased. A laboratory channel was also used to measure the wave properties of periodic permanent roll waves. For a given Froude number and channel slope the h_(max)/h_n vs. T' relation did not agree with a theory in which the weight of the shock front was neglected. After the theory was modified to include this weight, the observed values of h_(max)/h_n were within an average of 6.5 percent of the predicted values, and the maximum discrepancy was 13.5 percent. For h_(max)/h_n sufficiently large (h_(max)/h_n > approximately 1.5) it was found that the h_(max)/h_n vs. T' relation for natural roll waves was practically identical to the h_(max)/h_n vs. T' relation for periodic permanent roll waves at the same Froude number and slope. As a result of this correspondence between periodic and natural roll waves, the growth rate ∂h_(max)/∂ℓ of shock waves was predicted to depend on the channel slope, and this slope dependence was observed in the experiments.

No.: 16
ID: CaltechKHR:KH-R-16

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Abstract: Theoretical and experimental studies were made on two classes of buoyant jet problems, namely: 1) an inclined, round buoyant jet in a stagnant environment with linear density-stratification; 2) a round buoyant jet in a uniform cross stream of homogeneous density. Using the integral technique of analysis, assuming similarity, predictions can be made for, jet trajectory, widths, and dilution ratios, in a density-stratified or flowing environment. Such information is of great importance in the design of disposal systems for sewage effluent into the ocean or waste gases into the atmosphere. The present study of a buoyant jet in a stagnant environment has extended the Morton type of analysis to cover the effect of the initial angle of discharge. Numerical solutions have been presented for a range of initial conditions. Laboratory experiments were conducted for photographic observations of the trajectories of dyed jets. In general the observed jet forms agreed well with the calculated trajectories and nominal half widths when the value of the entrainment coefficient was taken to be α = 0.082, as previously suggested by Morton. The problem of a buoyant jet in a uniform cross stream was analyzed by assuming an entrainment mechanism based upon the vector difference between the characteristic jet velocity and the ambient velocity. The effect of the unbalanced pressure field on the sides of the jet flow was approximated by a gross drag term. Laboratory flume experiments with sinking jets which are directly analogous to buoyant jets were performed. Salt solutions were injected into fresh water at the free surface in a flume. The jet trajectories, dilution ratios and jet half widths were determined by conductivity measurements. The entrainment coefficient, α, and drag coefficient, Cd, were found from the observed jet trajectories and dilution ratios. In the ten cases studied where jet Froude number ranged from 10 to 80 and velocity ratio (jet: current) k from 4 to 16, a varied from 0.4 to 0.5 and Cd from 1.7 to 0.1. The jet mixing motion for distances within 250D was found to be dominated by the self-generated turbulence, rather than the free-stream turbulence. Similarity of concentration profiles has also been discussed.

No.: 15
ID: CaltechKHR:KH-R-15

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Abstract: There were four major objectives to this investigation: 1) the determination of the degree of stability of the island face when constructed of armor units of various weights; 2) the run-up for a two-dimensional wave system impinging on the island face; 3) the run-up envelope on the four sides of the island in a three-dimensional model; and 4) the wave patterns caused by the effect of the island on its wave environment. Models having three different length scales were tested in the wave tank (1:50, 1:45, and 1:40) and these models are referred to as the two-dimensional models. One model was tested in the wave basin at an undistorted scale of 1:150 and it is referred to in this report as the three-dimensional model. The first two-dimensional model was built to a scale of 1:50 and essentially corresponded to the original design proposed by Omar Lillevang, Consulting Engineer to the Bechtel Corporation. The prototype tribar weight, equivalent to the model tribar used, was 18.9 tons. This structure was stable; however, it was overtopped by waves. With an increase in the crest elevation from +30 ft. to +40 ft. some overtopping was still experienced. The second model was built at an increased scale, 1:40. At the same time the composite slope which existed in the original design was changed so that the island face had a continuous slope of 3 horizontal to 1 vertical with the crest of the defense at elevation +40 ft. This particular model scale was chosen so that, according to the literature, the tribars would be at a condition of incipient failure for high waves. Since the same armor units were used in this model as were used in the 1:50 scale model, the increase in model scale reduced the equivalent weight of the tribars to 9.7 tons and the maximum weight of the armor rock "B" from 10 tons to 5.1 tons. The prototype structure which corresponds to this model was found to be unstable, as expected. It was observed in testing that a critical feature of the construction which contributes to the stability of the structure is the degree to which the cap-rock section is interlocked with the tribar section. The modification made to the slope of the island face and the increased crest elevation eliminated the problem of overtopping, and the maximum run-up for a 14-sec. wave was to elevation +38 ft. Since the model having a 1:40 length scale was unstable and that with a scale of 1:50 was stable, a third model was constructed with a model scale between these two values, a scale of 1:45. The equivalent prototype tribar weight and the maximum weight of the "B" rock for this third model, still using the same model armor units, were increased to 13.8 tons and 7.3 tons respectively by this change. The slope of the wave defense and the crest elevation were the same for this structure as they were in the 1:40 scale model, i. e., a continuous slope of the island face of 3 horizontal to 1 vertical and a crest elevation of +40 ft. This model was satisfactory both with respect to stability and to run-up. Run-up measurements were made for waves of various heights at wave periods of 16 sec., 14 sec., and 12 sec. The maximum run-up was to elevations +39 ft., +35 ft., and +31 ft. respectively for these three wave periods. The three-dimensional model of the ocean bottom and the island was built to an undistorted scale of 1:150 with the island constructed the same as the 1:45 scale two-dimensional model. In these tests in the large wave basin the wave direction was varied as well as the wave period and wave height. The run-up envelopes obtained showed that, for comparable wave heights, the worst condition of run-up was for normally incident waves impinging on the seaward face of the island. The run-up measured for the normally incident direction was usually approximately 10% less than the run-up in the two-dimensional model for the same wave periods and wave heights. For the case of oblique wave incidence the maximum run-up was at the island corner first attacked by the wave with the run-up decreasing with distance from this corner, and this run-up was comparable to the maximum run-up experienced at normal wave incidence. However, the maximum average run up for the oblique case was significantly less than that experienced in the case of normal wave incidence. The run-up on the shoreward face of the island for all wave directions was of the order of 1/10th of that experienced on the seaward face. Detailed observations of the wave pattern in the lee of the island indicated that there were regions near the beach where the currents were in a direction opposite to the observed general current. From overhead photographs it was found that generally this occurred in regions where the waves which diffract from around the sides of the island intersect. Measurements were made of the maximum elevation of the water surface in the region of the causeway for the case of oblique wave incidence.

No.: 14
ID: CaltechKHR:KH-R-14

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Abstract: A study was made of the means by which turbulent flows entrain sediment grains from alluvial stream beds. Entrainment was considered to include both the initiation of sediment motion and the suspension of grains by the flow. Observations of grain motion induced by turbulent flows led to the formulation of an entrainment hypothesis. It was based on the concept of turbulent eddies disrupting the viscous sublayer and impinging directly onto the grain surface. It is suggested that entrainment results from the interaction between fluid elements within an eddy and the sediment grains. A pulsating jet was used to simulate the flow conditions in a turbulent boundary layer. Evidence is presented to establish the validity of this representation. Experiments were made to determine the dependence of jet strength, defined below, upon sediment and fluid properties. For a given sediment and fluid, and fixed jet geometry there were two critical values of jet strength: one at which grains started to roll across the bed, and one at which grains were projected up from the bed. The jet strength, K, is a function of the pulse frequency, [omega] , and the pulse amplitude, A, defined by K=A[omega]^-s where s is the slope of a plot of log A against log [omega]. Pulse amplitude is equal to the volume of fluid ejected at each pulse divided by the cross sectional area of the jet tube. Dimensional analysis was used to determine the parameters by which the data from the experiments could be correlated. Based on this, a method was devised for computing the pulse amplitude and frequency necessary either to move or project grains from the bed for any specified fluid and sediment combination. Experiments made in a laboratory flume with a turbulent flow over a sediment bed are described. Dye injection was used to show the presence, in a turbulent boundary layer, of two important aspects of the pulsating jet model and the impinging eddy hypothesis. These were the intermittent nature of the sublayer and the presence of velocities with vertical components adjacent to the sediment bed. A discussion of flow conditions, and the resultant grain motion, that occurred over sediment beds of different form is given. The observed effects of the sediment and fluid interaction are explained, in each case, in terms of the entrainment hypothesis. The study does not suggest that the proposed entrainment mechanism is the only one by which grains can be entrained. However, in the writer's opinion, the evidence presented strongly suggests that the impingement of turbulent eddies onto a sediment bed plays a dominant role in the process.

No.: 13
ID: CaltechKHR:KH-R-13

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Abstract: This study concerns the longitudinal dispersion of fluid particles which are initially distributed uniformly over one cross section of a uniform, steady, turbulent open channel flow. The primary focus is on developing a method to predict the rate of dispersion in a natural stream. Taylor's method of determining a dispersion coefficient, previously applied to flow in pipes and two-dimensional open channels, is extended to a class of three-dimensional flows which have large width-to-depth ratios, and in which the velocity varies continuously with lateral cross-sectional position. Most natural streams are included. The dispersion coefficient for a natural stream may be predicted from measurements of the channel cross-sectional geometry, the cross-sectional distribution of velocity, and the overall channel shear velocity. Tracer experiments are not required. Large values of the dimensionless dispersion coefficient D / rU* are explained by lateral variations in downstream velocity. In effect, the characteristic length of the cross section is shown to be proportional to the width, rather than the hydraulic radius. The dimensionless dispersion coefficient depends approximately on the square of the width to depth ratio. A numerical program is given which is capable of generating the entire dispersion pattern downstream from an instantaneous point or plane source of pollutant. The program is verified by the theory for two-dimensional flow, and gives results in good agreement with laboratory and field experiments. Both laboratory and field experiments are described. Twenty-one laboratory experiments were conducted: thirteen in two-dimensional flows, over both smooth and roughened bottoms; and eight in three-dimensional flows, formed by adding extreme side roughness to produce lateral velocity variations. Four field experiments were conducted in the Green-Duwamish River, Washington. Both laboratory and flume experiments prove that in three-dimensional flow the dominant mechanism for dispersion is lateral velocity variation. For instance, in one laboratory experiment the dimensionless dispersion coefficient D/rU* (where r is the hydraulic radius and U* the shear velocity) was increased by a factor of ten by roughening the channel banks. In three-dimensional laboratory flow, D/rU* varied from 190 to 640, a typical range for natural streams. For each experiment, the measured dispersion coefficient agreed with that predicted by the extension of Taylor's analysis within a maximum error of 15%. For the Green-Duwamish River, the average experimentally measured dispersion coefficient was within 5% of the prediction.

No.: 12
ID: CaltechKHR:KH-R-12

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Abstract: The mixing of two miscible fluids in motion in a saturated isotropic porous medium and the stability of the density interface between them has been studied. The density interface was formed by a line source introducing a denser fluid into a uniform confined horizontal flow. It was shown that the half-body thus formed may be approximated to within the density difference by the shape when the densities are equal. The mixing of the two fluids by lateral dispersion along such an interface was investigated experimentally and it was found that up to density differences of at least 1 per cent there was no observable effect on the lateral dispersion coefficient. A theoretical investigation has been made of the stability of the uniform two-dimensional horizontal motion of two miscible fluids of different density in a saturated, isotropic, homogeneous porous medium. The fluid of higher density overlay the lower density fluid and both were moving with the same seepage velocity in the same direction. The analytical solution for the stability was obtained from the continuity equation, Darcy's law and the dispersion equation by investigating the stability of arbitrary sinusoidal perturbations to the velocity vector and the density profile prescribed by the lateral dispersion of one fluid into the other. A stability equation similar to the Orr-Sommerfeld equation was obtained and a neutral stability curve in a wave number-Rayleigh number plane was found by two approximate methods. The growth rates of instabilities were investigated for a linear density profile and it has been found that although the flow was always unstable the growth rates of unstable waves could be so low as to form a quasi-stable flow; examples of such flows have been demonstrated experimentally.

No.: 11
ID: CaltechKHR:KH-R-11

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Abstract: The general objective of this research is to investigate the motion of small boats moored to fixed or floating platforms in a standing wave environment. The study is directed toward an understanding of the problems of mooring small craft in marinas and toward providing information that will assist in the planning and operation of marinas. This report deals with the first phase of the experimental study concerning the surge motions of a simply moored body in a standing wave system. The body is a rectangular parallelpiped moored to a fixed support by means of a linear spring. In general it can be stated that the inviscid theory proposed by Wilson (5) and Kilner (7) adequately describes the surge motion of this body for standing waves ranging from shallow-water to deep-water waves and for ratios of body length to wave length from 0.1 to 1.5. Agreement between the experimental data and the theoretical response curves is better for certain ranges of the ratio of the natural period of the body to the wave period than for others. This is attributed to the effect of wave generation by the body on its motion. The response curves become more selective with respect to frequency as the distance of the body from a reflecting surface increases. Therefore, coupling this with viscous effects it is possible to reduce the effect of resonance considerably simply by choosing the proper body location in its standing wave environment for a particular natural frequency. The coefficient of virtual mass of the body in surge (ratio of width to length, 1:4) determined from simple free oscillations was found to correlate best with the ratio of draft to beam. For a variation of draft to beam from 0.25 to 0.95 the coefficient of virtual mass varied from approximately 1.1 to 1.25. This study emphasizes the need for more field information on the characteristics of small craft, such as the elastic characteristics of the mooring system, natural frequencies of moored boats, and the relative importance of viscous effects upon boat motions.

No.: 10
ID: CaltechKHR:KH-R-10

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Abstract: Existing analytical solutions for vertical influent seepage flow to an infinite series of tile drains underlain by an impervious layer do not adequately consider the free surface nor give solutions for the drain diameter (see Figure 1). The theoretical investigations described herein basically sought to find a method whereby an engineer could find the required diameter, depth, and spacing of an adequate tile drainage system when given the ratio of infiltration to soil hydraulic conductivity and the depth of the impervious layer. From a study of the available literature it was decided the problem would be exceedingly difficult to solve exactly but it seemed as if an approximate solution of good accuracy could be obtained by approximating the shape of the impervious layer, where the flow is sluggish, and satisfying the conditions exactly at the free surface, a critical region of flow. Previously published solutions invariably adopt the opposite viewpoint, with a consequent loss in accuracy. The solution to the problem when the impervious layer is at infinite depth had been solved exactly using the rather laborious hodograph technique. This work employs to advantage an image method developed by Davison and Rosenhead (1940). Detailed results are obtained herein for the condition when no water stands over the tile lines and these are given in a graphical form which enables a ready computation of drain depth diameter and spacing when the field data are known (ratio of rate of infiltration to hydraulic conductivity and the depth of the impervious layer). A comparison with field results shows that the solutions are probably as accurate as could be desired. The case which occurs when water stands over the tile lines has not been extensively tabulated for reasons explained in the report. A method is given whereby adequate tile drainage systems may be designed on a long term basis. The design curves given are not for intermittent unsteady flows such as irrigation schemes (a more difficult problem) but should prove exceedingly useful for engineers concerned with land reclamation schemes and marsh drainage.

No.: 9
ID: CaltechKHR:KH-R-9

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Abstract: The stability of flow down an inclined plank has been investigated for the case of a stratified fluid system consisting of two layers of viscous fluid of different densities. This problem is an extension of the works of Benjamin and Yih for a homogeneous fluid; thus their results are a special case of the solution for this more general problem. Asymptotic cases for long and short wave-length disturbances are considered, and the neutral stability curve is estimated. Reynolds numbers for the bifurcation point of the neutral curve are found for various ratios of density and depth of the two layers. For long waves, shear wave instability is also studied and is found to be damped. It is found that the addition of another film of fluid of lighter density over the original film destabilizes the original free surface disturbances. It is hoped that this work will bear on problems of film flow stabilizing techniques, and will also be of interest in the study of the stability of undercurrents in reservoirs.

No.: 8
ID: CaltechKHR:KH-R-8

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Abstract: Experiments were made in a flume 15-3/8 in. wide by 12 ft long to determine the shear stress for critical motion of fine sediment in a growing boundary layer. Determinations were made for two sediments, a quartz sand with geometric mean sieve size of 0. 102 mm and glass beads with geometric mean sedimentation diameter of 0. 037 mm. The intensity of sediment motion was judged from the frequency of bursts of motion over a small area varying from 7 to 18 mm in diameter. When the burst frequency fell between 1/3 and 1 burst per second, critical conditions for inception of motion were considered to obtain. Values of shear velocity, u_*, and bed shear stress, τ_0, for turbulent flow were determined from measured velocity profile data by essentially two methods. In the first the slope, N, of a straight line fitted to a semilogarithmic graph of velocity profile data was used in Eq. (8) to obtain u_*. In the other, values of point velocity, u, at a distance of .03 ft from the bed was substituted into the logarithmic equation for velocity distribution at a smooth wall, Eq. ( 5 ) , to obtain u_*. The data obtained from Eq. (8) and plotted on Fig. 14a show wider scatter than those calculated from Eq. (5) and plotted on Fig. 14b. The data obtained by means of Eq. (5) are considered the more reliable and are presented on a complete Shields diagram in Fig. 15.

No.: 7
ID: CaltechKHR:KH-R-7

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Abstract: A theoretical and experimental investigation has been made for the problem of two-dimensional, viscous, incompressible, steady, slightly-stratified flow towards a line sink. The analytical solution was obtained from the Navier Stokes equations, the continuity equation, and the diffusion equation by making a boundary-layer-type assumption and by using a small perturbation technique based on a perturbation parameter proportional to the sink strength q. The effects of viscosity, diffusivity, and gravity have been included while the inertia effect is neglected in the zeroth order solution. The solution indicates that there exists a withdrawal layer which grows in thickness with the distance x from the sink at the rate x^(1/3) and that the velocity distributions u(y) are similar from one station x to another. Twenty-five tank experiments were performed using water stratified by means of either salt or temperature. Detailed measurements of the velocity field were made by means of photographs of vertical dye lines. The experiments verify the shape of the velocity profiles as well as their similarity in x as predicted by the theory. The applicability of these results to the problem of selective withdrawal from a reservoir is discussed and compared with nonviscous solutions by Yih (6) and Kao (7).

No.: 6
ID: CaltechKHR:KH-R-6

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Abstract: The sewage effluent from the new sewage treatment plant for the City of San Diego, located on a bluff 95 feet above sea level on Point Lorna, is discharged to the ocean through a long submarine outfall pipe. Under almost all conditions of flow, the hydraulic head at the treatment plant exceeds that required for flow through the outfall. Therefore, the excess energy must be dissipated in a special hydraulic drop structure located on the shoreline between the treatment plant and the ocean outfall. The laboratory model investigation described herein basically sought to find a method for dissipating this excess energy safely without heavy entrainment of air into the flow in the ocean outfall. Such air entrainment could cause unsteady conditions of the pipe flow, and possibly bubbling at the point of discharge in the ocean, both of which must be avoided. The responsibility of this laboratory was to develop the hydraulic principles and a recommended hydraulic configuration which would provide assurance that the prototype to be designed by the sponsors (Holmes and Narver-Montgomery) would give satisfactory hydraulic performance.

No.: 5
ID: CaltechKHR:KH-R-5

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Abstract: An exploratory study was made of open-channel flow over beds consisting either entirely or partially of large granular roughness. Steady, uniform flow was established at various depths and velocities over two types of beds, one rough over the entire width of a laboratory flume, the other rough only over half the width and smooth over the other half. Friction factors were determined for these flows, and detailed velocity distributions were measured in three runs. The friction factors for the entirely rough beds compared closely with those predicted by the Karman-Prandtl equations, and the velocity distributions strongly suggested the existence of secondary circulation of the second kind. Analysis is offered to show that subdivision of the cross section of a turbulent flow by curves normal to the equal velocity curves does not result in hydraulically independent zones of flow, in that there will be turbulent interchange of the longitudinal component of momentum among such zones; other methods of subdivision are considered and none found to be completely satisfactory. The customary side-wall correction method is reviewed and found to have no explicit rational basis, and although it is recognized that the method gives reliable results in the situations to which it is usually applied, its application to widely different situations should be undertaken with caution. Suggestions for needed further research are offered.

No.: 4
ID: CaltechKHR:KH-R-4

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Abstract: A laboratory study was made to determine the variation with depth and velocity of the hydraulic and sediment transport characteristics of a constant-discharge flow. Eight experimental runs were performed in a 60-foot long, 33.5-inch wide recirculating laboratory flume. The unit discharge for all runs was 0.50 cfs per ft. and the velocity was varied from 0.91 to 2.21 fps, corresponding to a change in depth from 0.550 to 0.228 ft. The bed sand used for these experiments had a geometric mean sieve diameter of 0.142 mm and a geometric standard deviation of 1.38. As the velocity was increased, the bed form changed from a dune-covered configuration to a flat bed, with sand waves occurring at intermediate velocities. It was found that for the unit discharge and bed sand used in this investigation, two different velocities and sediment transport rates are possible for a given slope, or a given bed shear velocity; however, this multiplicity is possible only in the range of slope and shear velocity where major changes in the bed configuration occur since it is a result of large variations in the bed roughness. Therefore the slope or shear velocity cannot logically be used as an independent variable since neither of these quantities uniquely determines the velocity or transport rate. However, if the velocity is used as the independent variable for a constant-discharge flow, the slope, shear velocity, and friction factor are all uniquely determined. The sediment transport rate was found to be a single-valued, uniformly increasing function of velocity, and it can therefore be used in place of the velocity as the independent variable. A comparison of data from this investigation with data from previous investigations which used the same sand showed that even a small decrease in the amount of fine material in the bed sand can have a significant effect on the transport rate. However, even relatively large changes in the standard deviation of the bed material have a small effect on the friction factor.

No.: 3
ID: CaltechKHR:KH-R-3

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Abstract: These notes have been prepared for a series of lectures on sediment transportation and channel stability given by the authors to a group of engineers and geologists of the U. S. Department of Agriculture assembled at Caltech on September 12-16,1960. The material herein is not intended to serve as a complete textbook, because it covers only subjects of the one-week sequence of lectures Due to limitation of space and time, coverage of many subjects is brief and others are omitted altogether. At the end of each chapter the reader will find a selected list of references for more detailed study.

No.: 1
ID: CaltechKHR:KH-R-1

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Abstract: A theoretical and laboratory investigation was made of antidunes and associated stationary waves. The objectives were to determine the factors involved in the formation of antidunes, the characteristics of the stationary waves, and the effects of antidunes and waves on the friction factor and sediment transport capacity of streams. In the potential flow solution for flow over a wavy bed it was hypothesized that the flow shapes the erodible sand bed by scour and deposition to conform to a streamline of the flow configuration for which the energy is a minimum. Under this hypothesis, flow over antidunes is the same as the segment of flow above an intermediate streamline of the fluid motion associated with stationary gravity waves (waves with celerity equal and opposite to the flow velocity) in a fluid of infinite depth. For a velocity V the wave length, L, is given by L = (2*pi*V^2)/g and waves break when their height reaches 0.142 L. Laboratory and field data for two-dimensional stationary waves and antidunes confirmed these relations. For the same velocity, short-crested, three-dimensional waves (rooster tails) have shorter wave lengths than two-dimensional waves. Forty-three experimental runs in laboratory flumes were made for different depths and velocities and bed sands of two different sizes (0.549 mm and 0.233 mm). No general criterion for the formation of antidunes or the occurrence of breaking waves could be formulated because of inadequate knowledge of the complex sediment transport phenomenon. Qualitatively, it was found that for a given sand, the critical Froude number for the occurrence of breaking waves decreased as the depth was increased. Over a certain range of depth and velocity it was found that the flow formed waves and antidunes or was uniform depending on whether or not the flow was disturbed to form an initial wave. Waves that did not break had no measurable effect on the transport capacity or friction factor, but breaking waves increased both of these quantities.

No.: 2
ID: CaltechKHR:KH-R-2

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Abstract: This report describes research work done under Contract No. DA-25-075-eng-3866 with the U. S. Army, Corps of Engineers, Missouri River Division, Omaha, during the period 1954-1957, on problems of suspended load transport in alluvial streams. A total of 94 experimental runs were made in two laboratory flumes charged with fine sand of several size distributions. Special attention was given to the variation of the friction factor caused by the changing bed configuration and the damping effect of suspended sediment. The relationship between the sediment transportation rate and the hydraulic variables was also investigated. Most of the runs (General Studies, Chap. V) were made with the bed of the flume completely covered with loose sand but some special runs (Special Studies, Chap. VII) were made with the sand bed chemically solidified in place to prevent sediment transport while preserving the bed configuration previously generated by a natural flow of the same velocity with loose sand. The principal laboratory results are as follows: 1. The friction factor f for a stream with a movable sand bed may vary several fold, being highest at low or medium flow velocities and lowest at high velocity. 2. The principal cause of the variation in f is the appearance of dunes at low or medium velocities and disappearance at high velocities. 3. A secondary cause for the reduction in f for high sediment transport rates is the damping effect of the suspended sediment on the turbulence, and the concomitant reduction in the turbulent diffusion coefficients. The maximum observed reduction due directly to the sediment load was only about 28 percent. 4. The discharge and sediment transportation rate are not unique functions of depth and slope because of the variable roughness. Slope (or shear) must probably be considered a dependent variable for alluvial streams because several equilibrium flows can yield the same slope and shear stress. The laboratory data are compared with similar data for natural streams, and the most promising existing analyses for roughness and sediment load are discussed in the light of the present findings. In addition, a critical review of early and recent literature on the resistance of sediment-laden streams is presented in Chapter II.

ID: CaltechKHR:SedLabRpt-E-68

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Abstract: [No abstract]

ID: CaltechKHR:HydroLabpub167

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