CaltechDATA: Monograph
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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 28 Mar 2024 10:45:37 -0700Exploratory Studies of Open-Channel Flow over Laterally Varying Roughness
https://resolver.caltech.edu/CaltechTHESIS:04132011-080538095
Year: 1961
DOI: 10.7907/VHGK-9950
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.
https://resolver.caltech.edu/CaltechTHESIS:04132011-080538095Suspensions of Granular Particles Generated by an Upward Flow
https://resolver.caltech.edu/CaltechTHESIS:04242012-142541079
Year: 1963
DOI: 10.7907/E8SA-YB56
<p>A laboratory study was made of the local properties of suspensions
of granular particles generated by an upward flow of water. Four
granular materials covering a range of particle sizes having particle
Reynolds numbers between 10 and 70 were studied by making detailed
measurements within ten suspensions. Measurements were made of the
mean properties of over one hundred suspensions. Concentrations in
the suspensions generated by upward flow were generally greater than
those of typical hindered settling experiments, but less than those of
typical fluidization experiments by chemical engineers.</p>
<p>Measurements of the mean concentration for an entire suspension
and the ratio of superficial velocity to particle free-fall velocity yielded
a separate relationship for each material studied. These relationships
are strongly dependent on the standard deviation of particle sizes for
the parent materials.</p>
<p>Recognizing that granular materials are never perfectly uniform,
measurements of concentration and particle size were made on a local
basis. The suspensions were found to sort themselves with the fine particles
near the top and the coarse particles at the bottom, and the local
concentration was observed to decrease from the bottom to the top of
the suspension.</p>
<p>Granular particles with mass densities approximately two and
one-half times the density of water and having particle Reynolds numbers
in the range from 10 to 70 produce highly turbulent systems when fluidized
with water. It was observed that there is local generation of
turbulence throughout the suspension with the highest intensity of turbulence
being in the region where the local concentration is the largest.</p>
<p>Measurements of the hindered settling velocity of a suspension
and the superficial velocity necessary to maintain the suspension show
the two quantities to be identical for all practical purposes. The turbulence
was observed visually to be less for the settling suspension than
for the fluidized suspension.</p>https://resolver.caltech.edu/CaltechTHESIS:04242012-142541079Studies on gravitational spreading currents
https://resolver.caltech.edu/CaltechTHESIS:09302010-090407312
Year: 1980
DOI: 10.7907/16RG-AZ72
<p>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.</p>
<p>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.</p>https://resolver.caltech.edu/CaltechTHESIS:09302010-090407312Viscous Stratified Flow Towards a Line Sink
https://resolver.caltech.edu/CaltechETD:etd-09252002-135207
Year: 1964
DOI: 10.7907/YXY3-GG82
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
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 first making a boundary-layer-type assumption and then using a small perturbation technique based on a perturbation parameter proportional to the sink strength q. The effects of the viscosity, the diffusivity, and the 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[superscript 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.
Except for scale, this is very similar to the problem of selective withdrawal from a reservoir.https://resolver.caltech.edu/CaltechETD:etd-09252002-135207Studies on the Mixing in a Density-Stratified Shear Flow
https://resolver.caltech.edu/CaltechTHESIS:10172017-162001547
Year: 1979
DOI: 10.7907/G80K-5566
<p>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.</p>
<p>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<sup>-3</sup> 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.</p>
<p>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 Δρ/ρ<sub>o</sub>gl<sub>T</sub><sup>*</sup>/Δu<sup>-</sup><sub>o</sub><sup>2</sup>, where l<sub>T</sub><sup>*</sup> 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.</p>
<p>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.</p>
<p>The flux Richardson number, R<sub>f</sub>, 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, (-u<sup>1</sup>v<sup>1</sup>)<sup>‾</sup> ϑu<sup>‾</sup>/ϑuy, was the largest source of turbulent kinetic energy, it was found that R<sub>f</sub> < 0.3, and when the flow was strongly stratified, then R<sub>f</sub> < 0.2. If the diffusion of turbulent kinetic energy 1/2 ϑ(u<sup>'2</sup> + v<sup>'2</sup>)v<sup>'</sup><sup>‾</sup>/ϑy = ϑq<sup>*2</sup>v<sup>'</sup>/ϑy 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 R<sub>f</sub>. 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.</p>https://resolver.caltech.edu/CaltechTHESIS:10172017-162001547Prediction of Flow Depth and Sediment Discharge in Open Channels
https://resolver.caltech.edu/CaltechETD:etd-12192006-152351
Year: 1982
DOI: 10.7907/100Z-Z157
<p>In recent years attempts have been made to develop numerical models for unsteady flows in channels with sediment transport. This work 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.</p>
<p>A data base containing 7027 records (5263 laboratory records and 1764 field records) in 77 data files was assembled and is provided (Appendix B). The data base was used to examine existing relationships and to develop new ones. Six existing hydraulic relationships are reworked and examined. Detailed statistical analyses are provided for 13 existing techniques for predicting sediment concentration.</p>
<p>Relying heavily on statistical analysis of dimensionless groups, new relationships have been developed. The new hydraulic relationship solves for flow depth for upper and lower regime flow separately and then provides a method for determining which flow regime one might expect. The new method for predicting sediment transport, which is easy to use, appears to be more accurate than the 13 existing methods, and suggests that complex procedures for calculating concentration are not warranted.</p>
<p>A four-point implicit finite difference scheme has been presented to demonstrate the feasibility of applying the new hydraulic and sediment relationships to a numerical solution of the differential equations.</p>https://resolver.caltech.edu/CaltechETD:etd-12192006-152351The Stability and Mixing of a Density-Stratified Horizontal Flow in a Saturated Porous Medium
https://resolver.caltech.edu/CaltechETD:etd-09302002-124434
Year: 1965
DOI: 10.7907/3THV-YS27
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.https://resolver.caltech.edu/CaltechETD:etd-09302002-124434Transfer of solutes into and out of streambeds
https://resolver.caltech.edu/CaltechETD:etd-07092007-074127
Year: 1991
DOI: 10.7907/JBTC-ZX91
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.https://resolver.caltech.edu/CaltechETD:etd-07092007-074127Stationary Waves and Antidunes in Alluvial Channels
https://resolver.caltech.edu/CaltechETD:etd-06222006-153051
Year: 1960
DOI: 10.7907/Y27F-NR79
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
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, [lambda] is given by [lambda] and waves break when their height reaches 0.142[lambda]. Laboratory and field data for two-dimensional antidunes confirmed these relations.
Forty-three experimental runs in laboratory flumes were made for different depths and velocities and bed sands of two different sizes (0.55 mm and 0.23 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.https://resolver.caltech.edu/CaltechETD:etd-06222006-153051Flow Resistance of Dunes in Alluvial Streams
https://resolver.caltech.edu/CaltechETD:etd-05092003-173224
Year: 1965
DOI: 10.7907/HRDZ-N222
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Studies were made of the hydrodynamic resistance of channels with beds covered with dunes generated by flows over granular sediments of the kind normally found in alluvial rivers. The principal objectives of the studies were to determine the pertinent geometric properties of a dune bed by means of which one can express the dune resistance and to establish a quantitative relation between resistance and these geometric quantities. The main results reported here were obtained through experiments in laboratory flumes.
A series of 23 experiments with flows over dune-covered beds of fine sand were performed in tilting flumes 130 ft. and 40 ft. in length respectively. In addition, two dune beds generated by different flows were stabilized chemically without disturbing their surface configurations and texture. By doing this, it was possible to explore velocity and pressure distributions in the flow fields and to determine the effect of Reynolds number on the friction factor of the dune beds.
It was found that the hydrodynamic roughness of a dune field can be described by the average dune height and the exposure parameter which is the fraction of the total bed area occupied by the horizontal projection of the steep lee slopes of the dunes. It was also found from the results of flume experiments that the bed friction factor due to dunes is a function of the modified relative roughness, [...] , where r[?] is the bed hydraulic radius, e is the exposure parameter defined above and [...] is the average dune height.
A function for dune resistance in straight uniform channels, that is, Equation (6-1) was established from experimental results obtained in the flume. Friction factors for typical alluvial rivers cannot be calculated from Equation (6-1) above because some important features of streams, such as meandering, which contribute to resistance are not reproduced in flumes.https://resolver.caltech.edu/CaltechETD:etd-05092003-173224Mixing of Density-Stratified Impoundments with Buoyant Jets
https://resolver.caltech.edu/CaltechTHESIS:02052018-100847353
Year: 1971
DOI: 10.7907/4RYG-QZ06
<p>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 counter acted 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.</p>
<p>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.</p>
<p>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.</p>
<p>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).</p>
<p>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.</p>
https://resolver.caltech.edu/CaltechTHESIS:02052018-100847353Turbulent Buoyant Jets into Stratified or Flowing Ambient Fluids
https://resolver.caltech.edu/CaltechTHESIS:11232015-162414440
Year: 1967
DOI: 10.7907/C69V-BE23
<p>Theoretical and experimental studies were made on two classes of buoyant jet problems, namely:</p>
<p>1) an inclined, round buoyant yet in a stagnant environment with linear density-stratification;</p>
<p>2) a round buoyant jet in a uniform cross stream of homogenous density.</p>
<p>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.</p>
<p>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.</p>
<p>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, C<sub>d</sub>, 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, α varied from 0.4 to 0.5 and C<sub>d</sub> from 1.7 to 0.1. The jet mixing motion for distance 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. </p>
https://resolver.caltech.edu/CaltechTHESIS:11232015-162414440Longitudinal dispersion in laboratory and natural streams
https://resolver.caltech.edu/CaltechTHESIS:09292015-082820697
Year: 1966
DOI: 10.7907/8D5C-BV11
<p>This study concerns the longitudinal dispersion of fluid particles which are initially distributed uninformly 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. </p>
<p>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. </p>
<p>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. </p>
<p>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. </p>
<p>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. </p>
<p>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 factory 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. </p>https://resolver.caltech.edu/CaltechTHESIS:09292015-082820697Wave uplift pressures on horizontal platforms
https://resolver.caltech.edu/CaltechTHESIS:08052015-104412384
Year: 1970
DOI: 10.7907/AKKA-X706
<p>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.</p>
<p>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.</p>
<p>The problem of a d equate 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 pressure 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.</p>
<p>The hydrodynamics of the flow beneath the platform are described
qualitatively by a si1nple 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.</p>
<p>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.</p>
https://resolver.caltech.edu/CaltechTHESIS:08052015-104412384Turbulence and Turbulent Transport in Sediment-Laden Open-Channel Flows
https://resolver.caltech.edu/CaltechETD:etd-03042008-133940
Year: 1987
DOI: 10.7907/G5WF-5K07
<p>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.</p>
<p>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.</p>
https://resolver.caltech.edu/CaltechETD:etd-03042008-133940Digested sludge: delineation and modeling for ocean disposal
https://resolver.caltech.edu/CaltechTHESIS:04292014-113745649
Year: 1976
DOI: 10.7907/j7nk-g480
<p>Experimental work was performed to delineate the system of digested
sludge particles and associated trace metals and also to measure the
interactions of sludge with seawater. Particle-size and particle number
distributions were measured with a Coulter Counter. Number
counts in excess of 10<sup>12</sup> particles per liter were found in both the City
of Los Angeles Hyperion mesophilic digested sludge and the Los Angeles
County Sanitation Districts (LACSD) digested primary sludge. More than
90 percent of the particles had diameters less than 10 microns.</p>
<p>Total and dissolved trace metals (Ag, Cd, Cr, Cu, Fe, Mn, Ni, Pb,
and Zn) were measured in LACSD sludge. Manganese was the only metal
whose dissolved fraction exceeded one percent of the total metal.
Sedimentation experiments for several dilutions of LACSD sludge in seawater
showed that the sedimentation velocities of the sludge particles
decreased as the dilution factor increased. A tenfold increase in
dilution shifted the sedimentation velocity distribution by an order
of magnitude. Chromium, Cu, Fe, Ni, Pb, and Zn were also followed
during sedimentation. To a first approximation these metals behaved
like the particles.</p>
<p>Solids and selected trace metals (Cr, Cu, Fe, Ni, Pb, and Zn)
were monitored in oxic mixtures of both Hyperion and LACSD sludges for
periods of 10 to 28 days. Less than 10 percent of the filterable
solids dissolved or were oxidized. Only Ni was mobilized away from
the particles. The majority of the mobilization was complete in less
than one day.</p>
<p>The experimental data of this work were combined with oceanographic,
biological, and geochemical information to propose and model the
discharge of digested sludge to the San Pedro and Santa Monica Basins.
A hydraulic computer simulation for a round buoyant jet in a density
stratified medium showed that discharges of sludge effluent mixture
at depths of 730 m would rise no more than 120 m. Initial jet mixing
provided dilution estimates of 450 to 2600. Sedimentation analyses
indicated that the solids would reach the sediments within 10 km of
the point discharge.</p>
<p>Mass balances on the oxidizable chemical constituents in sludge
indicated that the nearly anoxic waters of the basins would become wholly
anoxic as a result of proposed discharges. From chemical-equilibrium
computer modeling of the sludge digester and dilutions of sludge in
anoxic seawater, it was predicted that the chemistry of all trace
metals except Cr and Mn will be controlled by the precipitation of metal
sulfide solids. This metal speciation held for dilutions up to
3000.</p>
<p>The net environmental impacts of this scheme should be salutary.
The trace metals in the sludge should be immobilized in the anaerobic
bottom sediments of the basins. Apparently no lifeforms higher than
bacteria are there to be disrupted. The proposed deep-water discharges
would remove the need for potentially expensive and energy-intensive
land disposal alternatives and would end the discharge to the highly
productive water near the ocean surface.</p>
https://resolver.caltech.edu/CaltechTHESIS:04292014-113745649Characterization of Large Earthquakes on the San Andreas Fault in the Carrizo Plain: Implications for Fault Mechanics and Seismic Hazard
https://resolver.caltech.edu/CaltechTHESIS:01072013-092342447
Year: 1993
DOI: 10.7907/zs8s-9j51
<p>Despite the widespread use of geomorphic offset measurements for
calculating earthquake probabilities, little attention has been paid to either the
uncertainties in the interpretation of offset geomorphic features, or the effects
of these uncertainties on fault models and estimates of seismic hazard.
Interpretation of offsets along the San Andreas fault in the Carrizo Plain have
been the basis of hypotheses of a strong Carrizo fault segment which regularly
breaks in great earthquakes several centuries apart with dextral surface slip on
the order of 10 m per event.</p>
<p>The smallest geomorphic offset measurements along a 6 km stretch of
the fault southeast of Wallace Creek vary between ~6.5 m and ~10m. A 3-D
excavation of alluvial deposits at the Phelan fan shows that at least 6.6 to 6.9
m of dextral slip occurred during the 1857 Fort Tejon earthquake, and that the
penultimate earthquake occurred several centuries prior to 1857. Thus, either
the amount of surface slip varied several meters over a 2-3 km stretch of the
fault in 1857, or 2 to 3 meters of slip in a penultimate earthquake was
followed by ~7 m of slip in 1857.</p>
<p>Two monuments from an 1855 survey which spans the San Andreas
fault in the Carrizo Plain have been displaced 11.0 ± 2.5m right-laterally by the
great earthquake of 1857. This magnitude of offset is consistent with
geomorphic indications that slip across the fault during the 1857 earthquake
and associated foreshocks and aftershocks varied from 6.6 to 10 m over 2.6 km
along this section. Comparison of recent geodetic measurements with the
late Holocene slip rate at Wallace Creek shows that fault slip rates determined
from short-term wide aperture measurements are indistinguishable from
rates determined from long-term narrow aperture measurements. Using
radiocarbon dates of the penultimate large earthquake and measurements of
slip in 1857, we calculate an average slip rate for the last complete earthquake
cycle that is at least 25% lower than the late Holocene slip rate on the main
fault trace. This suggests that variation in fault slip during the 1857
earthquake left a slip deficit in at least the upper 1km of crust at Wallace
Creek. Slip in future earthquakes may compensate this deficit.</p>
<p>Three trenches across the San Andreas fault on the Bidart fan in the
Carrizo Plain record evidence of 7 previous earthquakes. Radiocarbon dating
indicates five earthquakes, including the 1857 earthquake, have occurred
since A.D. 1218. The penultimate earthquake, event B, occurred between 1405
and 1510 A.D. Several centuries before 1857, events B, C, D and E occurred in
a temporal cluster after approximately 1218 A.D. and prior to 1510 A.D. The
average recurrence interval within this cluster ranges from 73 to 116 years,
depending on assumptions. Events B and D may correlate with prehistoric
earthquakes recorded in sediments elsewhere along the southern San
Andreas fault. Events C and E appear to have ruptured locally in smaller
magnitude earthquakes. Surface slip from either event B, or events B and C
combined, totals 7 to 11 m.</p>
<p>If fault strength is defined by long earthquake repeat time, then the
Carrizo segment of the San Andreas is not inherently stronger than the
Mojave segment. The temporal and spatial distribution of large earthquakes
on the San Andreas fault is difficult to reconcile with slip-based theories of
segmentation of strike-slip faults. Temporal patterns of seismicity may be
more robust than spatial trends. Clusters of large earthquakes analogous to
sequences of foreshocks, mainshocks and aftershocks may occur on longer
time scales of seismic "supercycles."</p>
https://resolver.caltech.edu/CaltechTHESIS:01072013-092342447Laboratory Analysis of Settling Velocities of Wastewater Particles in Seawater using Holography
https://resolver.caltech.edu/CaltechETD:etd-02022007-152444
Year: 1988
DOI: 10.7907/0zds-gj34
<p>Ocean discharge of treated sewage and digested sludge has been a common practice for the disposal of municipal and industrial wastewaters for years. Since the particles in the discharge cause much of the adverse effect on the marine environment, the transport processes and the final destinations of particles and the associated pollutants have to be studied to evaluate the environmental impact and the feasibility of disposal processes. The settling velocity of particles and the possible coagulation inside the discharge plume are among the most important factors that control the transport of particles.</p>
<p>A holographic camera system was developed to study the settling characteristics of sewage and sludge particles in seawater after simulated plume mixing with possible coagulation. Particles were first mixed and diluted in a laboratory reactor, which was designed to simulate the mixing conditions inside a rising plume by varying the particle concentration and turbulent shear rate according to predetermined scenarios. Samples were then withdrawn from the reactor at different times for size and settling velocity measurements. Artificial seawater without suspended particles was used for dilution.</p>
<p>An in-line laser holographic technique was employed to measure the size distributions and the settling velocities of the particles. Doubly exposed holograms were used to record the images of particles for the fall velocity measurement. Images of individual particles were reconstructed and displayed on a video monitor. The images were then digitized by computer for calculating the equivalent diameter, the position of the centroid, the deviations along the principal axes, and the orientation of particles. A special analysis procedure was developed to eliminate sampling biases in the computation of cumulative frequency distributions. The principal advantages of this new technique over the conventional settling column (used in the early part of this research) are that: (1) the coagulation and settling processes can be uncoupled by use of extremely small concentrations (less than 2 mg/l) in the holographic sample cell, and (2) the individual particle sizes and shapes can be observed for correlation with measured fall velocities.</p>
<p>Four sets of experiments were conducted with blended primary/secondary effluent from the County Sanitation Districts of Los Angeles County and the digested primary sludge from the County Sanitation Districts of Orange County (proposed deep ocean outfall) using different mixing processes. Experimental results show that the sludge and effluent particles have very similar settling characteristics, and that particle coagulation is small under the simulated plume mixing conditions used in these experiments. The median and 90-percentile fall velocities and the fractions of particles with fall velocities larger than 0.01 cm/sec of the digested primary sludge and the effluent are summarized in the following table. The experimental results from the conventional settling column are also included for comparison. In general, the holographic technique indicates slower settling velocities than all the previous investigations by other procedures.</p>
<p>[Table; see abstract in scanned thesis for details.]</p>https://resolver.caltech.edu/CaltechETD:etd-02022007-152444The transport of nonlinearly adsorbing compounds between stream water and sediment bed in a laboratory flume
https://resolver.caltech.edu/CaltechETD:etd-02042008-085125
Year: 1998
DOI: 10.7907/vj00-a140
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.
https://resolver.caltech.edu/CaltechETD:etd-02042008-085125Incipient transport of silt-sized sediments
https://resolver.caltech.edu/CaltechETD:etd-10202005-130933
Year: 1998
DOI: 10.7907/E67A-3484
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
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 [...] 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 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 NaCI and CaCI2 electrolytes at differing concentrations up to [...]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 [...] = 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 [...] = 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.
https://resolver.caltech.edu/CaltechETD:etd-10202005-130933Transport of adsorbing metal ions between stream water and sediment bed in a laboratory flume
https://resolver.caltech.edu/CaltechETD:etd-10182005-135501
Year: 1994
DOI: 10.7907/ZATX-S424
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
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 [...] and 195 [...]. 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.https://resolver.caltech.edu/CaltechETD:etd-10182005-135501Particle transport in flow through porous media : advection, longitudinal dispersion, and filtration
https://resolver.caltech.edu/CaltechETD:etd-08202007-142809
Year: 1992
DOI: 10.7907/4JBE-GH29
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, 1.0, 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.
https://resolver.caltech.edu/CaltechETD:etd-08202007-142809Observations in a Sediment-Laden Flow by Use of Laser-Doppler Velocimetry
https://resolver.caltech.edu/CaltechETD:etd-01192007-155029
Year: 1982
DOI: 10.7907/X24M-0R50
<p>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.</p>
<p>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.</p>
<p>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.</p>
<p>The data demonstrate the shortcomings of the continuum approach to the mechanics of the suspension of 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.</p>
<p>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.</p>https://resolver.caltech.edu/CaltechETD:etd-01192007-155029Exchange of colloidal kaolinite between stream and sand bed in a laboratory flume
https://resolver.caltech.edu/CaltechETD:etd-01152008-142257
Year: 1997
DOI: 10.7907/FYMP-BR13
Experiments were conducted in a recirculating flume to study the exchange of colloids between a stream and sand bed. Observations of the net transport of kaolinite clay from the stream to the bed were used to validate models for colloid exchange which include the hydraulics of water exchange along with the particle-specific effects of filtration and settling.
The flume allowed extensive control of the stream conditions (slope, depth, velocity) and bed parameters (bed depth, bedform height, wavelength, and velocity). All experiments had steady, uniform stream flow and well-developed bedforms. To define the chemistry of the system, the composition of the flume water was controlled, the clay was reproducibly prepared, and the sand was cleaned prior to every experiment.
Experiments involved observing the exchange of both a conservative lithium chloride tracer and the kaolinite tracer. Net exchange was determined by measuring the change of tracer concentration in the stream water. Vertical profiles of the tracer distribution in the bed were also measured.
Column experiments were performed to measure kaolinite filtration by the bed sediment. The pH and ionic strength of both the flume and column water were controlled to vary the extent of filtration.
Two mechanisms are responsible for exchange between the stream and stream bed--an advective pore-water flow driven by bedform-induced pressure variations at the surface of the bed (pumping), and the burial and release of water due to bedform motion (turnover). Pumping causes kaolinite to be carried deep in the bed where it is trapped due to filtration and settling. Turnover causes continuous mixing of the uppermost portion of the bed which hinders penetration of clay to the deeper bed.
Models incorporating the relevant physical and chemical processes controlling colloid transport were developed to predict the net exchange of kaolinite between the stream and sand bed. Model parameters were nondimensionalized so the models can be applied to problems of any scale. Models for conservative solutes were developed to predict the exchange with a finite bed and exchange due to fast-moving bedforms. Models for colloid transport were developed which are based on the solute transport models, but include the impact of settling on particle flow paths and filtration along path lines. When input data were taken from laboratory experiments, the models generally predicted the flume results well with no calibration. In all flume experiments, filtration and settling of colloids in the bed were sufficiently high so that it could be assumed that all colloid which entered the bed was irreversibly trapped.
Additional model simulations were performed to demonstrate the effect of major input variables on exchange. These simulations cover cases not examined in experiments and provide a sensitivity analysis for the model inputs.
https://resolver.caltech.edu/CaltechETD:etd-01152008-142257Thermal plumes from staged multiport diffusers in uniform quiescent environment
https://resolver.caltech.edu/CaltechETD:etd-05172007-152237
Year: 1990
DOI: 10.7907/58bk-6222
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 a 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, D0, the horizontal orientation of the jet, [alpha], the total discharge flow rate, QT0, 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 D0 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, is relatively insensitive to n. It is also concluded that the horizontal orientation of the jet, at ±25° 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 is not significantly modified.https://resolver.caltech.edu/CaltechETD:etd-05172007-152237Longitudinal Dispersion in Nonuniform, Isotropic Porous Media
https://resolver.caltech.edu/CaltechETD:etd-01122007-131711
Year: 1984
DOI: 10.7907/0vtp-g766
<p>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.</p>
<p>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 flowing through individual, random capillary tubes. However, shear dispersion within individual capillary tubes (discussed in Appendix C) 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.</p>
<p>The experimental investigation of longitudinal dispersion is carried out by measuring (with conductivity probes) the development of an initially sharp miscible displacement surface. 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.</p>
<p>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.</p>https://resolver.caltech.edu/CaltechETD:etd-01122007-131711Characteristics of Transverse Mixing in Open-Channel Flows
https://resolver.caltech.edu/CaltechTHESIS:05142018-094038251
Year: 1971
DOI: 10.7907/JTHM-FS72
<p>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. </p>
<p>Tracer concentration was analyzed in two phases. </p>
<p>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 the flow velocity was greatest. In contrast to previous speculation, the ratio of the depth-averaged coefficient of transverse mixing <sup>-</sup>D<sub>z</sub> to the product of the (bed) shear velocity u<sub>*</sub> and the flow depth d was not a constant but depended on the aspect ratio λ= d/W, where W = flume width. For laboratory experiments<sup>-</sup>D<sub>z</sub>/u<sub>*</sub>d decreased from o. 24 to 0.093
as λ increased from O. 015 to O. 200.</p>
<p>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<sub>b</sub>; an intermittency region where c(t) was only intermittently greater than C<sub>b</sub>; and the outer region
Where c<sub>b</sub> 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. </p>
<p>Finally the results of the two phases of study were interrelated to evaluate their contributions to the transverse spreading of the plume. </p>
https://resolver.caltech.edu/CaltechTHESIS:05142018-094038251Stability of Bottom Armoring Under the Attack of Solitary Waves
https://resolver.caltech.edu/CaltechTHESIS:02232017-105808087
Year: 1976
DOI: 10.7907/TMPB-2078
<p>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.</p>
<p>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.</p>
<p>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.</p>
<p>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.</p>
<p>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.</p>
<p>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<sub>s</sub>, h, and H, where D<sub>s</sub> 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.</p>
https://resolver.caltech.edu/CaltechTHESIS:02232017-105808087Effects of density differences on lateral mixing in open-channel flows
https://resolver.caltech.edu/CaltechTHESIS:08252015-081521032
Year: 1970
DOI: 10.7907/WEDF-B722
<p>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.</p>
<p>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.</p>
<p>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. </p>
https://resolver.caltech.edu/CaltechTHESIS:08252015-081521032