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.

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.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {List, E. John}, } @phdthesis{10.7907/TMPB-2078, author = {Naheer, Ehud}, title = {Stability of Bottom Armoring Under the Attack of Solitary Waves}, school = {California Institute of Technology}, year = {1976}, doi = {10.7907/TMPB-2078}, url = {https://resolver.caltech.edu/CaltechTHESIS:02232017-105808087}, 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.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Raichlen, Fredric}, } @phdthesis{10.7907/9XZ5-FA91, author = {Taylor, Brent Dalton}, title = {Temperature effects in alluvial streams}, school = {California Institute of Technology}, year = {1972}, doi = {10.7907/9XZ5-FA91}, url = {https://resolver.caltech.edu/CaltechTHESIS:09062016-161209389}, 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’

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Vanoni, Vito A.}, } @phdthesis{10.7907/AKKA-X706, author = {French, Jonathan Akin}, title = {Wave uplift pressures on horizontal platforms}, school = {California Institute of Technology}, year = {1970}, doi = {10.7907/AKKA-X706}, url = {https://resolver.caltech.edu/CaltechTHESIS:08052015-104412384}, 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 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.

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.

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.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Raichlen, Fredric}, } @phdthesis{10.7907/E2V8-1794, author = {Brock, Richard Runyon}, title = {Development of roll waves in open channels}, school = {California Institute of Technology}, year = {1968}, doi = {10.7907/E2V8-1794}, url = {https://resolver.caltech.edu/CaltechTHESIS:11302015-161200702}, 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_{o} 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_{nmax} 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_{o} 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 /hh^{-}_{max}/h_{n} the growth rate of δh^{-}_{max}/h^{-}_{max}δl 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 δh^{-}_{max}/h^{-}_{max}δl of shock waves was predicted to depend on the channel slope, and this slope dependence was observed in the experiments.

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, ω, and the pulse amplitude, A, defined by

K = Aω^{-s}

Where s is the slope of a plot of log A against log ω. 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.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Vanoni, Vito A.}, } @phdthesis{10.7907/8D5C-BV11, author = {Fischer, Hugo Breed}, title = {Longitudinal dispersion in laboratory and natural streams}, school = {California Institute of Technology}, year = {1966}, doi = {10.7907/8D5C-BV11}, url = {https://resolver.caltech.edu/CaltechTHESIS:09292015-082820697}, abstract = {

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.

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 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.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Brooks, Norman H.}, } @phdthesis{10.7907/HRDZ-N222, author = {Hwang, Li-San}, title = {Flow resistance of dunes in alluvial streams}, school = {California Institute of Technology}, year = {1965}, doi = {10.7907/HRDZ-N222}, url = {https://resolver.caltech.edu/CaltechETD:etd-05092003-173224}, abstract = {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.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Vanoni, Vito A.}, } @phdthesis{10.7907/Y27F-NR79, author = {Kennedy, John Fisher}, title = {Stationary waves and antidunes in alluvial channels}, school = {California Institute of Technology}, year = {1960}, doi = {10.7907/Y27F-NR79}, url = {https://resolver.caltech.edu/CaltechETD:etd-06222006-153051}, abstract = {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.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Brooks, Norman H. and Vanoni, Vito A.}, } @phdthesis{10.7907/QZ0J-A652, author = {Nomicos, George N.}, title = {Effects of sediment load on the velocity field and friction factor of turbulent flow in an open channel}, school = {California Institute of Technology}, year = {1956}, doi = {10.7907/QZ0J-A652}, url = {https://resolver.caltech.edu/CaltechETD:etd-06182004-105138}, abstract = {An experimental investigation was made of the friction characteristics of streams with sediment load. Measurements of velocity and sediment profiles, and calculations of friction factor, f, and von Karman’s constant, k, were made in a 40-foot tilting flume. Several runs were made with uniform flow and various bed configurations using sands of two sizes (.10 mm and .16 mm). For better understanding of the effect of sediment on von Karman’s constant k and the friction factor, uniform clear water flows were established on stabilized natural sand beds. The depth and the mean velocity were kept the same as those of the movable bed stream for which the sand bed was stabilized, and a direct comparison was made. Then, by adding loose sand in steps and establishing uniform flow, the change in von Karman’s constant and the friction factor with sediment load was studied. It was found that both the friction coefficient f, and von Karman’s k, decreased as the sediment load was increased, although the coefficient f decreased by a much smaller percentage than the constant k. It is hypothesized that the sediment load appreciably reduces the rate of turbulent energy diffusion, thus reducing the turbulence level of the fully established uniform flow and changing the balance of turbulence energy.

In a very small region near the bed the turbulent energy production, diffusion, viscous action and dissipation of energy due to sediment in suspension are all of about equal importance. A theoretical study was made of the distribution of both the production of turbulent energy and the dissipation of energy by the sediment along a vertical profile for hydrodynamically smooth bed,and it was made possible to integrate them to the bottom of the stream.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Vanoni, Vito A.}, } @phdthesis{10.7907/JB2P-1H91, author = {Brooks, Norman H.}, title = {Laboratory studies of the mechanics of streams flowing over a movable bed of fine sand}, school = {California Institute of Technology}, year = {1954}, doi = {10.7907/JB2P-1H91}, url = {https://resolver.caltech.edu/CaltechETD:etd-05152003-113520}, abstract = {A laboratory study was made of the characteristics of streams flowing over a loose bed of fine sand in order to determine what factors govern the equilibrium rate of transportation of fine sand in suspensions. Twenty-two experimental runs were performed in a 40-foot tilting flume for various conditions with bed sand of two different sizes (0.10 mm and 0.16 mm). Each run represented a uniform open-channel flow in equilibrium with the sand bed. It was found that more than one equilibrium flow velocity and sediment discharge existed for a given depth, slope, and size of sand because of the extreme variability of channel roughness. At low velocities, the large irregular dunes which formed on the stream bed made the bed friction factor over six times larger than the friction factor for the smooth sand beds obtained at higher flow rates. Thus the transportation rate could not be expressed as a unique function of the bed shear stress, the channel geometry, and properties of the sand as has been supposed in all previous theories for the equilibrium transportation rate of suspended load. By using the mean velocity and the depth (or the water discharge and sediment discharge) as independent variables, and slope as a dependent variable, an orderly qualitative relationship between the pertinent variables was obtained. Because of the importance of the dunes in the mechanics of sediment-laden streams, a special study was made of their characteristics and the mechanisms of their formation and movement. The studies also included some theoretical and experimental investigations of the distribution of velocity and suspended sediment within the flow for runs with a smooth bed.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Vanoni, Vito A.}, } @phdthesis{10.7907/FR64-QE92, author = {Ismail, Hassan M.}, title = {Study of suspended sediment in closed channels}, school = {California Institute of Technology}, year = {1949}, doi = {10.7907/FR64-QE92}, url = {https://resolver.caltech.edu/CaltechETD:etd-04262004-152823}, abstract = {NOTE: Text or symbols not renderable in plain ASCII are indicated by […]. Abstract is included in .pdf document.

Tests on a rectangular channel 10.5 by 3 inches in cross-section transporting water mixed with different amounts of sand are described in this thesis. Two sizes of sand were used. They are of mean sedimentation diameter of 0.10 mm. and 0.16 mm.

Th experimental data were used to study both the effects of the presence of sand in suspension on the characteristics of the flow, and the concentration transfer coefficient at the middle of the channel, assuming a two-dimensional flow.

It was found the the von Karman universal constant of turbulent exchange k decreases with the increase of the suspended material. k decreased to 0.20 when a total load of about 25 kilograms was added to the flume, i.e., 43 grams were added to each liter. No limit was approached for the decreased of k. The friction coefficient […] was hardly affected by the presence of the sand when the velocity of flow was higher than a certain velocity. This critical velocity increased with the total load in the flume and the size of the sand used. It is related to the bed load and it is the velocity at which all the dunes on the bed are carried in suuspension. Below that critical velocity […] exceeds that of clear water.

The sediment transfer coefficient […] was found to be equal to 1.5, the momentum transfer coefficient […] for the 0.10 mm. sand, and to 1.3 […] for the 0.16 mm. sand. […] follows the normal parabolic form of […] at the outer two-thirds of the channel and has a constant value at the middle third.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Vanoni, Vito A.}, }