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.

\n \nAn experimental investigation was made to measure the mixing in a two-layered density-stratified shear flow in a flume 40-meters long, with a cross-section of 110 cm wide by 60 cm deep. Both mean temperatures and the mean velocities of the two layers could be independently controlled, and steps were taken to ensure that the temperatures and velocities of the two layers remained nearly constant at the inlet. The relative density difference between the layers was 10^{-3} or less. A laser-Doppler velocimeter, designed for this study, allowed measurements of two components of velocity simultaneously, while a sensitive thermistor was used to measure the temperature. The temperature and velocity measurements were recorded and later analyzed.

The initial mixing layer which developed at the inlet was found to be dominated by large, two-dimensional vortex structures. When the flow was sufficiently stratified, these structures would collapse in a short distance and the flow would develop a laminar shear layer at the interface. It was found that the bulk-Richardson number Δρ/ρ_{o}gl_{T}^{*}/Δu^{-}_{o}^{2}, where l_{T}^{*} is the maximum-slope thickness of the temperature profile, attained a maximum value of between 0.25 and 0.3 when the mixing layer collapsed.

Downstream, much less turbulent mixing took place in the stratified flows than homogeneous flows. The depth-averaged turbulent diffusivities for heat and momentum were often 30 to 100 times smaller in stratified flows than in homogeneous flows. The turbulence downstream was found to be dominated by large turbulent bursts, during which the vertical turbulent transport of momentum, heat and turbulent kinetic energy are many times larger than their mean values. It was found these bursts were responsible for most of the total turbulent transport of momentum, heat and turbulent kinetic energy, even though the bursts were found only intermittently.

\n \nThe flux Richardson number, R_{f}, 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^{1}v^{1})^{‾} ϑu^{‾}/ϑuy, was the largest source of turbulent kinetic energy, it was found that R_{f} < 0.3, and when the flow was strongly stratified, then R_{f} < 0.2. If the diffusion of turbulent kinetic energy 1/2 ϑ(u^{'2} + v^{'2})v^{'}^{‾}/ϑy = ϑq^{*2}v^{'}/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_{f}. 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.

The various aspects of the propagation of long waves onto a shelf (i.e., reflection, transmission and propagation on the shelf) are examined experimentally and theoretically. The results are applied to tsunamis propagating onto the continental shelf.

\n \nA numerical method of solving the one-dimensional Boussinesq equations for constant depth using finite element techniques is presented. The method is extended to the case of an arbitrary variation in depth (i.e., gradually to abruptly varying depth) in the direction of wave propagation. The scheme is applied to the propagation of solitary waves over a slope onto a shelf and is confirmed by experiments.

\n \nA theory is developed for the generation in the laboratory of long waves of permanent form, i.e., solitary and cnoidal waves. The theory, which incorporates the nonlinear aspects of the problem, applies to wave generators which consist of a vertical plate which moves horizontally. Experiments have been conducted and the results agree well with the generation theory. In addition, these results are used to compare the shape, celerity and damping characteristics of the generated waves with the long wave theories.

\n \nThe solution of the linear nondispersive theory for harmonic waves of a single frequency propagating over a slope onto a shelf is extended to the case of solitary waves. Comparisons of this analysis with the nonlinear dispersive theory and experiments are presented.

\n \nComparisons of experiments with solitary and cnoidal waves with the predictions of the various theories indicate that, apart from propagation, the reflection of waves from a change in depth is a linear process except in extreme cases. However, the transmission and the propagation of both the transmitted and the reflected waves in general are nonlinear processes. Exceptions are waves with heights which are very small compared to the depth. For these waves, the entire process of propagation onto a shelf in the vicinity of the shelf is linear . Tsunamis propagating from the deep ocean onto the continental shelf probably fall in this class.

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