Studies on the Mixing in a Density-Stratified Shear Flow

Citation

Gartrell, Gregory Jr. (1979) Studies on the Mixing in a Density-Stratified Shear Flow. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/G80K-5566. https://resolver.caltech.edu/CaltechTHESIS:10172017-162001547

Abstract

The objective of this study was to examine in a fundamental way the mixing processes in a stably-stratified shear flow. The results of the experimental program have yielded information on the nature of turbulence and mixing in density-stratified fluids. The results can be applied to such problems as the determination of the spreading and mixing rates of heated effluents discharged to lakes or the ocean, as well as to many geophysical problems.

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

The initial mixing layer which developed at the inlet was found to be dominated by large, two-dimensional vortex structures. When the flow was sufficiently stratified, these structures would collapse in a short distance and the flow would develop a laminar shear layer at the interface. It was found that the bulk-Richardson number Δρ/ρ_ogl_T^*/Δu^-_o², 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.

The 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, (-u¹v¹)^‾ 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^*2v^'/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.

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