Studies on the mixing in a density-stratified shear flow
Creators: name: Gartrell, Gregory, Jr.
Publisher: name: California Institute of Technology
Year: 1979

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

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

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

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

The flux Richardson number, Rf, in the flow was examined and found to be related to the local mean-Richardson number in many cases.  When production of turbulent kinetic energy from the mean shear,
  , was the largest source of turbulent kinetic energy, it was found that Rf < 0.3, and when the flow was strongly stratified, then Rf < 0.2.  If the diffusion of turbulent kinetic energy 
 was the largest source of turbulent kinetic energy, then the flux-Richardson number often attained large values, and the quantity   was found to be a more useful parameter than Rf.  It was found that, in almost all cases, the rate at which the potential energy of the fluid increased due to turbulent mixing was much less than the estimated rate of viscous dissipation of turbulent kinetic energy.
description: © 1979 W. M. Keck Laboratory of Hydraulics and Water Resources. California Institute of Technology. 

There are so many people to whom I owe so much, I feel I could write another volume the size of this one and still not thank everyone adequately. There are several friends who have been especially helpful over the last few years, and who have contributed to this work in many vital ways; I am sincerely grateful for the time, effort and friendship these people have offered me. The two people to whom I owe the most are Professors Norman H. Brooks and E. John List. Dr. Brooks, my principal advisor on this project, suggested the topic and provided patient guidance and understanding as the work progressed. His warm sense of humor brightened countless days for me, and he always provided encouragement when it was needed. Dr. List has been especially helpful. He has provided encouragement and friendship, and has always been willing to share a few moments to discuss new ideas and provide helpful insights. I owe more than I can ever repay to these two friends. I would especially like to thank Elton Daly, whose special genius has never ceased to amaze me. No matter what needed to be built in the laboratory, Elton always had a better, simpler way to do it. He has been a close friend and an inspiration to me.
There are several other people who made valuable contributions to this work. I would like to thank Dr.
Robert C.Y. Koh, who provided help in the data analysis and whose "MAGIC" language saved me hours of programming. I would also like to thank Professor Fred Raichlen, with
whom I had many valuable discussions.

Professor Vito A. Vanoni deserves special thanks for the time and help he provided. His awesome dedication and vitality acted as a constant encouragement. Joan Mathews typed a seemingly endless thesis, and retyped the corrected versions, a Sisyphean task. She provided friendship throughout the past years, and kind encouragement when it was greatly needed the last few weeks. I am truly thankful.
During the summer of 1977, I participated in the Geophysical Fluid Dynamics Program at the Woods Hole Oceanographic Institution. My visit there as a pre-doctoral fellow provided me with the opportunity not only to meet with many interesting and knowledgeable people, but also to take some time to reflect on this research and to hear fresh ideas. I returned from Woods Hole with a deeper understanding of the subject, and an enthusiasm that has stayed with me to this day. I would like to thank the Woods Hole Oceanographic Institution and the Geophysical
Fluid Dynamics Program for the support they provided. I would also like to thank Professor George Veronis, who directed the program, and Professor Mllrten T. Landahl, with whom I had many worthwhile discussions, and who taught me so much about the subject of turbulence. No one can conduct an experimental program alone, and in this instance I had valuable help from Joe Fontana, Rich Eastvedt and Dave
Byrum. The fine talents of Joe Fontana and Rich Eastvedt turned rough sketches into apparatus that not only worked as intended, but also looked like works of art. Dave Byrum provided help with the experiments, especially the photography, and did a magnificent job with more drawings
than he or I would ever care to see again. I would also like to thank Phil Cormier, who helped take data and
who, along with Dale Ota, helped in the data reduction. This research could never have been completed without the signal processor for the laser-Doppler system. Marc Donner designed and built the first working model. I would also like to thank Larry McClellan and Catharine van Ingen for their help. There are several others who provided friendship, advice and assistance. I would specially like to thank Jill Pankow, Steve Wright, Phil Roberts, Jacqueo Lavalle and Jing-Chang Chen. I want to thank Kary Eichbauer for her love and encouragement and patience. I hope I can
give as much aa she continues with a task similar to this one. I would like to thank the California Institute of Technology for providing facilities which made this study possible, and the National Science Foundation for providing financial support under Grants GK35774X, ENG75-02985, ENG77-27398; the Environmental Protection Agency under Grant T-900137; the National Institutes of Environmental Health Science under Training Grant 5T01 8800004-15 and the Ford Motor Company Fund/Ford Energy Research Program. This report was submitted on May 22, 1979 as a thesis for the degree of Doctor of Philosophy in Environmental Engineering Science at the California Institute of Technology.