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On mixing and transport at a sheared density interface

Sullivan, Greg D. and List, E. John (1994) On mixing and transport at a sheared density interface. Journal of Fluid Mechanics, 273 . pp. 213-239. ISSN 0022-1120. doi:10.1017/S0022112094001916.

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Mixing and transport of a stratifying scalar are investigated at a density interface imbedded in a turbulent shear flow. Steady-state interfacial shear flows are generated in a laboratory water channel for layer Richardson numbers, Ri, between about 1 and 10. The flow field is made optically homogeneous, enabling the use of laser-induced fluorescence with photodiode array imaging to measure the concentration field at high resolution. False-colour images of the concentration field provide valuable insight into interfacial dynamics: when the local mean shear Richardson number, Ri_s, is less than about 0.40–0.45, interfacial mixing appears to be dominated by Kelvin–Helmholtz (K–H) instabilities; when Ri_s is somewhat larger than this, interfacial mixing appears to be dominated by shear-driven wave breaking. In both cases, vertical transport of mixed fluid from the interfacial region into adjacent turbulent layers is accomplished by large-scale turbulent eddies which impinge on the interface and scour fluid from its outer edges. Motivated by the experimental findings, a model for interfacial mixing and entrainment is developed. A local equilibrium is assumed in which the rate of loss of interfacial fluid by eddy scouring is balanced by the rate of production (local mixing) by interfacial instabilities and molecular diffusion. When a single layer is turbulent and entraining, the model results are as follows: in the molecular-diffusion-dominated regime, δ/h ~ Pe^(−1/2) and E ~ Ri^(−1)Pe^(−1/2); in the wave-breaking-dominated regime, δ/h ~ Ri^(−1/2) and E ~ Ri^(−3/2); and in the K–H-dominated regime, δ/h ~ Ri^(−1) and E ~ Ri^(−2), where δ is the interface thickness, h is the boundary-layer thickness, Pe is the Péclet number, and E is the normalized entrainment velocity. In all three regimes, the maximum concentration anomaly, Γ_m ~ Ri^(−1). When both layers are turbulent and entraining, E and δ depend on combinations of parameters from both layers.

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Additional Information:© 1994 Cambridge University Press. (Received 22 June 1992 and in revised form 18 February 1994) We would like to thank the entire staff of the W. M. Keck Hydraulics Laboratory for their valuable assistance throughout this study. The first author would like to thank Professor P. J. Sullivan for some valuable discussions and helpful advice and Professor H. J. S. Fernando for some useful comments. We would also like to thank Professor J. S. Turner for some thoughtful comments on an early version of the manuscript. The authors also express their appreciation for numerous comments received from anonymous reviewers, all of which materially improved the final manuscript. The majority of this work is taken from the first author's doctoral dissertation, financed in part by the US National Science Foundation through Award number CTS-8819584, by the US Department of the Interior, Geological Survey through Grant number 14-08-0001-G1628, through the State Water Resources Research Institute, Project number G1550, and by the University of California Water Resources Center, Project UCAL-WRC-W-735. Contents of this publication do not necessarily reflect the views and policies of the US Department of the Interior, nor does mention of trade names or commercial products constitute their endorsement or recommendation for use by the US Government.
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State Water Resources Research InstituteG1550
University of California Water Resources CenterUCAL-WRC-W-735
Record Number:CaltechAUTHORS:20160418-125123356
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Official Citation:Greg D. Sullivan and E. John List (1994). On mixing and transport at a sheared density interface. Journal of Fluid Mechanics, 273, pp 213-239 doi:10.1017/S0022112094001916
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66248
Deposited By: George Porter
Deposited On:18 Apr 2016 20:23
Last Modified:10 Nov 2021 23:55

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