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Rayleigh–Taylor mixing in an otherwise stable stratification

Published online by Cambridge University Press:  03 November 2011

Andrew G. W. Lawrie  and
Stuart B. Dalziel
Andrew G. W. Lawrie*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Stuart B. Dalziel
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: A.G.W.Lawrie@damtp.cam.ac.uk
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Abstract

We seek to understand the distribution of irreversible energy conversions (mixing efficiency) between quiescent initial and final states in a miscible Rayleigh–Taylor driven system. The configuration we examine is a Rayleigh–Taylor unstable interface sitting between stably stratified layers with linear density profiles above and below. Our experiments in brine solution measure vertical profiles of density before and after the unstable interface is allowed to relax to a stable state. Our analysis suggests that less than half the initially available energy is irreversibly released as heat due to viscous dissipation, while more than half irreversibly changes the probability density function of the density field by scalar diffusion and therefore remains as potential energy, but in a less useful form. While similar distributions are observed in Rayleigh–Taylor driven mixing flows between homogeneous layers, our new configuration admits energetically consistent end-state density profiles that span all possible mixing efficiencies, ranging from all available energy being expended as dissipation, to none. We present experiments that show that the fluid relaxes to a state with a significantly lower mixing efficiency than the value for ideal mixing in this configuration, and deduce that this mixing efficiency more accurately characterizes Rayleigh–Taylor driven mixing than previous measurements. We argue that the physical mechanisms intrinsic to Rayleigh–Taylor instability are optimal conditions for mixing, and speculate that we have observed an upper bound to fluid mixing in general.

JFM classification

Convection: Buoyancy-driven instability Turbulent Flows: Stratified turbulence Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 688 , 10 December 2011 , pp. 507 - 527
Copyright
Copyright © Cambridge University Press 2011

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