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On the meaning of mixing efficiency for buoyancy-driven mixing in stratified turbulent flows

Published online by Cambridge University Press:  17 September 2015

Megan S. Davies Wykes ,
Graham O. Hughes  and
Stuart B. Dalziel
Megan S. Davies Wykes*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Graham O. Hughes
Affiliation:
Research School of Earth Sciences, The Australian National University, Canberra, ACT 0200, Australia
Stuart B. Dalziel
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: megan.davieswykes@cantab.net
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Abstract

The concept of a mixing efficiency is widely used to relate the amount of irreversible diabatic mixing in a stratified flow to the amount of energy available to support mixing. This common measure of mixing in a flow is based on the change in the background potential energy, which is the minimum gravitational potential energy of the fluid that can be achieved by an adiabatic rearrangement of the instantaneous density field. However, this paper highlights examples of mixing that is primarily ‘buoyancy-driven’ (i.e. energy is released to the flow predominantly from a source of available potential energy) to demonstrate that the mixing efficiency depends not only on the specific characteristics of the turbulence in the region of the flow that is mixing, but also on the density profile in regions remote from where mixing physically occurs. We show that this behaviour is due to the irreversible and direct conversion of available potential energy into background potential energy in those remote regions (a mechanism not previously described). This process (here termed ‘relabelling’) occurs without requiring either a local flow or local mixing, or any other process that affects the internal energy of that fluid. Relabelling is caused by initially available potential energy, associated with identifiable parcels of fluid, becoming dynamically inaccessible to the flow due to mixing elsewhere. These results have wider relevance to characterising mixing in stratified turbulent flows, including those involving an external supply of kinetic energy.

JFM classification

Geophysical and Geological Flows: Stratified flows Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 781 , 25 October 2015 , pp. 261 - 275
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Copyright
© Crown Copyright. Published by Cambridge University Press 2015 

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