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Available potential energy and mixing in density-stratified fluids

Published online by Cambridge University Press:  26 April 2006

Kraig B. Winters ,
Peter N. Lombard ,
James J. Riley  and
Eric A. D'Asaro
Kraig B. Winters
Affiliation:
Applied Physics Laboratory, University of Washington, Seattle, WA 98105, USA Department of Applied Mathematics, University of Washington, Seattle, WA 98105, USA
Peter N. Lombard
Affiliation:
Department of Mechanical Engineering, University of Washington, Seattle, WA 98105, USA
James J. Riley
Affiliation:
Department of Applied Mathematics, University of Washington, Seattle, WA 98105, USA Department of Mechanical Engineering, University of Washington, Seattle, WA 98105, USA
Eric A. D'Asaro
Affiliation:
Applied Physics Laboratory, University of Washington, Seattle, WA 98105, USA School of Ocean and Fishery Sciences, University of Washington, Seattle, WA 98105, USA
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Abstract

A conceptual framework for analysing the energetics of density-stratified Boussinesq fluid flows is discussed. The concept of gravitational available potential energy is used to formulate an energy budget in which the evolution of the background potential energy, i.e. the minimum potential energy attainable through adiabatic motions, can be explicitly examined. For closed systems, the background potential energy can change only due to diabatic processes. The rate of change of background potential energy is proportional to the molecular diffusivity. Changes in the background potential energy provide a direct measure of the potential energy changes due to irreversible diapycnal mixing. For open systems, background potential energy can also change due to boundary fluxes, which can be explicitly measured. The analysis is particularly appropriate for evaluation of diabatic mixing rates in numerical simulations of turbulent flows. The energetics of a shear driven mixing layer is used to illustrate the analysis.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 289 , 25 April 1995 , pp. 115 - 128
Copyright
© 1995 Cambridge University Press

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