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Local available energetics of multicomponent compressible stratified fluids

Published online by Cambridge University Press:  12 March 2018

Rémi Tailleux Open the ORCID record for Rémi Tailleux [Opens in a new window]
Rémi Tailleux*
Affiliation:
Department of Meteorology, University of Reading, Earley Gate, PO Box 243, Reading RG6 6BB, UK
*
†Email address for correspondence: R.G.J.Tailleux@reading.ac.uk
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Abstract

We extend the local theory of available potential energy (APE) to a general multicomponent compressible stratified fluid, accounting for the effects of diabatic sinks and sources. As for simple compressible fluids, the total potential energy density of a fluid parcel is the sum of its available elastic energy and APE density. These respectively represent the adiabatic compression/expansion work needed to bring it from its reference pressure to its actual pressure and the work against buoyancy forces required to move it from its reference state position to its actual position. Our expression for the APE density is new and is derived using only elementary manipulations of the equations of motion; it is significantly simpler than existing published expressions, while also being more transparently linked to the relevant form of APE density for the Boussinesq and hydrostatic primitive equations. Our new framework is used to clarify the links between some aspects of the energetics of Boussinesq and real fluids, as well as to shed light on the physical basis underlying the choice of reference state(s) in local APE theory.

JFM classification

Geophysical and Geological Flows: Stratified flows Mixing: Turbulent mixing
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 842 , 10 May 2018 , R1
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Copyright
© 2018 Cambridge University Press 

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