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On the validity of single-parcel energetics to assess the importance of internal energy and compressibility effects in stratified fluids

Published online by Cambridge University Press:  13 February 2015

Rémi Tailleux
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

It is often assumed on the basis of single-parcel energetics that compressible effects and conversions with internal energy are negligible whenever typical displacements of fluid parcels are small relative to the scale height of the fluid (defined as the ratio of the squared speed of sound to the gravitational acceleration). This paper shows that the above approach is flawed, however, and that a correct assessment of compressible effects and internal energy conversions requires the consideration of the energetics of at least two parcels or, more generally, of mass-conserving parcel rearrangements. As a consequence, it is shown that it is the adiabatic lapse rate and its derivative with respect to pressure, rather than the scale height, that controls the relative importance of compressible effects and internal energy conversions when considering the global energy budget of a stratified fluid. Only when mass conservation is properly accounted for is it possible to explain why the available internal energy can account for up to 40 % of the total available potential energy in the oceans. This is considerably larger than the prediction of single-parcel energetics, according to which this number should be no more than approximately 2 %.

JFM classification

Turbulent Flows: Compressible turbulence Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Stratified flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 767 , 25 March 2015 , R2
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Copyright
© 2015 Cambridge University Press 

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