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Rigorous entropy formulation of the anelastic liquid equations in an ideal gas

Published online by Cambridge University Press:  08 November 2017

Krzysztof A. Mizerski Open the ORCID record for Krzysztof A. Mizerski [Opens in a new window]
Krzysztof A. Mizerski*
Affiliation:
Department of Magnetism, Institute of Geophysics, Polish Academy of Sciences, ul. Ksiecia Janusza 64, 01-452 Warsaw, Poland
*
†Email address for correspondence: kamiz@igf.edu.pl
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Abstract

The point of this short paper is to provide a useful set of equations governing stratified convection, expressed solely in terms of two thermodynamic variables, i.e. the pressure and the entropy, and the velocity field of the flow, free from any additional assumptions about the properties of turbulence. The pressure fluctuation is entirely eliminated from the energy equation and it appears only in the momentum balance, easily removable by taking its curl. This goal is achieved through the well-known anelastic approximation and an assumption of constant thermal diffusivity coefficient. The rigorously derived system of anelastic liquid equations constitutes a useful tool for modelling the dynamics of stellar interiors.

JFM classification

Convection: Convection Mathematical Foundations: Mathematical Foundations Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 833 , 25 December 2017 , pp. 677 - 686
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Copyright
© 2017 Cambridge University Press 

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