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ISRN Thermodynamics
Volume 2012 (2012), Article ID 609701, 15 pages
Research Article

Thermodynamics/Dynamics Coupling in Weakly Compressible Turbulent Stratified Fluids

Department of Meteorology, University of Reading, Earley Gate, P.O. Box 243, Reading RG6 6BB, UK

Received 6 December 2011; Accepted 22 January 2012

Academic Editors: E. Curotto and N. Marmier

Copyright © 2012 Rémi Tailleux. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In traditional and geophysical fluid dynamics, it is common to describe stratified turbulent fluid flows with low Mach number and small relative density variations by means of the incompressible Boussinesq approximation. Although such an approximation is often interpreted as decoupling the thermodynamics from the dynamics, this paper reviews recent results and derive new ones that show that the reality is actually more subtle and complex when diabatic effects and a nonlinear equation of state are retained. Such an analysis reveals indeed: (1) that the compressible work of expansion/contraction remains of comparable importance as the mechanical energy conversions in contrast to what is usually assumed; (2) in a Boussinesq fluid, compressible effects occur in the guise of changes in gravitational potential energy due to density changes. This makes it possible to construct a fully consistent description of the thermodynamics of incompressible fluids for an arbitrary nonlinear equation of state; (3) rigorous methods based on using the available potential energy and potential enthalpy budgets can be used to quantify the work of expansion/contraction 𝐵 in steady and transient flows, which reveals that 𝐵 is predominantly controlled by molecular diffusive effects, and act as a significant sink of kinetic energy.