Thermodynamics/dynamics coupling in weakly compressible turbulent stratiﬁed fluids
Tailleux, R. (2012) Thermodynamics/dynamics coupling in weakly compressible turbulent stratiﬁed fluids. ISRN Thermodynamics, 2012. 609701. ISSN 2090-5211
To link to this article DOI: 10.5402/2012/609701
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.