Asymptotic aspects of the Boussinesq approximation for gases and liquids
- 1 July 1991
- journal article
- research article
- Published by Taylor & Francis in Geophysical & Astrophysical Fluid Dynamics
- Vol. 58 (1-4) , 45-55
- https://doi.org/10.1080/03091929108227330
Abstract
The asymptotic formulation of the Boussinesq approximation relates the pressure of the fluid to a thermodynamical quantity involving the heat capacity cPo . In this paper we examine the implications of such a scaling, in particular: (i) the singular degeneracy of the equation of state ρ = ρ* (1 −α* (T−;T*)) of a liquid: this equation of state is valid only for small values of the coefficient α T*; (ii) in which manner the scaling introduces the Mach number of the flow as a small parameter e for a compressible fluid. The equations at order zero with respect to ϵ are the same equations for gases and for liquids only if the thermodynamics of the medium is described by using the Brunt-Väisälä frequency instead of the temperature.Keywords
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