### Weakly compressible flows II: particular scaling regimes and thermodynamic consistency

Klein, R *(Freie Universität Berlin)*

Wednesday 03 October 2012, 14:00-14:30

Seminar Room 1, Newton Institute

#### Abstract

Building on the morning lecture "Weakly compressible flows I: regime of validity of sound-proof appoximaitons", I will discuss regimes of length scales different from the orginal design regime of sound-proof models, which involves tropospheric flows at horizontal scales of 10-100 km and associated advective scales. In particular, I will show that short wave internal wave packets in the stratosphere can be described by the pseudo-incompressible approximation, but that the anelastic model looses its formal validity in this case.

At very small scales the pseudo-incompressible model reduces to the zero Mach number variable density equations, whereas the anelastic model reduces to the more restrictive Boussinesq approximation.

Sound-proofing appoximations affect the thermodynamic relationships. I will introduce a definition for the notion of "thermodynamic consistency" of sound-proof approximations, show how complying anelastic and pseudo-incompressible models can be formulated, and discuss their regimes of validity.