The breakdown of the anelastic approximation in rotating compressible convection: implications for astrophysical systems

Proceedings. Mathematical, Physical, and Engineering Sciences
Michael A CalkinsPhilippe Marti

Abstract

The linear theory for rotating compressible convection in a plane layer geometry is presented for the astrophysically relevant case of low Prandtl number gases. When the rotation rate of the system is large, the flow remains geostrophically balanced for all stratification levels investigated and the classical (i.e. incompressible) asymptotic scaling laws for the critical parameters are recovered. For sufficiently small Prandtl numbers, increasing stratification tends to further destabilize the fluid layer, decrease the critical wavenumber and increase the oscillation frequency of the convective instability. In combination, these effects increase the relative magnitude of the time derivative of the density perturbation contained in the conservation of mass equation to non-negligible levels; the resulting convective instabilities occur in the form of compressional quasi-geostrophic oscillations. We find that the anelastic equations, which neglect this term, cannot capture these instabilities and possess spuriously growing eigenmodes in the rapidly rotating, low Prandtl number regime. It is shown that the Mach number for rapidly rotating compressible convection is intrinsically small for all background states, regardless of the de...Continue Reading

References

May 31, 1996·Science·J Christensen-DalsgaardR K Ulrich
Apr 10, 2013·Proceedings of the National Academy of Sciences of the United States of America·Eric M King, Jonathan M Aurnou

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Citations

Jan 1, 2017·Living Reviews in Computational Astrophysics·Friedrich Kupka, Herbert J Muthsam
Dec 11, 2019·British Journal of Cancer·Christiane A OpitzSaskia Trump

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