2014/09/30 by Michael A. Calkins, Keith Julien, Philippe Marti · 1 citation
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Astro and Planetary Science #Classical mechanics #Compressibility #Convection #Geomagnetism and Paleomagnetism Studies #Instability #Mach number #Mechanics #Physics #Prandtl number #Solar and Space Plasma Dynamics #Stratification (seeds) #Wavenumber #physics.flu-dyn #physics.geo-ph
paper · pdf · doi:10.1098/rspa.2014.0689
published as Proc.R.Soc.A 471 (2015) 20140689 · 16 pages, 6 figures, 1 table. Changes made: added new Figure 1, added discussion of Mach number, added references, added Table of linear stability data
arxiv created 2014/12/05 · openalex publication_date 2015/02/04 · arxiv updated 2015/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 departure from adiabaticity.