Oscillatory convection and limitations of the Boussinesq approximation

Abstract

We determine the asymptotic conditions under which the Boussinesq approximation is valid for oscillatory convection in a rapidly rotating fluid. In the astrophysically relevant parameter regime of small Prandtl number, we show that the Boussinesq prediction for the onset of convection is valid only under much more restrictive conditions than those that are usually assumed. In the case of an ideal gas, we recover the Boussinesq results only if the ratio of the domain height to a typical scale height is much smaller than the Prandtl number. This requires an extremely shallow domain in the astrophysical parameter regime. Other commonly-used "sound-proof" approximations generally perform no better than the Boussinesq approximation. The exception is a particular implementation of the pseudo-incompressible approximation, which predicts the correct instability threshold beyond the range of validity of the Boussinesq approximation.

arXiv comment13 pages, 1 figure, accepted for publication in JFM

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Cited by in corpus (5)

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• Acoustic and inertial modes in planetary-like rotating ellipsoids
• Validity of Sound-Proof Approaches in Rapidly-Rotating Compressible Convection: Marginal Stability vs. Turbulence
• Large-time behavior of the 2D thermally non-diffusive Boussinesq equations with Navier-slip boundary conditions
• Perturbation analysis of baroclinic torque in low-Mach-number flows