Stability of variable density rotating flows: Inviscid case and viscous effects in the limit of large Reynolds numbers

TL;DR

This paper analyzes the linear stability of rotating flows with variable density, deriving dispersion relations and viscous corrections, and validates predictions through numerical simulations in the high Reynolds number regime.

Contribution

It provides an analytical framework for stability analysis of variable density rotating flows, including viscous effects at large Reynolds numbers, and confirms results with numerical methods.

Findings

Instability of Rayleigh-Taylor type in cylindrical rotating flows.

Derived viscous correction for large Reynolds numbers.

Validated theoretical predictions with numerical simulations.

Abstract

Linear stability of solid body rotating flows with axisymmetric density variations is addressed analytically. Considering inviscid disturbances, a non trivial dispersion relation is obtained and it is shown that the instability is of Rayleigh-Taylor type in cylindrical frame. The viscous correction is derived, in the limit of large Reynolds numbers and large azimuthal wave numbers, allowing the determination of the most unstable mode. Theoretical predictions are checked by comparing them to (spectrally accurate) computed eigenvalues and direct numerical simulations.