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

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.