Convective overstability

An adverse radial specific entropy gradient can drive an oscillatory instability through the finite lag supplied by thermal conduction or relaxation. This differs from a viscous-convective instability, in which viscosity changes rotational stabilization.

For $|N^2|\ll {\Omega }^2$, this leading amplitude-growth rate is largest at thermal diffusion rate of a Fourier mode $\beta =\Omega$, giving ${\sigma }_{\max }=-N^2/(4\Omega )$ when $N^2<0$.