Rayleigh discriminant ($\Phi =r^{-3}(r^4{\Omega }^2{)}^{\prime }$)

For inviscid axisymmetric disturbances to a rotating flow, the Rayleigh discriminant measures the radial gradient of squared specific angular momentum.

An inviscid rotating flow is centrifugally stable to axisymmetric disturbances when $(r^2\Omega {)}^2$ is nondecreasing with radius. An outward decrease permits centrifugal instability.