= Rayleigh centrifugal stability criterion
{c}
{title2=$\kappa^2=r^{-3}(l^2)\prime$}
For inviscid cylindrical rotation without a <magnetic field>, an axisymmetric radial interchange conserves each parcel's <specific angular momentum> $l=r^2\Omega$. Its restoring coefficient is $\kappa^2=r^{-3}d(l^2)/dr$. Increasing $l^2$ gives centrifugal stability; decreasing $l^2$ gives an exponentially growing interchange mode when radial displacement is allowed by the boundaries. A vanishing derivative is marginal, not a strictly restoring condition.
// Target: astrophysics.bigb
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