= Radial Solberg–Høiland instability criterion
{title2=$N_r^2+\kappa^2<0$}
= Solberg–Høiland radial instability criterion
{c}
{synonym}
For ideal axisymmetric radial displacements in a <Keplerian shearing sheet>, the hydrodynamic squared oscillation frequency is $N_r^2+\kappa^2$, with <radial epicyclic frequency> $\kappa=\Omega$. Exponential instability occurs when $N_r^2+\kappa^2<0$. This is the radial special case of rotating-fluid convective stability, rather than the complete set of three-dimensional Solberg–Høiland criteria.
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