Short wavelength instabilities of rotating, compressible fluid masses
Abstract
The equations describing the linear stability of a rotating, axisymmetric, selfgravitating fluid mass are considered in a short wavelength limit which takes proper account of boundary conditions. The wellknown Hoiland criterion for axisymmetric perturbations is recovered and found to be a sufficient condition for instability even if nonaxisymmetric perturbations are allowed. The spectrum of the linear stability problem is not only continuous but also, in the unstable case, occupies a nonzero area in the complex spectral plane.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 August 1992
 DOI:
 10.1098/rspa.1992.0106
 Bibcode:
 1992RSPSA.438..265L
 Keywords:

 Compressible Fluids;
 Flow Stability;
 Perturbation Theory;
 Rotating Fluids;
 Wave Interaction;
 Boundary Conditions;
 Boundary Value Problems;
 Fluid Flow;
 Partial Differential Equations;
 SpaceTime Functions;
 Fluid Mechanics and Heat Transfer