Short wavelength instabilities of Riemann ellipsoids
Valeri P
Author: Lebovitz N, Lifschitz A
Publisher: Philosophical Transactions of the Royal Society, London, 1996, Series A, Vol: 354, Pages: 927-950
Description:
Perturbations of incompressible S-type Riemann ellipsoids are considered in the limit of short wavelength. This complements the classical consideration of perturbations of long wavelength. It is shown that there is very little of the parameter space in which the laminar, steady-state flow can exist in a stable state. This confirms, in a physically consistent framework, hydrodynamic-stability results previously obtained in the context of unbounded, two-dimensional flows. The configurations stable to perturbations of arbitrarily short wavelength include the rigidly rotating configurations of Maclaurin and Jacobi as well as a narrow continuum centred on the family of irrotational ellipsoids and including the nonrotating sphere. However, most configurations departing even slightly from axial symmetry are unstable. Some of the implications of these results for the complexity of astrophysical flows are discussed.