Astronomy and Astrophysics – Astrophysics
Scientific paper
Aug 1985
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985a%26a...149..487b&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 149, no. 2, Aug. 1985, p. 487, 488. SERC-supported research.
Astronomy and Astrophysics
Astrophysics
5
Dynamic Stability, Hydrodynamic Equations, Rotating Fluids, Stellar Rotation, Boundary Value Problems, Ideal Fluids, Modes (Standing Waves)
Scientific paper
In a study of the stability of rotating stars, the partial differential equations describing the normal modes of an axisymmetric, isentropic, differentially rotating, self-gravitating perfect fluid are shown to be of a mixed type. It is shown that the surface of co-rotation is a characteristic surface, indicating that the continuous spectrum of eigenfrequencies associated with it is generic in such fluids. In examining the character of the normal mode equations, it is seen that the equations are hyperbolic in a certain spatial region, rather than elliptic. This has consequences for the numerical determination of discrete normal modes, since problems of such mixed character require careful treatment to obtain an accurate solution. The hyperbolic region may also be related to the existence of a dense spectrum of discrete modes.
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