A simple stability criterion for isothermal spherical self-similar flow

Details A simple stability criterion for isothermal spherical self-similar flow A simple stability criterion for isothermal spherical self-similar flow

Oct 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988mnras.234..821o&link_type=abstract

Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 234, Oct. 15, 1988, p. 821-829. Sponsorship: U.S.-Israe

Statistics

Computation

33

Computational Fluid Dynamics, Flow Geometry, Flow Stability, Gravitational Collapse, Computerized Simulation, Cosmology, Equations Of Motion, Isothermal Flow, Perturbation Theory, Shock Waves

Scientific paper

The dynamics of weak discontinuities at the sonic point is studied, and a necessary condition for the stability of Newtonian self-similar spherical isothermal flow (collapse and expansion) is derived. This stability criterion depends only on the value of the spatial derivative of the velocity at the sonic point. In collapse, all primary-direction solutions, including the homogeneous-collapse solution, are unstable, while all the secondary-direction solutions, including the Penston-Larson solution (Penston, 1969; Larson, 1969), satisfy this stability criterion. The situation is reversed in expansion.

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