Convective instability of self-similar spherical expansion into a vacuum

Details Convective instability of self-similar spherical expansion into a vacuum Convective instability of self-similar spherical expansion into a vacuum

Dec 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979jfm....95..779b&link_type=abstract

Journal of Fluid Mechanics, vol. 95, Dec. 27, 1979, p. 779-786. Navy-supported research.

Physics

10

Convective Flow, Flow Stability, Gas Expansion, Hydrodynamic Equations, Ideal Gas, Vacuum Systems, Gas Density, Gravitational Fields, Perturbation Theory, Polytropic Processes, Unsteady State

Scientific paper

The present study is restricted to the case where the radius of an ideal gas sphere varies between a minimum (at a turning point) and infinity. The well-known class of self-similar solution for an ideal polytropic gas sphere of radius R(t) expanding into a vacuum with velocity u(r,t) = rR'/R is shown to be convectively unstable. The position R at time t of a fluid element whose position at t = 0 was r is required to satisfy R = rf(t) where f(0) = 1 and f'(0) = 0. The physical mechanism results from the buoyancy force experienced by anisentropic distributions in the inertial (effective gravitational) field. Analysis of the linearized fluid equations confirms the existence of the instability and yields both the space and time dependence of the perturbations in closed form. It is seen on energetic grounds that a certain class of spherical ideal gas expansion can be expected to be unstable whenever the entropy-density gradient decreases with increasing r.

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