Self-consistent stability analysis of spherical shocks |
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| Authors: | J Sanz S Bouquet M Murakami |
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| Institution: | 1.ETSI Aeronauticos,Universidad Politecnica de Madrid,Madrid,Spain;2.CEA-DAM-DIF,Arpajon,France;3.Institute of Laser Engineering,Osaka University,Osaka,Japan |
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| Abstract: | In this paper, we study self-similar solutions, and their linear stability as well, describing the flow within a spherical
shell with finite thickness, expanding according to a power law of time, t
q
, where q>0. The shell propagates in a medium with initially uniform density and it is bounded by a strong shock wave at its outer
border while the inner face is submitted to a time-dependent uniform pressure. For q=2/5, the well-known Sedov–Taylor solution is recovered. In addition, although both accelerated and decelerated shells can
be unstable against dynamic perturbations, they exhibit highly different behaviors. Finally, the dispersion relation derived
earlier by Vishniac (Vishniac, E.T. in Astrophys. J. 274:152, 1983) for an infinitely thin shell is obtained in the limit of an isothermal shock wave. |
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