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Published May 2009 | Published
Journal Article Open

Discrete self-similarity in type-II strong explosions

Abstract

We present new solutions to the strong explosion problem in a nonpower law density profile. The unperturbed self-similar solutions discovered by Waxman and Shvarts describe strong Newtonian shocks propagating into a cold gas with a density profile falling off as r^(−ω), where ω>3 (type-II solutions). The perturbations we consider are spherically symmetric and log periodic with respect to the radius. While the unperturbed solutions are continuously self-similar, the log periodicity of the density perturbations leads to a discrete self-similarity of the perturbations, i.e., the solution repeats itself up to a scaling at discrete time intervals. We discuss these solutions and verify them against numerical integrations of the time dependent hydrodynamic equations. Finally we show that this method can be generalized to treat any small, spherically symmetric density perturbation by employing Fourier decomposition.

Additional Information

© 2009 American Institute of Physics. Received 22 January 2009; accepted 2 April 2009; published 28 May 2009. The authors wish to thank Professor Tsvi Piran for fruitful discussions. This research was partially supported by a NASA grant, an IRG grant, and a Packard Fellowship.

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August 21, 2023
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