Discrete self-similarity in type-II strong explosions

Yonatan Oren*, Re'em Sari

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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, 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.

Original languageAmerican English
Article number056101
JournalPhysics of Fluids
Issue number5
StatePublished - 2009

Bibliographical note

Funding Information:
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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