Discrete Self-Similarity in Type-II Strong Explosions

Details Discrete Self-Similarity in Type-II Strong Explosions Discrete Self-Similarity in Type-II Strong Explosions

2009-07-10

arxiv.org/abs/0907.1731v1

Phys.Fluids 21:056101,2009

Astronomy and Astrophysics

Astrophysics

High Energy Astrophysical Phenomena

Scientific paper

10.1063/1.3139307

We present new solutions to the strong explosion problem in a non-power law density profile. The unperturbed self-similar solutions discovered by Waxman & Shvarts describe strong Newtonian shocks propagating into a cold gas with a density profile falling off as $r^{-\omega}$, where $\omega>3$ (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.

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