Self-similarity of the Third Type in the Strong Explosion Problem

2003/03/11 by Andrei Gruzinov, Gruzinov, Andrei
Physics and Astronomy · #Astrophysics (astro-ph) #FOS: Physical sciences #astro-ph

paper · pdf · doi:10.48550/arxiv.astro-ph/0303242

4 pages, 3 figures

arxiv created 2003/03/11 · arxiv updated 2009/12/01

Abstract

Propagation of a blast wave due to strong explosion in the center of a power-law-density (ρ∝ r^-α) spherically symmetric atmosphere is studied. For adiabatic index of 5/3, the solution was known to be self-similar, (of type I) for α<3, self-similar (of type II) for α>3.26, and unknown in between. We find a self-similar solution for 3<α<3.26, and give a (tentative) numerical proof that this solution is indeed an asymptotic of the strong explosion. This self-similar solution is neither of type I (dimensional analysis does not work), nor of type II (the index of the solution is known without solving an eigenvalue problem).

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