## Abstract

Self-similarity allows for analytic or semi-analytic solutions to many hydrodynamics problems. Most of these solutions are one-dimensional. Using linear perturbation theory, expanded around such a one-dimensional solution, we find self-similar hydrodynamic solutions that are two- or three-dimensional. Since the deviation from a one-dimensional solution is small, we call these slightly two-dimensional and slightly three-dimensional self-similar solutions, respectively. As an example, we treat strong spherical explosions of the second type. A strong explosion propagates into an ideal gas with negligible temperature and density profile of the form ρ(r, θ, φ{symbol}) = r-ω[1 + σF(θ, φ{symbol})], where ω > 3 and σ ≪ 1. Analytical solutions are obtained by expanding the arbitrary function F(θ, φ{symbol}) in spherical harmonics. We compare our results with two-dimensional numerical simulations, and find good agreement.

Original language | American English |
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Article number | 087102 |

Journal | Physics of Fluids |

Volume | 24 |

Issue number | 8 |

DOIs | |

State | Published - 16 Aug 2012 |

### Bibliographical note

Funding Information:We thank Yonatan Oren for helpful discussions. This research was partially supported by ERC and IRG Grants and by a Packard fellowship. R.S. is a Guggenheim fellow and a Radcliffe fellow. A.I.M. acknowledges support from NSF Grant No. AST-1009863 and NASA Grant No. NNX10AF62G.