### 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 | English (US) |
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Article number | 087102 |

Journal | Physics of Fluids |

Volume | 24 |

Issue number | 8 |

DOIs | |

Publication status | Published - Aug 16 2012 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physics of Fluids*,

*24*(8), [087102]. https://doi.org/10.1063/1.4737622