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) |
---|---|
Article number | 087102 |
Journal | Physics of Fluids |
Volume | 24 |
Issue number | 8 |
DOIs | |
State | Published - Aug 16 2012 |
ASJC Scopus subject areas
- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Fluid Flow and Transfer Processes