Astronomy and Astrophysics – Astrophysics – High Energy Astrophysical Phenomena
Scientific paper
2011-09-15
Astronomy and Astrophysics
Astrophysics
High Energy Astrophysical Phenomena
Submitted to Physics of Fluids
Scientific paper
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 rho(r,theta,phi)=r^{-omega}[1+sigma*F(theta,phi)], where omega>3 and sigma << 1. Analytical solutions are obtained by expanding the arbitrary function F(theta,phi) in spherical harmonics. We compare our results with two dimensional numerical simulations, and find good agreement.
Bode Nate J.
MacFadyen Andrew
Sari Re'em
Yalinewich Almog
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