Slightly Two or Three Dimensional Self-Similar Solutions
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 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.
Cite
@article{arxiv.1109.3451,
title = {Slightly Two or Three Dimensional Self-Similar Solutions},
author = {Re'em Sari and J. Nate Bode and Almog Yalinewich and Andrew MacFadyen},
journal= {arXiv preprint arXiv:1109.3451},
year = {2015}
}
Comments
Submitted to Physics of Fluids