Exact Solutions of Compressible Flow Equations with Spherical Symmetry

Sachdev, PL and Joseph, KT and Haque, Ejanul M (2005) Exact Solutions of Compressible Flow Equations with Spherical Symmetry. In: Studies in Applied Mathematics, 114 (4). pp. 325-342.

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Abstract

In this paper, we construct spherically symmetric solutions of the equations of compressible flow, which are important in the theory of explosion waves in air, water, and other media. Following McVittie [1], we write a general solution form, in terms of velocity potential,as a product of a function of time and a function of a similarity variable. First, we find solutions to the equations of motion and continuity without reference to adiabatic or isentropic relation. These solutions are quite general and can be applied to nonadiabatic motions,such as the motions of interstellar gas clouds that lose energy by radiation. All the solutions found by McVittie [ 1] have linear velocity profile with respect to distance. We introduce a nonlinear form of the velocity function containing an arbitrary function of the similarity variable. Adiabatic conditions lead to a second-order ODE,which we discuss in some detail. We relate our work to the earlier investigations of Taylor [ 2], McVittie [ 1], and Keller [ 3].

Item Type:	Journal Article
Publication:	Studies in Applied Mathematics
Publisher:	Blackwell Publishing Ltd
Additional Information:	Copyright for this article belongs to Blackwell Publishing Ltd.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	17 May 2005
Last Modified:	19 Sep 2010 04:18
URI:	http://eprints.iisc.ac.in/id/eprint/3193

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