Generic behaviour of nonlinear sound waves near the surface of a star: smooth solutions
Generic behaviour of nonlinear sound waves near the surface of a star: smooth solutions
We are interested in the generic behavior of nonlinear sound waves as they approach the surface of a star, here assumed to have the polytropic equation of state P=K??. Restricting to spherical symmetry, and considering only the region near the surface, we generalize the methods of Carrier and Greenspan (1958) for the shallow water equations on a sloping beach to this problem. We give a semiquantitative criterion for a shock to form near the surface during the evolution of generic initial data with support away from the surface. We show that in smooth solutions the velocity and the square of the sound speed remain regular functions of Eulerian radius at the surface.
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc
Please, Colin
118dffe7-4b38-4787-a972-9feec535839e
6 March 2009
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc
Please, Colin
118dffe7-4b38-4787-a972-9feec535839e
Gundlach, Carsten and Please, Colin
(2009)
Generic behaviour of nonlinear sound waves near the surface of a star: smooth solutions.
Physical Review D, 79 (6).
(doi:10.1103/PhysRevD.79.067501).
Abstract
We are interested in the generic behavior of nonlinear sound waves as they approach the surface of a star, here assumed to have the polytropic equation of state P=K??. Restricting to spherical symmetry, and considering only the region near the surface, we generalize the methods of Carrier and Greenspan (1958) for the shallow water equations on a sloping beach to this problem. We give a semiquantitative criterion for a shock to form near the surface during the evolution of generic initial data with support away from the surface. We show that in smooth solutions the velocity and the square of the sound speed remain regular functions of Eulerian radius at the surface.
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Published date: 6 March 2009
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Local EPrints ID: 144865
URI: http://eprints.soton.ac.uk/id/eprint/144865
ISSN: 2470-0029
PURE UUID: abbc69b5-44d5-4701-8187-1c5db3715ece
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Date deposited: 15 Apr 2010 12:58
Last modified: 14 Mar 2024 02:44
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Author:
Colin Please
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