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Universality in the run-up of shock waves to the surface of a star

Universality in the run-up of shock waves to the surface of a star
Universality in the run-up of shock waves to the surface of a star
We investigate the run-up of a shock wave from inside to the surface of a perfect fluid star in equilibrium and bounded by vacuum. Near the surface we approximate the fluid motion as plane-symmetric and the gravitational field as constant. We consider the ‘hot’ equation of state P = (? ? 1)?e and its ‘cold’ (fixed entropy, barotropic) form P = K0?? (the latter does not allow for shock heating). We numerically find that the evolution of generic initial data approaches universal similarity solutions sufficiently near the surface, and we explicitly construct these similarity solutions. The two equations of state show very different behaviour because shock heating becomes the dominant effect when it is allowed. In the barotropic case, the fluid velocity behind the shock approaches a constant value, while the density behind the shock approaches a power law in space, as the shock approaches the surface. In the hot case with shock heating, the density jumps by a constant factor through the shock, while the sound speed and fluid velocity behind the shock diverge in a whiplash effect. We tabulate the similarity exponents as a function of the equation of state parameter ? and the stratification index n?
0022-1120
237-264
Gundlach, C.
586f1eb5-3185-4b2b-8656-c29c436040fc
LeVeque, R.J.
3203cf82-c42e-464d-a4ec-9719f51c464d
Gundlach, C.
586f1eb5-3185-4b2b-8656-c29c436040fc
LeVeque, R.J.
3203cf82-c42e-464d-a4ec-9719f51c464d

Gundlach, C. and LeVeque, R.J. (2011) Universality in the run-up of shock waves to the surface of a star. Journal of Fluid Mechanics, 676, 237-264. (doi:10.1017/S0022112011000425).

Record type: Article

Abstract

We investigate the run-up of a shock wave from inside to the surface of a perfect fluid star in equilibrium and bounded by vacuum. Near the surface we approximate the fluid motion as plane-symmetric and the gravitational field as constant. We consider the ‘hot’ equation of state P = (? ? 1)?e and its ‘cold’ (fixed entropy, barotropic) form P = K0?? (the latter does not allow for shock heating). We numerically find that the evolution of generic initial data approaches universal similarity solutions sufficiently near the surface, and we explicitly construct these similarity solutions. The two equations of state show very different behaviour because shock heating becomes the dominant effect when it is allowed. In the barotropic case, the fluid velocity behind the shock approaches a constant value, while the density behind the shock approaches a power law in space, as the shock approaches the surface. In the hot case with shock heating, the density jumps by a constant factor through the shock, while the sound speed and fluid velocity behind the shock diverge in a whiplash effect. We tabulate the similarity exponents as a function of the equation of state parameter ? and the stratification index n?

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Published date: 9 April 2011
Organisations: Mathematics

Identifiers

Local EPrints ID: 180575
URI: https://eprints.soton.ac.uk/id/eprint/180575
ISSN: 0022-1120
PURE UUID: 816f5dee-75fa-4ecd-8b4f-32e6c7308504
ORCID for C. Gundlach: ORCID iD orcid.org/0000-0001-9585-5375

Catalogue record

Date deposited: 11 Apr 2011 08:43
Last modified: 20 Jul 2018 00:34

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