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

by Carsten Gundlach and Randall J Leveque. *J. Fluid Mech.*,
676
(2011), pp. 237 - 264 .
DOI:
http://dx.doi.org/10.1017/jfm.2011.42

**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
polytropic equation of state $P=K_0\rho^\Gamma$ and the related ideal gas equation of
state $P=(\Gamma-1)\rho e$. We find numerically that the evolution of generic initial data
approaches universal similarity solutions sufficiently near the surface, and we construct
these similarity solutions explicitly. The two equations of state show very different
behaviour, because shock heating becomes the dominant effect in the ideal gas case. In the
polytropic case, the fluid velocity behind the shock approaches a constant value, while
the density behind the shock approaches a power law. In the ideal gas case, 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 $\Gamma$ and the stratification index $n_*$.

**Preprint:** arXiv:1008.2834v1 [astro-ph.SR]

Simulations and code to accompany this paper

**bibtex entry:**

@article{cg-rjl:shockvacuum, author="C. Gundlach and R. J. LeVeque", title="Universality in the run-up of shock waves to the surface of a star", journal="J. Fluid Mech.", volume="676", year="2011", pages="237-264", url="http://arxiv.org/abs/1008.2834" }