Korean J. Math. Vol. 19 No. 2 (2011) pp.191
DOI: https://doi.org/10.11568/kjm.2011.19.2.191

LARGE AMPLITUDE THEORY OF A SHOCK-ACCELERATED INSTABILITY IN COMPRESSIBLE FLUIDS

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Sung-Ik Sohn

Abstract

The interface between fluids of different densities is unstable under acceleration by a shock wave. A previous small amplitude linear theory for the compressible Euler equation failed to provide a quantitatively correct prediction for the growth rate of the unstable interface. In this paper, to include dominant nonlinear effects in a large amplitude regime, we present high-order perturbation equations of the Euler equation, and boundary conditions for the contact interface and shock waves.



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