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We examine the nonlinear behavior of radiative shocks. We model this phenomenon using a third order hydrodynamic code and considering the cooling function $\Lambda = \Lambda_o\rho^2 T^\alpha$. Radiative shocks perturbed from steady state are known to exhibit oscillatory behavior in an attempt to achieve a state of equilibrium. The observable quantities concentrated upon in this study are the frequencies and the growth or decay rates of these oscillations. We find that our simulations produce results in agreement with those of earlier analytic (Chevalier and Imamura 1982) and numerical work (Imamura, Wolff, and Durisen 1984).
We then study numerically perturbed steady-state shock profiles, noting the qualitative effects of changes in Mach number, $\cal M$, and power-law exponent, $\alpha$, on the observables. We find that growth rates increase with increasing $\cal M$. We find the behavior of the growth rate as a function of $\alpha$ to be consistent with previous results in the linear regime. However, in the nonlinear regime values of $\alpha$ previously purported to be overstable are found to saturate quickly, producing oscillations which deteriorate into multiple modes and phases with no apparent growth or decay rates.
We are currently extending this one-dimensional work to two-dimensions. In this phase we explore the effects of wave number on stability when the initial perturbation varies sinusoidally along the shock interface. We will compare the results of these 2D simulations with the earlier analytic analysis of Bertschinger (1986) in the linear regime and extend those results into the nonlinear regime. Future work will involve spherical shock waves applicable to supernova remnants entering the radiative phase of their evolution.
