The Numerical Simulation of Radiative Shocks. II. Thermal Instabilities in Two-dimensional Models

We present the results of high-resolution hydrodynamic simulations of stable and overstable radiative shocks. A one-dimensional resolution study, incorporating both power-law and realistic astrophysical cooling functions, agrees well with analytical solutions both in the spatial structure of the shocked zone and in the frequencies of overstable oscillations. This builds upon previous work by Strickland & Blondin, evaluating the accuracy of our code and estimating the resolution required to construct credible multi-dimensional models of interstellar radiative shocks. These models show that accurate modeling of the spatial and temporal structure induced by cooling processes in a multidimensional hydrodynamic simulation requires high resolution. We then present inhomogeneous two-dimensional models with varying input density fluctuation spectra and show that the resulting postshock density and velocity structures are largely independent of the initial seed fluctuation spectrum and that small fluctuations can result in a dense filamentary structure in two dimensions being fully developed in a single cooling timescale. These inhomogeneous two-dimensional structures are described by a fractal dimension, which takes a characteristic value in these two-dimensional simulations. Cooling inhomogeneous shocks have enhanced cooling efficiency, due to their fractal structure, compared to homogeneous one- and two-dimensional models. The increased radiative efficiency is accompanied by a decrease in the conversion of kinetic to thermal energy as the additional degrees of freedom in the two-dimensional models allow kinetic energy to be redirected in other directions, resulting in two-dimensional turbulence