Interaction of a Thin Shock With Turbulence: Effect on Shock Structure, Analytic Model

A 2D hydrodynamical model describing the interaction of thin shock with turbulence is developed by adopting a multi-scale perturbation analysis. This is extended to a 2D MHD model. The interaction is found to be governed by a two-dimentional Burger's equation involving "perturbation terms". Different prescribed perturbation profiles are tested with numerical simulation to show how the shock front is modified by turbulence. The results indicate that while turbulence is balancing the nonlinear steepening of shock waves at some regions, it also help to create a higher jump in physical quantities at other regions. The plasma medium in these regions can therefore experience higher compression, which will result in a downstream state that differs from the usual Rankine-Hugoniot state.