Characteristic analysis of a complex two-dimensional magnetohydrodynamic bow shock flow with steady compound shocks

Abstract

A simple, compact, and systematic derivation is given of the characteristic properties of the magnetohydrodynamic (MHD) equations with two independent variables (time-dependent MHD in the xt plane and steady MHD in the xy plane), based on the symmetrizable Galilean invariant form of the equations and using a matrix approach. A numerically obtained stationary planar field-aligned MHD bow shock flow with interacting shocks is then analyzed in terms of hyperbolic and elliptic regions, steady xy characteristics, limiting lines, and allowed shock transitions. With the help of this analysis, a wave structure present in the bow shock flow can be interpreted as a double steady compound shock. This interpretation is based on the complete analogy demonstrated in our analysis, between the xy characteristic structure of this novel steady compound shock and the xt characteristic structure of the well-known time-dependent MHD compound shock.