Magnetohydrodynamic waves in non-uniform flows I: a variational approach

Abstract

The interaction of magnetohydrodynamic (MHD) waves in a non-uniform, time-dependent background plasma flow is investigated using Lagrangian field theory methods. The analysis uses Lagrangian maps, in which the position of the fluid element constant. The form of the characteristic manifolds for both time-dependent and steady MHD flows are developed. The bi-characteristics for steady MHD waves in a steady background flow are related to the group velocity surface and Mach cone for the waves, and determine when the flow is elliptic, hyperbolic, or of mixed hyperbolic-elliptic type. The wave interaction equations are decomposed into coupled equations for the compressible and incompressible perturbations.