The laws of reflection and refraction of incompressible magnetohydrodynamic waves at a fluid-solid interface

Abstract

The laws of reflection and refraction of incompressible magnetohydrodynamic (MHD) waves at a fluid-solid interface are derived by matching inhomogeneous electromagnetic plane wave solutions in a finitely conducting solid with homogeneous MHD plane wave solutions in a semi-infinite, perfectly conducting, inviscid fluid. In the undisturbed state both media contain a constant and uniform magnetic field H 0 of arbitrary orientation with respect to the interface. The solid solution represents a refracted wave which attenuates due to ohmic dissipation as it penetrates the solid, while the fluid solution consists of unattenuated incident and reflected waves plus a disturbance travelling parallel to the interface whose amplitude decreases exponentially (without dissipation) with distance from the interface. Modification of the Ferraro-Roberts law of reflection is required to insure that incident and reflected waves propagate in opposite directions along H 0. Since the law is independent of the fluid and solid parameters, it is also valid in the fluid-fluid and fluid-free-space cases. Owing to the anisotropy imparted to the fluid by H 0, the law of refraction is antisymmetric about normal incidence and, as a result, most waves from an isotropic source are refracted into the quadrant of the plane of incidence containing a component of H 0.