Propagation of Alfven-gravitational waves in a stratified perfectly conducting flow with transverse magnetic field

Abstract

Alfven-gravitational waves are found to propagate in a Boussinesq, inviscid, adiabatic, perfectly conducting fluid in the presence of a uniform transverse magnetic field in which the mean horizontal velocity U is independent of vertical height z. The governing wave equation is a fourth-order ordinary differential equation with constant coefficients and is not singular when the Doppler-shifted frequency Ω_d = 0, but is singular when the Alfven frequency Ω_A = 0. If Ω²_d < O²_A the waves are attenuated by a factor exp - [2O_A(N²-O²_d)^½-O²_d + O²_A]z, which tends to zero as z [rightward arrow] [infty infinity]. This attenuation is similar to the viscous attenuation of waves discussed by Hughes & Young (1966). The interpretation of upward and downward propagation of waves is given.