Propagation of internal Alfvén—acoustic—gravity waves in a perfectly conducting isothermal compressible fluid

Abstract

Internal Alfvén-acoustic-gravity waves propagating in an isothermal, perfectly electrically conducting, plane stratified, inviscid, compressible atmosphere permeated by a horizontal stratified magnetic field in which the mean horizontal velocity U(z) depends on the height z only exhibit singular properties at the Doppler-shifted frequencies \[ \Omega_{d} = 0,\quad\pm\Omega_A,\quad\pm\Omega_A/(1+M^2)^{\frac{1}{2}},\quad\pm (\Omega_c/2^{\frac{1}{2}})[1+M^2\pm \{(1+M^2)^2 - 4\Omega^2_A/\Omega^2_c\}^{\frac{1}{2}}]^{\frac{1}{2}} \] where ΩA is the Alfvén frequency, Ωc the sonic frequency and M the magnetic Mach number. The phenomenon of critical-layer absorption is studied using the momentum-transport approach of Booker & Bretherton (1967), the wave-packet approach (which is a consequence of the WKBJ approximation) of Bretherton (1966) and the technique involving wave normal curves of McKenzie (1973). The absorption effects are also illustrated, following Acheson (1972), by drawing ray trajectories. We find that the waves are absorbed at the critical levels Ωd = ± ΩA and ± ΩA/(1 + M2)½, and in particular we observe that these levels do not act like valves as observed by Acheson (1972). We also conclude that the combined effect of velocity shear and density and magnetic-field stratification is to increase the number of absorption levels.