Interaction of Hydromagnetic Waves with Hydromagnetic Shocks

Abstract

The problem of the interaction of small-amplitude plane hydromagnetic waves with plane, oblique hydromagnetic shocks is treated. When the perturbations of the flow field on either side of the shock are expanded in terms of incident and diverging eigenwaves, the linearized de Hoffmann-Teller relations across the shock yield a system of equations for the amplitudes of the diverging waves and the motion of the perturbed shock. The shock motion and the amplitudes of the diverging waves as a function of the amplitude and direction of any given incident wave are found using this system of seven linear, inhomogeneous equations, along with Snell's laws. Snell's laws are interpreted graphically by making use of the geometry of the hydromagnetic wave normal surfaces in a moving medium. By considering some special cases it is shown that hydromagnetic waves are amplified on passage through a fast shock. The turbulent character of the region between the bow shock of the earth and the magnetopause may be due in part to the amplification of turbulent waves in the solar wind on passing through the bow shock.