Propagation of leaky surface waves on contact magnetohydrodynamic discontinuities in incompressible plasmas

We study the wave propagation on a magnetohydrodynamic contact discontinuity. Using the Laplace transform, we obtain the solution to the initial value problem describing the evolution of a perturbation of the discontinuity. We use this solution to study the leaky modes that determine the asymptotic behaviour of the solution for large time. We find the approximate expressions describing the leaky modes for a small inclination angle of the magnetic field. We also discuss the transition to the tangential discontinuity as the inclination angle tends to zero. We show that there is no continuous transition from the leaky modes on a contact discontinuity to the surface modes on a tangential discontinuity. However, such a transition exists if we take the average quantities describing the leaky modes.