On the behavior of hydromagnetic surface waves

The behavior of velocity, magnetic field, and pressure perturbations about a continuously varying interface in pressure equilibrium is investigated in detail within ideal incompressible magnetohydrodynamics. A specific initial value problem is solved in quadrature for a thin interface and compared with the solution for a discontinuous interface. The unattenuated surface wave about a discontinuous interface is replaced at a thin interface by a collective surface disturbance which decays, with the associated energy density flowing into local oscillations within the interface. At long times the envelope of the local oscillations is concentrated within a small fraction of the thin interface (gradients within the envelope increase linearly with time, eventually resulting in a breakdown of the linearized ideal theory). Thus, the derived decay rate of the surface disturbance gives a mode-conversion rate rather than a heating rate. In applications to the propagation and dissipation of surface waves in the solar corona, this rate cannot in general be interpreted as a coronal heating rate.