Effects of Steady Flow on Magnetoacoustic-Gravity Surface Waves: I. The Weak Field Case

Magnetoacoustic gravity (MAG) waves have been studied for some time. In this article, we investigate the effect that a shear flow at a tangential discontinuity embedded in a gravitationally stratified and magnetised plasma has on MAG surface waves. The dispersion relation found is algebraically analogous to the relation of the non-flow cases obtained by Miles and Roberts (Solar Phys. 141, 205, 1992), except for the introduction of a Doppler-shifted frequency for the eigenvalue. This feature, however, introduces rather interesting physics, including the asymmetric presence of forward- and backward-propagating surface waves. We find that increasing the equilibrium flow speed leads to a shift in the permitted regions of propagation for surface waves. For most wave number combinations this leads to the fast mode being completely removed, as well as more limited phase speed regimes for slow-mode propagation. We also find that upon increasing the flow, the phase speeds of the backward propagating waves are increased. Eventually, at high enough flow speeds, the wave's direction of propagation is reversed and is in the positive direction. However, the phase speed of the forward-propagating wave remains mainly the same. For strong enough flows we find that the Kelvin-Helmholtz instability can also occur when the forward- and backward-propagating modes couple.