SURFACE-WAVES IN AN INCOMPRESSIBLE FLUID - RESONANT INSTABILITY DUE TO VELOCITY SHEAR

We consider the effects of velocity shear on the resonance absorption of incompressible magnetohydrodynamic surface waves. We find that there are generally values of the velocity shear for which the surface wave decay rate becomes zero. In some cases, the resonance absorption goes to zero even for very small velocity shears. We also find that the resonance absorption can be strongly enhanced at other values of the velocity shear. The presence of flows may therefore be generally important in determining the effects of resonance absorption, such as might occur in the interaction of p-modes with sunspots, for example. The most interesting result of our work is the fact that there can exist resonances which lead to instability of the global surface mode, and that instability can occur for velocity shears significantly below the Kelvin-Helmholz threshold. These instabilities may play a role in the development of turbulence in regions of strong velocity shear in the solar wind or the Earth's magnetosheath, but an extension of our work to include compressibility is required before we can say anything definitive about those regions.