The influence of resonant MHD wave coupling in the boundary layer on the reflection and transmission process

When a wave is incident on an inhomogeneous boundary layer separating two plasmas in relative motion, it is often argued that the resonant absorption rate can become negative when there is a sufficiently large velocity shear, thus giving energy back to the wave. However such treatment fails to distinguish the two energy exchange processes that are operative: extraction of wave energy by dissipative processes around the resonance point and energy exchange between the wave and the ow of the medium. By aid of the proper wave energy definitions recently discussed by Walker (2000), rather than by the conventional concept of negative energy waves we reveal the important dependence of the resonant amplification process on the precise structure of the boundary layer profiles. We conclude that stratification in boundary layers is very important not only because the resulting wave coupling can cause resonant instabilities for velocity shears below the Kelvin-Helmholtz threshold, but also because the coupling can stabilize the Kelvin-Helmholtz instability above this threshold.