On the stability and over-reflexion of hydromagnetic-gravity waves

The stability of a magnetic-velocity shear layer, of thickness L, to hydromagnetic-gravity waves of zonal wavenumber k is investigated analytically, within the Boussinesq approximation, in the situation where ∊(= kL) is small. It is found that, in addition to the unstable modes of the corresponding sheet, new modes of instability of growth rate of order ∊² are also present provided one critical level exists within the layer. The existence of one critical level also effects over-reflexion of stable modes. Furthermore it is shown that a magnetic shear acting alone can lead to instability as well as effecting over-reflexion of stable modes.