Helmholtz instability in stratified shear flows with magnetic fields

The stability characteristics of a Helmholtz velocity profile in a stratified Boussinesq fluid in the presence of a rigid boundary is studied. A jump in the magnetic field is introduced at a level different from the velocity discontinuity. New unstable modes in addition to the Kelvin-Helmholtz mode are found. The wavelengths of these unstable modes are close to the wavelengths of internal Alfvén gravity waves in the atmosphere.