Magnetohydrodynamic shear instabilities arising from interacting vorticity waves

The presence of a background magnetic field is known to have a stabilising as well as a destabilising effect for shear flow instabilities. To explain the reason for this, we extend the Counter-propagating Rossby Waves mechanism, well known in the geophysical fluid dynamics community, to the magnetohydrodynamic setting. It is demonstrated here that wave displacement leads to a magnetic field configuration that results in an appropriate vorticity distribution, and, via the non-local velocity field generated by the local vorticity anomalies, action-at-a-distance results in a constructive interaction between two waves and leads to shear instability. The existence of shear instability then rests upon whether the chosen basic state supports such a configuration required for constructive interference.