Interacting vorticity waves as an instability mechanism for MHD shear instabilities

The interacting vorticity wave formalism for shear flow instabilities is extended here to the magnetohydrodynamic (MHD) setting, to provide a mechanistic description for the stabilising and destabilising of shear instabilities by the presence of a background magnetic field. The interpretation relies on local vorticity anomalies inducing a non-local velocity field, resulting in action-at-a-distance. It is shown here that the waves supported by the system are able to propagate vorticity via the Lorentz force, and waves may interact; existence of instability then rests upon whether the choice of basic state allows for phase-locking and constructive interference of the vorticity waves via mutual interaction. To substantiate this claim, we solve the instability problem of two representative basic states, one where a background magnetic field stabilises an unstable flow and the other where the field destabilises a stable flow, and perform relevant analyses to show how this mechanism operates in MHD.