Interacting vorticity waves as an instability mechanism for MHD shear instabilities

TL;DR

This paper extends the interacting vorticity wave framework to MHD shear flows, explaining how magnetic fields can stabilize or destabilize instabilities through wave interactions and phase-locking.

Contribution

It introduces a mechanistic description of MHD shear instabilities using vorticity wave interactions, incorporating magnetic effects into the formalism.

Findings

Magnetic fields can both stabilize and destabilize shear flows.

Vorticity waves propagate via Lorentz force in MHD.

Instability depends on phase-locking of vorticity waves.

Abstract

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.