Abstract

The problem of linear stability and nonlinear evolution of magnetohydrodynamic (MHD) shear flows in two-dimensional, homogeneous, incompressible MHD is revisited. In the equivalent hydrodynamic setting, the instability mechanism is typically interpreted in terms of the Counter-propagating Rossby Wave (CRW) mechanism, and as the instability reaches finite amplitude, the shear flow rolls up into vortices that, in a two-dimensional homogeneous system, is stable and long-lived. The talk will focus on the MHD modifications to the CRW mechanism as well as the potential disruption of such long-lived vortices from MHD feedback. An estimate based on the scaling arguments of Weiss (1966) is performed which predicts that vortices will be disrupted when M^2 Rm = O(1), where M is a measure of the initial field strength and Rm is the magnetic Reynolds number. A vortex disruption parameter based on the Okubo—Weiss criterion is utilised to analyse direct numerical simulations of MHD shear flows, and the analyses lend support to the theoretical estimate.