The Okubo-Weiss Type Criteria in Two-Dimensional Hydrodynamic and Magnetohydrodynamic Flows

The Okubo-Weiss type criteria for 2D quasi-geostrophic (QG) flows (via the potential divorticity framework) and 2D magnetohydrodynamic (MHD) flows are formulated, and are interpreted in terms of the intrinsic metric properties of the underlying appropriate vorticity manifold. The Okubo-Weiss parameter is shown to remain robust under the beta-plane approximation to the Coriolis parameter, while the Okubo-Weiss type parameter is shown to provide a useful diagnostic tool to parametrize the magnetic field topology in 2D MHD flows. The ability of the Okubo-Weiss type criteria to separate the flow-field into coherent elliptic structures and hyperbolic flow configurations is validated via numerical simulations of quasi-stationary vortices in QG flows and 2D MHD flows in the decaying turbulence regime (in the presence of viscosity).