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

TL;DR

This paper reinterprets the Okubo-Weiss criterion for 2D flows using the Beltrami condition, extending it to quasi-geostrophic, MHD, and electron MHD flows with topological insights.

Contribution

It provides a new logical interpretation of the Okubo-Weiss criterion and extends its application to various 2D flow models.

Findings

Reinterpretation of the Okubo-Weiss criterion using the Beltrami condition.

Extension of the criterion to quasi-geostrophic and MHD flows.

Topological interpretation of flow properties in different models.

Abstract

The Okubo [2]-Weiss [3] criterion is recast by using the 2D hydrodynamic Beltrami condition (Shivamoggi et al.[13]) that approximates the slow flow-variation ansatz imposed in its derivation. This turns out to provide an interesting interpretation of the Okubo-Weiss criterion very logically in terms of the topological properties of the underlying vorticity manifold. These developments are then extended to 2D quasi-geostrophic flows (via the potential divorticity framework), magnetohydrodynamic flows and electron magnetohydrodynamic flows (via the generalized magnetic flux framework) and the Okubo-Weiss criteria for these cases are considered.