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The Okubo–Weiss-type topological criteria in two-dimensional magnetohydrodynamic flows

Published online by Cambridge University Press:  16 April 2024

B.K. Shivamoggi Open the ORCID record for B.K. Shivamoggi [Opens in a new window] ,
G.J.F. van Heijst  and
L.P.J. Kamp
B.K. Shivamoggi*
Affiliation:
Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA
G.J.F. van Heijst
Affiliation:
J. M. Burgers Centre and Fluid Dynamics Laboratory, Eindhoven University of Technology, NL-5600MB Eindhoven, The Netherlands
L.P.J. Kamp
Affiliation:
J. M. Burgers Centre and Fluid Dynamics Laboratory, Eindhoven University of Technology, NL-5600MB Eindhoven, The Netherlands
*
†Email address for correspondence: bhimsen.shivamoggi@ucf.edu
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Abstract

The Okubo–Weiss (Okubo, Deep-Sea Res., vol. 17, issue 3, 1970, pp. 445–454; Weiss, Physica D, vol. 48, issue 2, 1991, pp. 273–294) criterion has been widely used as a diagnostic tool to divide a two-dimensional (2-D) hydrodynamical flow field into hyperbolic and elliptic regions. This paper considers extension of these ideas to 2-D magnetohydrodynamic (MHD) flows, and presents an Okubo–Weiss-type criterion to parameterize the magnetic field topology in 2-D MHD flows. This ensues via its topological connections with the intrinsic metric properties of the underlying magnetic flux manifold, and is illustrated by recasting the Okubo–Weiss-type criterion via the 2-D MHD stationary generalized Alfvénic state condition to approximate the slow-flow-variation ansatz imposed in its derivation. The Okubo–Weiss-type parameter then turns out to be related to the sign definiteness of the Gaussian curvature of the magnetic flux manifold. A similar formulation becomes possible for 2-D electron MHD flows, by using the generalized magnetic flux framework to incorporate the electron-inertia effects. Numerical simulations of quasi-stationary vortices in 2-D MHD flows in the decaying turbulence regime are then given to demonstrate that the Okubo–Weiss-type criterion is able to separate the MHD flow field into elliptic and hyperbolic field configurations very well.

Keywords

plasma nonlinear phenomenaplasma dynamics
Type
Research Article
Information
Journal of Plasma Physics , Volume 90 , Issue 2 , April 2024 , 905900214
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Copyright
Copyright © The Author(s), 2024. Published by Cambridge University Press

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