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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

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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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