The Okubo-Weiss criterion in hydrodynamic flows: Geometric aspects and further extension

B.K. Shivamoggi (Corresponding author), G.J.F. van Heijst (Corresponding author), L.P.J. Kamp

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)
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Abstract

The Okubo (1970 Deep Sea Res. 17 445)-Weiss (1991 Physica D 48 273) criterion, has been extensively used as a diagnostic tool to divide a two-dimensional (2D) hydrodynamical flow field into hyperbolic and elliptic regions and to serve as a useful qualitative guide to the complex quantitative criteria. The Okubo-Weiss criterion is frequently validated on empirical grounds by the results ensuing its application. So, we will explore topological implications into the Okubo-Weiss criterion and show the Okubo-Weiss parameter is, to within a positive multiplicative factor, the negative of the Gaussian curvature of the vorticity manifold. The Okubo-Weiss criterion is then reformulated in polar coordinates, and is validated for several examples including the Lamb-Oseen vortex, and the Burgers vortex. These developments are then extended to 2D quasi-geostrophic (QG) flows. The Okubo-Weiss parameter is shown to remain robust under the β-plane approximation to the Coriolis parameter. The Okubo-Weiss criterion is shown to be able to separate the 2D flow-field into coherent elliptic structures and hyperbolic flow configurations very well via numerical simulations of quasi-stationary vortices in QG flows. An Okubo-Weiss type criterion is formulate for 3D axisymmetric slows, and is validated via application to the round Landau-Squire Laminar jet flow.

Original languageEnglish
Article number015505
Number of pages18
JournalFluid Dynamics Research
Volume54
Issue number1
DOIs
Publication statusPublished - Feb 2022

Keywords

  • fluid flow diagnostic
  • fluid flow topology
  • Okubo-Weiss criterion

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