TY - JOUR
T1 - The Okubo-Weiss criterion in hydrodynamic flows
T2 - Geometric aspects and further extension
AU - Shivamoggi, B.K.
AU - van Heijst, G.J.F.
AU - Kamp, L.P.J.
N1 - Publisher Copyright:
© 2022 The Japan Society of Fluid Mechanics and IOP Publishing Ltd.
PY - 2022/2
Y1 - 2022/2
N2 - 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.
AB - 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.
KW - fluid flow diagnostic
KW - fluid flow topology
KW - Okubo-Weiss criterion
UR - http://www.scopus.com/inward/record.url?scp=85124133176&partnerID=8YFLogxK
U2 - 10.1088/1873-7005/ac495d
DO - 10.1088/1873-7005/ac495d
M3 - Article
AN - SCOPUS:85124133176
SN - 0169-5983
VL - 54
JO - Fluid Dynamics Research
JF - Fluid Dynamics Research
IS - 1
M1 - 015505
ER -