A Coulomb-Mohr Type Criterion for Matrix Mode Failure in a Lamina

2009 ◽  
pp. 237-237-20
Author(s):  
SN Chatterjee
Keyword(s):  
Type Criterion ◽  
Mode Failure ◽  
Matrix Mode

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

2022 ◽  
Author(s):  
Bhimsen Shivamoggi ◽  
G Heijst ◽  
Leon Kamp
Keyword(s):  
Flow Field ◽  
Polar Coordinates ◽  
Coriolis Parameter ◽  
Laminar Jet ◽  
Type Criterion ◽  
Burgers Vortex ◽  
2D Flow ◽  
Flow Configurations ◽  
Elliptic Regions ◽  
Oseen Vortex

Abstract The Okubo [5]-Weiss [6] 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 underlying vorticity manifold. The Okubo-Weiss criterion is reformulated in polar coordinates, and is validated via 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 -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 formulated for 3D axisymmetric flows, and is validated via application to the round Landau-Squire Laminar jet flow.

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