Okubo-Weiss Criterion Research Articles

An exact criterion for the stirring properties of nearly two-dimensional turbulence

An exact criterion can be found for partitioning the fluid into regions with different dynamical properties, from both the points of view of particle dispersion and tracer gradient evolution. This criterion differs markedly, both in its magnitude and spatial scales, from the Okubo-Weiss criterion which depends upon the differential geometry of the streamfunction field and coincides with the eigenvalues of the velocity gradient tensor. The new criterion corresponds to the eigenvalues of the acceleration gradient tensor, whose spatial distribution depends instead upon the topology of the pressure field. This result holds for all flows for which a continuous momentum equation can be prescribed. We provide numerical evidence for the quantitative importance of the time change of the strain-rate components in the dispersion problem in freely decaying two-dimensional turbulence.