ON THE VALIDITY OF THE WEISS CRITERION IN 2-DIMENSIONAL TURBULENCE

The ''Weiss criterion'' for two-dimensional incompressible turbulent flows separates flow regions where the motion is hyperbolic in character from regions where it is elliptic. This criterion is based on the hypothesis that the velocity gradient varies slowly with respect to the vorticity gradient. We inspected this hypothesis and derived a criterion linking its validity to the curvature of the pressure field. It turns out from numerical experiments that the hypothesis on which relies the ''Weiss criterion'' is nearly only valid in vortex cores, that is in strongly elliptic regions and near stagnation points (high pressures).