THE MOST PROBABLE CRITICAL DISTANCE FOR 2 UNEQUAL VORTICES IN 2-DIMENSIONAL TURBULENCE

Using a probabilistic formalism, a functional form for the critical separation distance d(c) is derived, to describe most probable inelastic interaction states of two unequal like-signed vortices in two-dimensional (2D) decaying turbulence. For a vortex pair of same vorticity amplitude with different sizes, the functional form approximates well to the numerical critical merger distance given by the vortex dynamical systems. Predictions and implications from this probabilistic solution are discussed.