The 2-$D$ constrained $NS$ equation and stochastic vortex theory

Abstract

We consider a modified version of the two-dimensional NS equation introduced in [4], [5] preserving energy and momentum of inertia. The physical motivation of this approach is the occurrence of di¤erent dissipation time scales. The constraint we consider is related to the gradient flow structure of the 2-D Navier-Stokes equation with respect to the Wasserstein metric. In this paper we justify the choice of this metric from the point of view of the stochastic vortex theory.