Dynamics of Coherent Hydrodynamic Systems and Geometry on the Monge Manifolds

Abstract

The concept of a metric on the manifold of Monge potentials is introduced for hydrodynamic vortex system. The concept of coherence of continuous vortex structures is formulated in terms of the deviation of geodesic lines on a given manifold. Criteria of decay and collapse of a vortex continual system are established.