On statistical mechanics of vortex lines

Abstract

A system of equations determining average velocity of ideal incompressible fluid is derived from the assumption that fluid motion is ergodic. Two flows are considered: one vortex line in a bounded cylindrical domain and a flow of almost circular vortex lines. In the first case the averaged equations have the form of an eigenvalue problem similar to that for Schro″dinger's equation. © 2008 Springer.