Material surfaces in stochastic flows: Integrals of motion and intermittency.

Abstract

We consider the line, surface, and volume elements of fluid in stationary isotropic incompressible stochastic flow in d-dimensional space and investigate the long-time evolution of their statistic properties. We report the discovery of a family of d!-1 stochastical integrals of motion that are universal in the sense that their explicit form does not depend on the statistics of velocity. Only one of them has been discussed previously.