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 their explicit form does not depend on the statistics of velocity. Only one of them has been discussed previously.

References in corpus (4)

• Special invited paper. Large deviations
• The statistical geometry of material loops in turbulence
• Non-Gaussian generalization of the Kazantsev-Kraichnan model
• Long-term properties of finite-correlation time isotropic stochastic systems

Cited by in corpus (2)

• Lagrangian stochastic integrals of motion in isotropic random flows
• Stochastic identities for random isotropic fields