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arXiv · 2212.10253

Material surfaces in stochastic flows: integrals of motion and intermittency

A. S. Il'yn·A. V. Kopyev·V. A. Sirota·K. P. Zybin
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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.

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A. S. Il'yn, A. V. Kopyev, V. A. Sirota, K. P. Zybin. 2022-12-20. Material surfaces in stochastic flows: integrals of motion and intermittency. https://doi.org/10.1103/physreve.107.l023101

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