Intermittency in random flows and stochastic integrals of motion

A.S. Il’yn^†^a, b, A.V. Kopyev^‡^a, V.A. Sirota^§^a, K.P. Zybin^*^a, b
^aLebedev Physical Institute, Russian Academy of Sciences, Leninsky prosp. 53, Moscow, 119991, Russian Federation
^bHSE University, ul. Myasnitskaya 20, Moscow, 101000, Russian Federation

This review presents recent advances in the study of frozen-in material lines and surfaces evolving in random flows. A remarkable feature of this process is the formation of long-lived coherent structures on surfaces, which are associated with certain stochastic integrals of motion. While the exact form of these integrals depends on flow properties, they become universal under the condition of local isotropy. We derive these integrals explicitly and discuss the elegant mathematics underlying this phenomenon.

Keywords: turbulence, advection, dynamo theory, random matrices
PACS: 02.50.−r, 47.27.−i, 91.25.Cw (all)
DOI: 10.3367/UFNe.2025.03.039940
URL: https://ufn.ru/en/articles/2025/8/b/
Web of Science

001606309600004
Scopus

2-s2.0-105016803040
ADS NASA

2025PhyU...68..747I
Citation: Il’yn A S, Kopyev A V, Sirota V A, Zybin K P "Intermittency in random flows and stochastic integrals of motion" Phys. Usp. 68 747–758 (2025)

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%0 Journal Article
%T Intermittency in random flows and stochastic integrals of motion
%A A. S. Il’yn
%A A. V. Kopyev
%A V. A. Sirota
%A K. P. Zybin
%I Physics-Uspekhi
%D 2025
%J Phys. Usp.
%V 68
%N 8
%P 747-758
%U https://ufn.ru/en/articles/2025/8/b/
%U https://doi.org/10.3367/UFNe.2025.03.039940

Received: 30th, June 2025, accepted: 5th, March 2025

Оригинал: Ильин А С, Копьев А В, Сирота В А, Зыбин К П «Перемежаемость в случайных потоках и стохастические интегралы движения» УФН 195 794–806 (2025); DOI: 10.3367/UFNr.2025.03.039940