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Issue 10, 2026
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On the 100th anniversary of Sergei Ivanovich Syrovatskii's birth. Conferences and symposia


Intermittency in random flows and stochastic integrals of motion

†  a, b, ‡  a, §  a, *  a, b
a Lebedev Physical Institute, Russian Academy of Sciences, Leninsky prosp. 53, Moscow, 119991, Russian Federation
b HSE 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.

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Fulltext is also available at DOI: 10.3367/UFNe.2025.03.039940
Correspondence should be addressed to
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/
001606309600004
2-s2.0-105016803040
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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Received: 30th, June 2025, 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

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