Intermittency in random flows and stochastic integrals of motion

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.