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Material surfaces in stochastic flows: Integrals of motion and intermittency
A S Il'yn1,2, A V Kopyev1, V A Sirota1
1P. N. Lebedev Physical Institute of RAS, 119991, Leninskij pr. 53, Moscow, Russia.
Physical Review. E
|March 18, 2023
Summary
Researchers discovered new universal stochastic integrals of motion in fluid dynamics. These integrals describe the long-time evolution of fluid elements in d-dimensional space and are independent of velocity statistics.
Area of Science:
- Fluid Dynamics
- Statistical Mechanics
- Stochastic Processes
Background:
- Understanding the long-time statistical properties of fluid elements is crucial in fluid dynamics.
- Previous studies have explored some aspects of stochastic flow, but a comprehensive set of conserved quantities remained elusive.
Purpose of the Study:
- To investigate the long-time evolution of statistical properties of line, surface, and volume elements in incompressible stochastic flow.
- To discover and characterize conserved quantities (stochastic integrals of motion) in such flows.
Main Methods:
- Analysis of fluid elements (line, surface, volume) in d-dimensional stationary, isotropic, incompressible stochastic flow.
- Mathematical derivation and identification of conserved quantities over extended time scales.
Main Results:
- Discovery of a family of d!-1 stochastic integrals of motion.
- Demonstration that these integrals are universal, meaning their form is independent of the specific velocity statistics.
- Identification of one previously known integral within this newly discovered family.
Conclusions:
- A new, universal set of conserved quantities has been identified in stochastic fluid flow.
- These findings provide a deeper understanding of the long-time behavior of incompressible stochastic flows.
- The universality of these integrals suggests broad applicability across different stochastic flow models.
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