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 that their explicit form does not depend on the statistics of velocity. Only one of them has been discussed previously.

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• Dynamo theory
• Homogeneous turbulence
• Intermittency
• Isotropic turbulence
• Random walks
• Three-dimensional turbulence
• Turbulence
• Two-dimensional turbulence
• Stochastic dynamical systems
• Lagrangian flow field
• Large deviation & rare event statistics
• Random matrix theory
• Statistical hydrodynamics
• Stochastic analysis
• Stochastic differential equations