Lagrangian stochastic integrals of motion in isotropic random flows

A set of exact integrals of motion is found for systems driven by homogenous isotropic stochastic flow. The integrals of motion describe the evolution of (hyper-)surfaces of different dimensions transported by the flow, and can be expressed in terms of local surface densities. The expression for the integrals is universal: it represents general geometric properties and does not depend on the statistics of the specific flow.