On the Existence of Invariant Measure for Lagrangian Velocity in Compressible Environments

摘要

We study transport of a passive tracer particle in a time dependent turbulent flow in the medium with positive molecular diffusivity. We show that there exists then a probability measure equivalent to the underlying physical probability, corresponding to the Eulerian velocity field, under which the particle Lagrangian velocity observations are stationary. As an application we derive the existence of the Stokes drift and the effective diffusivity—the characteristics of the long time behavior of the particle motion.