Percolation regime of turbulent transport in weak compressible flows

Abstract

This paper considers the influence of both weak compressibility and time-dependence effects in two-dimensional random flow on the passive scalar behavior in the framework of the continuum percolation approach. It is shown that there is a characteristic velocity scale, which corresponds to the dissipative process. The mean field estimate for a small percolation parameter is suggested in accordance with additional external influences superimposed on the system. In the framework of mean field theory, the balance of correlation scales is considered. This gives the characteristic time that corresponds to the percolation regime. A new scaling for the effective diffusivity is obtained.