Effective Diffusivity of Stationary Vector Fields with Short Time Correlations
Leonid Koralov · Random Operators and Stochastic Equations · 1997
We consider transport properties for a class of periodic, Gaussian, stationary, divergence free, random velocity fields in R 2 with a finite number of spatial modes. Full asymptotics of the effective diffusivity is obtained in the case of short time correlations, on a fully rigorous basis. Existence and uniqueness for a hypoelliptic partial differential equation coupling velocity Fourier modes to physical space transport provides the main technical step in the justification of the asymptotic analysis. 1 Introduction The problem of expressing the effective diffusivity, which is a Lagrangian characteristic of the flow, in terms of the correlation function of the flow vector field itself, which is Eulerian data, is an important question which has been discussed extensively in physical and mathematical publications. We refer to [6] for an introduction to this literature. Most of the results have been obtained in two cases. Either the time correlation scale of the random vector field is ...