Computation of the Effective Diffusivity Tensor for Transport of a Passive Scalar in a Turbulent Incompressible Flow

We consider the passive scalar transport in an incompressible random flow. Our basic result is a proof of the converge of a certain numerical scheme for the computation of the eddy diffusivity tensor. The scheme leads to the formula for the diffusivity expressed in terms of an infinite series. We give a rigorous proof of the geometric bounds on the magnitude of the terms of the series, provided that the Eulerian field is Markovian and Gaussian and its temporal dynamics has a sufficiently large spectral gap. The principal tools used in the proofs are the decomposition of the space of square integrable fields formed over the possible realizations of the Eulerian velocity field in the Gaussian chaos and the hypercontractivity properties of Gaussian measures. sec1