Journal of Statistical Physics, Vol. 98, Nos. 12, 2000, p. 405-418.
We study a model of turbulent transport described by the motion in a Gaussian random velocity field with Kolmogorov spectrum. The field is assumed to be divergence-free, homogeneous in time and space, and Markovian in time. The molecular viscosity defines the cutoff in the Fourier space, thus regularizing the vector field of the pure infinite-Reynolds-number Kolmogorov spectrum by vector fields with smooth realizations. We provide an asymptotic bound on the effective diffusivity of the finite-Reynolds number fields as R->oo. Namely, with macroscopic parameters of the system fixed and the viscosity tending to zero, the effective diffusivity is bounded above by a constant which does not depend on the Reynolds number.