Diffusion with stochastic transport is investigated here when the randomdriving process is a very general Gaussian process, including FractionalBrownian motion. The purpose is the comparison with a deterministic PDE, whichin certain cases represents the equation for the mean value. From thisequation we observe a reduced dissipation property for small times and anenhanced diffusion for large times, with respect to delta correlated noisewhen regularity is higher than the one of Brownian motion, a fact interpretedqualitatively here as a signature of the modified dissipation observed for 2Dturbulent fluids due to the inverse cascade. We give results also for thevariance of the solution and for a scaling limit of a two-component noise input.
Categories: math.PR