
Simple, and complex, stochastic models of turbulence play an important role in the mathematical understanding of turbulent fluids and flows. The Kraichnan model, and its variants, are an especially well-studied family, where turbulent advection is represented by a sum of vector fields multiplied by an independent Brownian motion. In this talk I will present ongoing work (joint with F. Butori and S. Morlacchi) concerning a Kraichnan type model with locally supported vector fields. We show that in a suitable high mode limit the stochastic advection-diffusion equation converges to a deterministic diffusion equation with homogenised coefficients and enhanced diffusion.