APDEs Seminar

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.