The hard membrane process and transport barriers of turbulent flows

Abstract: Motivated by the phenomenon of transport barriers in fusion plasma devices, we write a mathematical model of heat dispersion in a turbulent fluid with a transport barrier, properly idealized; in a scaling limit of the turbulence model with separation of scales we get a heat equation with space-dependent diffusion coefficient, poorly diffusing near the barrier; then we investigate the scaling limit when the diffused barrier converges to a sharp separating surface and describe the limit by means of the stochastic process called Brownian motion with hard membrane.