Dissipation enhancement by mixing

ABSTRACT:  We quantitatively study the interaction between diffusion and mixing in both the continuous and discrete time setting. In discrete time, we consider a mixing dynamical system interposed with diffusion. In continuous time, we consider the advection diffusion equation where the advecting vector field is assumed to be sufficiently mixing. The main result is to estimate the dissipation time and energy decay based on an assumption quantifying the mixing rate.