Margaret Beck, Boston University
Host: Darko Volkov
Title: Enhanced dissipation in fluids models
Fluids are well known to evolve on multiple time scales. For example, in many contexts a disturbed fluid will rapidly evolve to a state with many localized vortices, which then move and interact on a slower timescale, as the fluid relaxes to its rest state. In some situations the period of rapid evolution is associated with enhanced dissipation, meaning decay due to diffusion that occurs at a rate which is faster than one would naively expect. I will discuss two examples of this: convergence to bar states in the 2D Navier-Stokes equation, and Taylor Diffusion. In both cases I will describe the observed behavior and provide a mathematical explanation for it.