Uniform-in-diffusivity scalar mixing in stochastic fluids
Zoom link: https://princeton.zoom.us/j/9148065146
A fundamental problem in fluid mechanics concerns mixing behavior of the density of some scalar quantity being passively advected by an incompressible fluid velocity while also undergoing some small amount of diffusion. In this talk, I will discuss several results concerning mixing of scalars when the advecting velocity field satisfies random ergodic motion given by a number of stochastically forced fluid models, including the 2d Navier-Stokes equations at finite Reynolds number. We will see that such fluid motion gives rise to exponential mixing almost surely and uniformly with respect to the diffusivity parameter. The primary mechanism for mixing is the chaotic motion of Lagrangian trajectories, known as chaotic mixing. Uniformity of the mixing rate with respect to diffusivity is an important feature of this result and will be the primary focus of the talk.