Analysis of a Kraichnan-type Fluid Model
We study the turbulent transport of a passive scalar quantity in a stratified,
2-D random velocity field. It has been for a long time that the transport is described via the solution of a well-known stochastic partial differential equation. We show via a priori bounds that, typically, the solution decays with time; that the decay is typically superdiffusive and sometimes diffusive in some physically-interesting cases. More interesting still, the decay is shown to be “macroscopically multifractal” in special settings. The detailed analysis is based on a probabilistic representation of the solution, which is likely to have other applications as well. This is based on joint work with Jingyu Huang.
(Tea served in First Floor Commons Room at 3:30pm.)