Courant PIs Workshop 2022
Abstract: As repeatedly observed in geophysical and laboratory flows, and in numerical simulations of the incompressible Navier-Stokes equations, a 3D fluid that is stirred by a statistically stationary random force will eventually reach a statistically stationary state in which the velocity variance is finite. In order to efficiently dissipate all the energy that is constantly injected into the system, the fluid transfers the energy from large scales towards small scales, at which viscous diffusion efficiently acts. In this talk, we will propose a linear SPDE that serves as a toy model of this transfer of energy as a cascading process through the scales. This is a first model that aims to generate rough, Hölder-continuous, fractional Gaussian random fields from smooth forcing through a dynamical evolution. Joint work with G.B. Apolinário, G. Beck, L. Chevillard and I. Gallagher.
You can view the slides from this lecture here.