Seminar

Zoom Link

I will explain a joint work with Kyle Liss which proves the Batchelor spectrum for a time-periodic deterministic transport equation.  We consider a simple time-periodic wedge flow constructed from two alternating, divergence-free shear flows.

We prove that though the system formally conserves energy, the forced version converges to an infinite energy steady state,  even though there is no obvious source of dissipation. This infinite energy steady state satisfies the spectra suggested by Batchelor and Onsager for such systems.

I will also comment on why this is much harder than the stochastic setting. This work builds on the enhanced dissipation work for Tarek Elgindi  and Kyle Liss which considered the same time-periodic flow.