Applied Math Seminar

---

Singular measures and information capacity of turbulent cascades

Speaker: Gregory Falkovich, Weizmann Institute

Location: Warren Weaver Hall 1302

Date: Friday, September 24, 2021, 2:30 p.m.

Synopsis:

How weak is the weak turbulence? We analyze turbulence of weakly
interacting waves using the tools of information theory. It offers a
unique perspective for comparing thermal equilibrium and turbulence. The
mutual information between resonant modes in a finite box is shown to be
stationary and small in thermal equilibrium, yet to grow with time in
weak turbulence. We trace this growth to the concentration of
probability on the resonance surfaces, which can go all the way to a
singular measure. The surprising conclusion is that no matter how small
is the nonlinearity and how close to Gaussian is the statistics of any
single amplitude, a stationary phase-space measure is far from Gaussian,
as manifested by a large relative entropy. At the end I shall describe a
new class of the so-called Fibonacci models that describe resonantly
interacting waves and allow turbulence close to thermal equilibrium.
(0.1103/PhysRevLett.125.104501)