Fluid Turbulence, Thermal Noise and Spontaneous Stochasticity

I will explain that incompressible Navier-Stokes is the wrong equation to describe turbulence in low Mach number molecular fluids because it neglects the effects of thermal noise. There should, in fact, be strong effects of thermal noise throughout the dissipation range. Thermal noise will manifest itself also in the inertial-range dynamics, with the detailed large-scale flow depending upon the particular realization of the molecular noise in just a few large-eddy turnover times. This is due to the phenomenon of "spontaneous stochasticity". We will discuss a renormalization group approach to calculate the spontaneous statistics, their universality domains and the finite Reynolds-number corrections.  

G. L. Eyink & D. Bandak, “A Renormalization Group Approach to Spontaneous Stochasticity”,  Physical Review Research, 2, 043161 (2020), https://arxiv.org/abs/2007.01333