Towards a renormalization group theory of spontaneous stochasticity in fluid turbulence.

Spontaneous stochasticity is the phenomenon of intrinsic unpredictability in nearly singular systems with weak noise. Although conjectured to be ubiquitous in Nature, only relatively recently has it been understood in detail for Lagrangian fluid particles in turbulent flows. The phenomenon of spontaneous stochasticity is associated with a breakdown of uniqueness of solutions and underlies many fundamental and universal aspects of turbulence such as unpredictability beyond chaos, enhanced mixing, and anomalous dissipation. As such a renormalization group account of spontaneous stochasticity would be desirable. To this end, based on the analogy with zero-temperature phase transitions, we provide a renormalization group analysis of a minimal model that displays spontaneous stochasticity, characterizing the domains of attraction of each fixed point, and deriving the universal approach to the fixed points as a singular large-deviations scaling. We present numerical simulations that verify our theoretical predictions, and discuss wider applicability of the method to more realistic models of turbulence.