Emergent dynamical scaling in the inviscid limit of three-dimensional stochastic Navier–Stokes equation with thermal noise

In this work, we investigate the Navier-Stokes equation in the presence of thermal noise, both at finite viscosity (revisiting the seminal work by Forster-Nelson-Stephen) and in the inviscid limit,which has not yet been explored. We determine the space-time velocity correlations in this dynamics, using functional renormalization group (RG) and direct numerical simulations. While spectrally truncated three-dimensional (3D) Euler flows reach a stationary equilibrium state, they exhibit non-trivial temporal correlations. We show that these non-trivial correlations persist for small but finite viscosity, yielding an emergent τ∼k-1 dynamical scaling, where τ is the decorrelation time. We characterize the crossover from the scaling τ∼1/(νk2), expected at large viscosity, to the scaling τ∼1/(urmsk) found in the inviscid limit. This article is part of the theme issue 'Frontiers of turbulence and statistical physics'.