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

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Abstract
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’.
Funding Information
  • MSCA Cofund QuanG (101081458)
  • European Commission

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