Emergent dynamical scaling in the inviscid limit of 3D stochastic Navier-Stokes equation with thermal noise

Fuente: arXiv
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Auteurs principaux: Gosteva, Liubov, Brachet, Marc, Canet, Léonie
Format: Preprint
Publié: 2025
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author Gosteva, Liubov
Brachet, Marc
Canet, Léonie
author_facet Gosteva, Liubov
Brachet, Marc
Canet, Léonie
contents 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 renormalisation group and direct numerical simulations. While spectrally truncated three-dimensional 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 $τ\sim k^{-1}$ dynamical scaling, where $τ$ is the decorrelation time. We characterise the crossover from the scaling $τ\sim 1/(νk^2)$, expected at large viscosity, to the scaling $τ\sim 1/(u_{\rm rms}k)$ found in the inviscid limit.
format Preprint
id arxiv_https___arxiv_org_abs_2507_05811
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Emergent dynamical scaling in the inviscid limit of 3D stochastic Navier-Stokes equation with thermal noise
Gosteva, Liubov
Brachet, Marc
Canet, Léonie
Fluid Dynamics
Statistical Mechanics
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 renormalisation group and direct numerical simulations. While spectrally truncated three-dimensional 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 $τ\sim k^{-1}$ dynamical scaling, where $τ$ is the decorrelation time. We characterise the crossover from the scaling $τ\sim 1/(νk^2)$, expected at large viscosity, to the scaling $τ\sim 1/(u_{\rm rms}k)$ found in the inviscid limit.
title Emergent dynamical scaling in the inviscid limit of 3D stochastic Navier-Stokes equation with thermal noise
topic Fluid Dynamics
Statistical Mechanics
url https://arxiv.org/abs/2507.05811