Emergent dynamical scaling in the inviscid limit of 3D stochastic Navier-Stokes equation with thermal noise
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917155824467968 |
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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 |