Diffusive behavior of transport noise on $\mathbb{S}^2$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918115654238208 |
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| author | Ephrati, Sagy Jansson, Erik Papini, Andrea |
| author_facet | Ephrati, Sagy Jansson, Erik Papini, Andrea |
| contents | We investigate theoretically and numerically transport noise-induced diffusion in flows on the sphere. Previous analysis on the torus demonstrated that suitably chosen transport noise in the Euler equations leads to diffusive behavior resembling the Navier--Stokes equations. Here, we analyze dynamics on the sphere with noise-induced differential elliptic operator dissipation and characterize their energy and enstrophy decay properties. Through structure-preserving numerical simulations with the Zeitlin discretization, we demonstrate that appropriately scaled transport noise induces energy dissipation while preserving enstrophy and coadjoint orbits. The presented analysis lays a groundwork for further theoretical investigation of transport noise and supports the calibration of transport noise models as a parametrization for unresolved processes in geophysical fluid simulations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_02707 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Diffusive behavior of transport noise on $\mathbb{S}^2$ Ephrati, Sagy Jansson, Erik Papini, Andrea Numerical Analysis Probability Fluid Dynamics 60H15, 65M75, 35Q35, 76B03 We investigate theoretically and numerically transport noise-induced diffusion in flows on the sphere. Previous analysis on the torus demonstrated that suitably chosen transport noise in the Euler equations leads to diffusive behavior resembling the Navier--Stokes equations. Here, we analyze dynamics on the sphere with noise-induced differential elliptic operator dissipation and characterize their energy and enstrophy decay properties. Through structure-preserving numerical simulations with the Zeitlin discretization, we demonstrate that appropriately scaled transport noise induces energy dissipation while preserving enstrophy and coadjoint orbits. The presented analysis lays a groundwork for further theoretical investigation of transport noise and supports the calibration of transport noise models as a parametrization for unresolved processes in geophysical fluid simulations. |
| title | Diffusive behavior of transport noise on $\mathbb{S}^2$ |
| topic | Numerical Analysis Probability Fluid Dynamics 60H15, 65M75, 35Q35, 76B03 |
| url | https://arxiv.org/abs/2508.02707 |