Diffusive behavior of transport noise on $\mathbb{S}^2$

Sagy Ephrati; Erik Jansson; Andrea Papini

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arXiv · 2508.02707

Diffusive behavior of transport noise on $\mathbb{S}^2$

Sagy Ephrati·Erik Jansson·Andrea Papini

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Abstract

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.

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Sagy Ephrati, Erik Jansson, Andrea Papini. 2025-07-30. Diffusive behavior of transport noise on $\mathbb{S}^2$. https://arxiv.org/abs/2508.02707

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