Diffusive behavior of transport noise on S2

Journal article, 2026

We investigate theoretically and numerically transport noise-induced diffusion in flows on the sphere. Previous analysis on the torus has shown 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 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 provides a foundation 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.