2025/07/30 by Ephrati, Sagy, Jansson, Erik, Papini, Andrea · 1 citation
#35Q35 #60H15 #65M75 #76B03 #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Numerical Analysis (math.NA) #Probability (math.PR)
paper · doi:10.48550/arxiv.2508.02707
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.