Abstract
Stochastic partial differential equations (SPDEs) have emerged as a powerful framework for modelling uncertainty, multiscale interactions, and unresolved processes in fluid dynamics. Their development is motivated in part by the growing need for uncertainty quantification in weather, ocean, and climate prediction, where deterministic models often fail to adequately represent the influence of unresolved scales and model error.
This talk provides an overview of recent developments in stochastic fluid dynamics, with an emphasis on mathematically structured stochastic parametrisations. We discuss stochastic versions of several fundamental geophysical fluid dynamics models, including the two-dimensional Euler equation with transport noise, rotating shallow water equations with stochastic advection by Lie transport (SALT), and fluid models driven by fractional Brownian motion that incorporate memory effects and long-range temporal correlations. For these models, we review recent results on well-posedness, regularity, and qualitative properties of solutions.
The presentation also highlights connections with uncertainty quantification, data assimilation, and stochastic model calibration, including recent work arising from the ERC Synergy project Stochastic Transport in Upper Ocean Dynamics (STUOD). Particular attention will be given to the role of stochastic parametrisations in improving predictive skill and representing unresolved dynamics in geophysical flows.