Wave Current Interaction with stochastic advection by Lie transport (WCI-SALT)

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Holm (Proc. Roy. Soc 2015) introduced a variational framework for stochastically parametrising unresolved scales of hydrodynamic motion. This variational framework preserves fundamental features of fluid dynamics such as Kelvin's circulation theorem while also allowing for nonlinear wave propagation within a stratified fluid as well as at its free surface.The dynamics of nonlinear dispersive waves in shallow water involves the strong interaction of waves with currents. The project models WCI in the upper ocean dynamics above the ocean thermocline using the stochastic variational approach combined with a wide range of mathematical analysis and numerics. This project aims to formulate a new approach for developing stochastic parametrisation methods which are potentially useful for example in data analysis and uncertainty quantification of oceanic wave-current interaction. The project then aims to use data assimilation to reduce that uncertainty.The research methodology is based on a combination of new stochastic methods (SALT) in estimating uncertainty in data-driven modelling of fluid flows in combination with a new protocol for using particle filtering in data assimilation for reducing uncertainty. This project is aligned with EPSRC's strategic theme of Mathematical science and physical science. It also follows in the research areas Mathematical analysis numerical analysis Nonlinear systems and fluid dynamics.Collaborators include Prof E. Mémin at INRIA in Rennes FR and Prof B. Chapron at Ifremer in Brest FR.