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

霍尔姆（Proc. Soc 2015）引入了一个变分框架，用于随机参数化未解决的水动力运动尺度。这种变分框架保留了流体动力学的基本特征，如开尔文环流定理，同时也允许非线性波在分层流体中以及在其自由表面的传播。浅水中非线性色散波的动力学涉及波与流的强烈相互作用。该项目采用随机变分方法，结合广泛的数学分析和数值，对海洋温跃层上方的上层海洋动力学中的WCI进行建模。该项目旨在制定一种新的方法，用于开发可能有用的随机参数化方法，例如海洋波流相互作用的数据分析和不确定性量化。该项目的目的是利用数据同化来减少这种不确定性，其研究方法的基础是，将新的随机方法（SALT）与在数据同化中使用粒子过滤来减少不确定性的新协议相结合，以估计流体流动数据驱动模型的不确定性。该项目符合EPSRC的数学科学和物理科学的战略主题。数学分析、数值分析、非线性系统和流体动力学也是本课程的研究领域。法国雷恩INRIA的Mémin和教授B。Chapron在Ifremer在布雷斯特FR。

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.