Variational principles for continuum dynamics on geometric rough paths.

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Context of the research including potential impact. The project will develop a new methodology for uncertainty quantification and reduction of uncertainty in computational fluid dynamics by developing the theory of Geometric Rough Paths (GRP) based in the foundations of transformation theory and multi-time homogenisation for continuum dynamics. In our earlier results, the stochastic fluid velocity decomposition results of show that the principles of transformation theory and multi-time homogenisation enable a physically meaningful, data-driven and mathematically-based approach for decomposing the fluid transport velocity into its drift and stochastic parts. This approach can be applied immediately to the class of continuum flows whose deterministic motion is based on fundamental variational principles defined on geometric rough paths. * Aims and objectives: The project aims to decompose the Lagrangian trajectories in continuum dynamics into their fast and slow, or resolvable and unresolvable, components and extend our stochastic modelling experience to the realm of geometric rough flows as a basis for quantifying a priori uncertainty and then using data assimilation methods (e.g., particle filtering) for reducing the uncertainty. * Novelty of the research methodology: The field of variational principles for continuum dynamics on geometric rough paths has only one paper written about it so far, namely by Darryl Holm and his collaborators. * EPSRC strategic them is Mathematical Sciences * Research area is continuum mechanics * No companies involved yet. Collaborators involve several colleagues in the Imperial College Mathematics department