NSFGEO-NERC: Multiscale Stochastic Modeling and Analysis of the Ocean Circulation

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Turbulent oceanic flows consist of complex motions - jets, vortices and waves that co-exist on very different spatio-temporal scales but also without clear scale separation. Along with computational challenges to simulate multiscale oceanic circulation in high numerical resolution, as well as resulting difficulties in dynamically and kinematical understanding of multiscale flows, naturally goes practical need to develop prognostic models of reduced complexity that reproduce the whole complexity of turbulent oceanic motions across scales. This project aims to develop such reduced-order stochastic models by dynamical, i.e., equations-based as well as statistical data-driven reduction methods, describing the evolution of relatively few (from tens to hundreds) spatio-temporal modes and capturing essential statistical properties of the underlying multiscale oceanic flow and stratification. It will combine development and applications of state-of-the-art data-adaptive methods and rigorous mathematical theory for dynamical and empirical reduction in the hierarchy of oceanic models. The methods to be developed in this project are very general and can be easily extended to other problems in fluid mechanics and geophysical flows. The reduced-order stochastic models that emulate the turbulent flows in a coarse-grained sense can be adopted as efficient and low-cost oceanic components of general circulation models that could improve quantitative prediction of climate change. The Project will foster a USA-UK research collaboration and provide opportunities for cross-training in an international setting. The UK collaborator will recruit a PhD student via the EPSRC Centre for Doctoral Training "Mathematics of Planet Earth" at the Imperial College to work on development and applications of stochastic reduced-order ocean models.This Project aims to develop versatile and novel methods for constructing stochastic oceanic emulators of reduced complexity, based either on high-end model simulations or on underlying dynamical equations, or both, and for capturing oceanic variability across scales, i.e., from large-scale decadal variability to mesoscale eddies, and resulting dynamical and kinematical understanding of multiscale flows. The goals of this Project are (i) to extend recent theoretical results and to emulate the full spectrum of dynamically important scales including mesoscale eddies; (ii) to demonstrate that the stochastic flow emulators can provide fundamental novel insights into dynamical and kinematical properties of the multiscale transient flow patterns and their interactions, and to search for dynamical interpretations of mode interactions; (iii) to extend empirical and dynamical reduction methods to spatially inhomogeneous and turbulent flows; (iv) to consider several types of dynamically simulated eddying multiscale flows of the ocean circulation in the hierarchy of oceanic models of different complexity and geography, such as anisotropic turbulence on zonal currents and wind-driven gyres with western boundary currents, (v) to embed the stochastic flow emulators into non-eddy-resolving dynamical oceanic models as effective parameterizations of the eddy effects.