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

湍流海洋流动由复杂的运动组成--射流、漩涡和波浪在非常不同的时空尺度上共存，但也没有明确的尺度分离。随着以高数值分辨率模拟多尺度海洋环流的计算挑战，以及由此导致的对多尺度流动的动力学和运动学理解的困难，自然需要开发复杂性降低的预报模式，以再现跨尺度海洋湍流运动的全部复杂性。该项目旨在通过动力学的、即基于方程的简化方法以及统计数据驱动的简化方法来开发这种降阶随机模型，描述相对较少的(从几十个到数百个)时空模式的演变，并捕获基本的多尺度海洋流动和层结的基本统计特性。它将结合最先进的数据自适应方法的开发和应用，以及海洋模型层级中动力和经验简化的严格数学理论。该项目所开发的方法是非常通用的，可以很容易地推广到流体力学和地球物理流动的其他问题。降阶随机模式在粗粒度意义上模拟湍流流动，可以作为大气环流模式中有效和低成本的海洋组件，从而提高对气候变化的定量预测。该项目将促进美英研究合作，并提供在国际环境下进行交叉培训的机会。这位英国合作者将通过帝国理工学院EPSRC中心的博士生培训中心招聘一名博士生，从事随机降阶海洋模型的开发和应用。该项目旨在开发通用和新颖的方法，以构建降低复杂性的随机海洋模拟器，要么基于高端模型模拟，要么基于基本动力学方程，或者两者兼而有之，并捕捉不同尺度的海洋可变性，即从大尺度的年代际变化到中尺度的涡旋，以及由此产生的对多尺度流动的动力学和运动学理解。该项目的目标是：(I)推广最新的理论结果，模拟包括中尺度涡旋在内的各种动力重要尺度；(Ii)证明随机流模拟器可以提供对多尺度瞬变流型及其相互作用的动力学和运动学性质的基本新见解，并寻求对模式相互作用的动力学解释；(Iii)将经验和动力学折减方法扩展到空间非均匀和湍流；(4)在不同复杂程度和不同地理位置的海洋模式层级中考虑海洋环流的几种动态模拟的多尺度涡流，如纬向流上的各向异性湍流和具有西边界流的风生涡旋；(5)将随机流模拟器嵌入到非涡旋分辨动力海洋模式中，作为涡流效应的有效参数化。

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.