CMG Collaborative Research: Ocean Modeling by Bridging Primitive and Boussinesq Equations

CMG 合作研究：通过连接原始方程和 Boussinesq 方程进行海洋建模

• 批准号: 1025314
• 负责人: Traian Iliescu
• 金额: $ 20.83万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-15 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1025314&HistoricalAwards=false
• 关键词: CMG; Collaborative; Research; Ocean; Modeling

While vast regions of the ocean can be treated accurately within the framework of eddy-resolving ocean models integrating simplified equations, there are comparatively small regions in which rapidly-evolving three dimensional motions are important not only for local but also for large-scale dynamics, thereby playing an important role in the multi-scale dynamics of both coastal and global oceanic flows. The flow dynamics in these small regions are complex enough not to permit an accurate approximation by simple parameterizations, but rather demand solution of the full set of equations. The objective of this project is to build a modeling framework which can handle both energetically active motions and large scale general circulations simultaneously. This research-education project is an orchestrated effort of a collaboration synthesizing expertise in both mathematics and oceanography. The blend of mathematical, computational, and geophysical expertise of the project team is central to the success of this endeavor. It is also essential to the truly interdisciplinary training of graduate and undergraduate students, who will be involved in all the stages of a research project: Modeling, mathematical analysis, discretization, validation, computation, and data analysis.To model these challenging oceanic flows, a truly multi-scale modeling framework that will employ the computationally intensive Boussinesq equations only in the small regions of intense mixing and the computationally efficient primitive equations in the rest of the fluid domain is needed. The inherent multi-scale nature of the oceanic flows considered, however, makes the development of such a modeling framework challenging, both mathematically and computationally. Indeed, one needs to address outstanding open questions, such as, the mathematical bridging of two different systems of equations, the interfacing of computational meshes of vastly varying resolutions, the quantification and modeling of uncertainty in this complex framework and the modeling of oceanic flows over a range of scales where forward and backward energy cascades coexist. This new framework comprises several significant mathematical and computational developments: (i) a new multiphysics/multiresolution modeling approach based on domain decomposition that will allow an appropriate treatment of highly varying mesh resolutions and the interfacing of the non-hydrostatic and hydrostatic flow regimes; (ii) a novel spatio-temporal filtering methodology that provides an elegant mathematical approach for bridging two different sets of equations by creating a spectrum of intermediate models filling the gap between the two sets of equations in terms of computational efficiency and physical accuracy; (iii) new modeling strategies for the uncertainty in the system generated by the inherently stochastic nature of the Boussinesq-primitive equations coupling; and (iv) state-of-the-art turbulence modeling for an appropriate treatment of the markedly different turbulence character of the Boussinesq and primitive flow regimes by taking advantage of the mathematical nature of approximate deconvolution approaches.

虽然可以在整合简化方程式的涡流海洋模型的框架内准确处理海洋的巨大区域，但是在相对较小的区域中，迅速发展的三维运动不仅对本地动力学不仅重要，而且对大型动力学也很重要，从而在沿海和全球海洋水平的多尺度动力学中起着重要作用。这些小区域中的流动动力学足够复杂，不允许通过简单的参数化进行准确的近似，而是要求整个方程式的解决方案。该项目的目的是建立一个建模框架，该框架可以同时处理能量活跃的运动和大规模的一般循环。这个研究教育项目是数学和海洋学方面的协作综合专业知识的精心策划。项目团队的数学，计算和地球物理专业知识的融合对于这项工作的成功至关重要。对于研究生和本科生的真正跨学科培训也是必不可少的，他们将参与研究项目的所有阶段：建模，数学分析，离散化，验证，计算，计算和数据分析。建模这些具有挑战性的海洋流，即真正的多尺度建模框架，这些框架将仅采用计算中的计算方程式和典型的集约化区域，并在小规模上进行了繁华的组合，并在小规模的情况下进行了构建。需要在其余的流体结构域中。然而，考虑到海洋流的固有多尺度性质使这种建模框架在数学上和计算上都具有挑战性。 的确，一个人需要解决诸如两个不同方程式系统的数学桥接，诸如大大变化分辨率的计算网格的接口，这个复杂框架中不确定性的量化和建模以及海洋流动范围内的范围和后退能量库的范围内的海洋流动的建模。 该新框架包括几个重要的数学和计算发展：（i）基于域分解的新的多物理/多分辨率建模方法，该方法将允许对高度变化的网格分辨率进行适当处理，并将非静态和静水力流动状态的接口进行接口； （ii）一种新型的时空滤波方法，它通过创建一组中间模型来填充两组在计算效率和物理准确性方面的中间模型，从而提供了一种优雅的数学方法来弥合两组不同的方程式； （iii）由BousSinesQ-primitive方程耦合的固有随机性产生的系统中不确定性的新建模策略； （iv）通过利用近似反卷积方法的数学性质，对Boussinesq和原始流动方案的明显不同的湍流特征进行适当处理的最新湍流建模。