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: 1025422
• 负责人: Jinqiao Duan
• 金额: $ 21.69万
• 依托单位: Illinois Institute of Technology
• 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=1025422&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.

虽然可以在结合简化方程的涡旋解析海洋模型框架内准确处理大片海洋，但在相对较小的区域，快速演变的三维运动不仅对当地而且对大尺度动力学都很重要，从而在沿海和全球洋流的多尺度动力学中发挥重要作用。这些小区域内的流动动力学非常复杂，不能通过简单的参数化来进行精确的近似，而是需要求解整个方程组。这个项目的目标是建立一个模型框架，可以同时处理能量活跃的运动和大规模的一般环流。这个研究-教育项目是一项合作的精心策划的努力，综合了数学和海洋学方面的专业知识。项目团队的数学、计算和地球物理专业知识的融合是这项工作成功的核心。对研究生和本科生进行真正的跨学科培训也是至关重要的，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、计算和数据分析。为了对这些具有挑战性的海洋流动进行建模，需要一个真正的多尺度建模框架，它将仅在强烈混合的小区域使用计算密集型的Boussinesq方程，而在流体领域的其余部分使用计算高效的原始方程。然而，考虑到海洋流动固有的多尺度性质，使得开发这样一个模拟框架在数学和计算上都具有挑战性。事实上，人们需要解决悬而未决的问题，例如两个不同的方程组之间的数学联系，分辨率差异很大的计算网格的连接，这一复杂框架中不确定性的量化和建模，以及在向前和向后能量级联共存的一系列尺度上的海洋流动的建模。这一新的框架包括几个重要的数学和计算发展：(1)基于区域分解的新的多物理/多分辨率建模方法，它将允许适当地处理高度变化的网格分辨率以及非静力和流体静力流态的接口；(2)新的时空过滤方法，它通过创建一系列中间模型填补两组方程之间的计算效率和物理精度的缺口，为连接两组不同的方程提供了一种优雅的数学方法；(3)针对Boussinesq-原始方程耦合固有的随机性在系统中产生的不确定性的新的建模策略；以及(Iv)最先进的湍流模拟，通过利用近似反卷积方法的数学性质，适当地处理Boussinesq和原始流型的明显不同的湍流特征。