CMG POST-DOC: The Mathematics and Physics of Deep Spilling Flows and Boundary Currents in the Ocean

CMG 博士后：海洋深溢流和边界流的数学和物理

• 批准号: 0724696
• 负责人: Lawrence Pratt
• 金额: $ 33.54万
• 依托单位: Woods Hole Oceanographic Institution
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-12-01 至 2010-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0724696&HistoricalAwards=false
• 关键词: CMG; POST; DOC; Mathematics; Physics

The proposed research explores the mathematics and physics of spilling flows and deep boundary currents in the ocean. Loosely speaking, these flows form the lower limbs of the great ?conveyor? that carries heat and other properties through the oceans and is an important link in the world climate system. Deep transports and mixing depend on a chain of processes acting along the substantial paths that these flows take. Included are hydraulic control and hydraulic transitions, instability, entrainment, branching, eddy generation and other processes acting along the long paths of these flows. An understanding of these processes begins with knowledge about the natural modes of oscillation of the flow in different locations: the linear dynamical modes. The associated non-standard eigenvalue problems are more difficult than for text book models of ocean surface currents. Theorems that govern the properties of the eigenvalues, and that inform an understanding of the physical processes, are poorly developed. In addition, the numerical calculation of eigenvalues for idealized models of the deep currents, or for observation-based realizations of the currents, are more troublesome. This project will support a postdoctoral investigator who will attempt to advance the basic theory for the flow using a new mathematical approach that may allow formulation of stability criteria, bounds on growth rates and phase speeds, and other constraints. The approaches center on the derivation of Ricatti equations, and the use of Evans functions and Maslov indices. This work will be combined with numerical investigations of the normal modes calculated from models or realizations of the two applications that have motivated the work: the Barrow Canyon outflow in the western Arctic Ocean and the deep western boundary current in the N. Atlantic.Intellectual Merit: The primary intellectual merit lies in the novel application and extension of mathematical tools to advance physical understanding of complex and important physical processes in the deep ocean.Broader Impact: In terms of broader impact, the physical processes in question are important for the ocean climate system. The mathematical tools developed may be of use in other branches of oceanography or geophysical fluid dynamics. The project will also encourage interdisciplinary collaborations through the training at an oceanographic research institution of a postdoctoral investigator with a background in math.

拟议的研究探讨了海洋中溢出的流量和深边界电流的数学和物理。宽松地说，这些流程形成了大型输送机的下肢？这通过海洋携带热量和其他特性，是世界气候系统中的重要联系。深层运输和混合取决于沿这些流动所采取的实质路径作用的一系列过程。包括液压控制和液压过渡，不稳定性，夹带，分支，涡流产生和其他沿这些流动的长路径作用的过程。对这些过程的理解始于对不同位置流动振荡自然振荡的知识：线性动力学模式。与海面电流的教科书模型相比，相关的非标准特征值问题要困难。管理特征值的特性并了解对物理过程的理解的定理是不良发展的。此外，对于理想化的深电流模型或电流的基于观察的实现的特征值的数值计算更加麻烦。该项目将支持博士后调查员，他将尝试使用一种新的数学方法来推动流量的基本理论，该方法可以允许稳定标准，增长率和相位速度以及其他约束。该方法集中在Ricatti方程的推导以及Evans功能和Maslov指数的使用中。这项工作将结合对促进工作的两个应用程序计算出的正常模式的数值研究：北极海洋中的巴罗峡谷流出以及大西洋北大西洋的深层边界电流。智力优点：主要的​​知识分子优点在于，主要的工具在物理上的术语和延伸的重要工具中，重要的是，重要的是，重要的是，重要的是，重要的是，重要的是，重要的是，重要的是，重要的是，重要的是重要的。更广泛的影响，所讨论的物理过程对于海洋气候系统很重要。开发的数学工具可能用于海洋学或地球物理流体动力学的其他分支。该项目还将通过在具有数学背景的博士后研究人员的海洋研究机构进行培训来鼓励跨学科的合作。