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流和深边界流的数学和物理学。宽松地说，这些流动形成了伟大的“输送机”的下肢。它通过海洋携带热量和其他特性，是世界气候系统的重要环节。深度传输和混合取决于沿着这些流动所采取的实质路径起作用的一系列过程。其中包括液压控制和液压转换、不稳定性、夹带、分支、涡流产生以及沿着这些流动的长路径作用的其他过程。要了解这些过程，首先要了解不同位置的流动振荡的自然模式：线性动力模式。相关的非标准特征值问题比海洋表面流的教科书模型更困难。控制特征值属性并帮助理解物理过程的定理发展很差。此外，深海流理想化模型或基于观测的海流实现的特征值的数值计算更加麻烦。该项目将支持一名博士后研究员，他将尝试使用一种新的数学方法来推进流动的基本理论，该方法可以制定稳定性标准、增长率和相速度的界限以及其他约束。这些方法集中于 Ricatti 方程的推导以及 Evans 函数和 Maslov 指数的使用。这项工作将与根据激发这项工作的两个应用的模型或实现计算出的正常模式的数值研究相结合：北冰洋西部的巴罗峡谷外流和北大西洋的西部深边界流。 ：主要的智力价值在于数学工具的新颖应用和扩展，以促进对深海复杂而重要的物理过程的物理理解。更广泛的影响：就更广泛的影响而言，所讨论的物理过程对海洋气候很重要系统。开发的数学工具可用于海洋学或地球物理流体动力学的其他分支。该项目还将通过在海洋学研究机构培训具有数学背景的博士后研究员来鼓励跨学科合作。