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

拟议的研究探讨了海洋中溢出流和深层边界流的数学和物理学。不严格地说，这些流动形成了伟大的下肢？传送带？它通过海洋携带热量和其他属性，是世界气候系统的重要环节。深层的输送和混合取决于一系列的过程，这些过程沿着这些流动所经过的主要路径。包括水力控制和水力过渡、不稳定性、卷吸、分支、涡流产生和沿这些流的长路径沿着作用的其它过程。对这些过程的理解始于对不同位置的流动的自然振荡模式的了解：线性动力学模式。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。支配本征值性质的定理，以及为理解物理过程提供信息的定理，发展得很差。此外，数值计算的特征值的理想化模型的深电流，或基于观测实现的电流，是比较麻烦的。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，这种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。的方法集中在Ricatti方程的推导，并使用埃文斯函数和Maslov指数。这项工作将结合数值研究的正常模式计算模型或实现的两个应用程序，激发了工作：巴罗峡谷流出在北冰洋西部和深西部边界流在N。大西洋。智力优点：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。所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。该项目还将通过在一个海洋学研究机构培训一名具有数学背景的博士后调查员，鼓励跨学科合作。

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.