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

拟议的研究探索了海洋溢出流和深边界流的数学和物理。粗略地说，这些流形成了巨大的“传送带”的下肢。它通过海洋携带热量和其他特性，是世界气候系统的一个重要环节。深层输运和混合依赖于沿着这些流动所经过的主要路径作用的一系列过程。包括水力控制和水力转换、不稳定性、夹带、分支、涡流产生和沿着这些流动的长路径作用的其他过程。要理解这些过程，首先要了解不同位置的流动的自然振荡模式：线性动力模式。相关的非标准特征值问题比教科书上的海洋表面流模型更困难。支配特征值性质的定理，以及对物理过程的理解，还没有得到很好的发展。此外，对于理想的深流模型，或基于观测的深流实现，特征值的数值计算都比较麻烦。该项目将支持一名博士后研究人员，他将尝试使用一种新的数学方法来推进流动的基本理论，这种方法可能允许制定稳定性标准、增长率和相速度的界限以及其他限制。方法集中在Ricatti方程的推导，Evans函数和Maslov指数的使用。这项工作将与从模型或实现中计算出的正常模态的数值研究相结合，这两个应用推动了这项工作：北冰洋西部的巴罗峡谷流出和北大西洋的深西部边界流。智力价值：主要的智力价值在于数学工具的新颖应用和扩展，以推进对深海中复杂和重要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系统很重要。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。该项目还将通过在海洋学研究机构培训具有数学背景的博士后研究员，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.