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

这项拟议的研究探索了海洋中溢流和深边界流的数学和物理学。粗略地说，这些流动形成了大传送带的下部。它通过海洋输送热量和其他特性，是世界气候系统中的重要一环。深层输送和混合依赖于一系列过程，这些过程沿着这些流动所走的实质性路径发挥作用。包括水力控制和水力过渡、不稳定、卷吸、分支、涡旋生成和其他作用于这些流动的长路径上的过程。要理解这些过程，首先要了解不同位置流动的自然振荡模式：线性动力模式。与海洋表面流的教科书模型相比，相关的非标准特征值问题更加困难。支配本征值性质的定理，以及提供对物理过程的理解的定理，都发展得很差。此外，对于深部海流的理想化模型或基于观测的海流实现来说，特征值的数值计算更加麻烦。该项目将支持博士后研究人员，他们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条件。这些方法的核心是Ricatti方程的推导，以及Evans函数和Maslov指数的使用。这项工作将结合对从两个应用程序的模型或实现计算出的正常模式的数值研究，这两个应用程序推动了这项工作：西部北冰洋的巴罗峡谷外流和北大西洋西部深层的边界流。智力上的优点：主要的智力价值在于对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。广泛影响：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能在海洋学或地球物理流体动力学的其他分支中有用。该项目还将通过在一家海洋研究机构培训一名具有数学背景的博士后研究员来鼓励跨学科合作。

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.