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

Woods Hole Oceanographic Institution, Woods Hole MA

Investigators

Abstract

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.