Constraints on Cross-shelf Exchange Imposed by Boundary Layer Buoyancy Arrest

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One of the classic problems in coastal oceanography is the question of how flow on the shelf responds to conditions farther offshore. The most common dynamical framework for thinking about this issue has been the idea that bottom Ekman transport allows the geostrophic (Taylor-Proudman) prohibition of cross-isobath flow to be relaxed. This paradigm needs to be revisited because of our improved understanding of bottom boundary layers.In an ocean with density stratification, bottom friction and a sloping bottom, cross-isobath buoyancy transport arrests the bottom velocity, and so steady along-isobath flow experiences no along-isobath bottom friction. Consequently, steady flow over the shelf, once it adjusts, has to follow isobaths exactly, provided the flow does not have large inertia in the Rossby number sense. Cross-shelf scales are set by rotation, bottom slope, stratification and flow volume (but not bottom friction). This result very much brings into question (during stratified conditions) the enduring 'diffusive' model that shows that steady flows can cross isobaths because of the mitigating effects of bottom friction.It is argued that if flow goes onto the shelf from offshore, the current will be relatively wide as it flows away toward the left (facing onshore, in the Northern Hemisphere). However, if, at the shelf edge, flow is drawn offshore, the width of the associated shelf current will be much less as it flows in from the left as one faces onshore. In this case, bottom Ekman transport is up-slope. Preliminary numerical results verify these conclusions with regard to current width and boundary layer properties, at least qualitatively.The goal of this project is to address how an ocean with a realistic representation of bottom boundary layer arrest behaves with regard to coupling between the shelf and the open ocean. Within this broader question, the problem will be broken up to address the shelf-slope system for 1) onshore flows, 2) offshore flows, 3) inertial effects, and 4) the possibility that buoyancy arrest physics, in combination with regional onshore flow, can account for undercurrent systems such as the California Undercurrent.The broader impact of this work is two-fold. First, the project will have impact over the wide range of ocean sciences where cross-shelf exchange is an important issue. For example, one specific result of this project will be to quantify the distance onto the shelf that an oceanic flow can penetrate (and, the rather different scale over which water from over the shelf can be drawn offshore). Second, this project will contribute to the health of the ocean science community by contributing to the education of a PhD graduate student.