Rapid Spin Up and Spin Down of Flow Along Slopes

TL;DR

This paper extends a one-dimensional model of stratified flow over slopes to include rapid spin up and spin down dynamics, capturing the physics of interior return flows driven by Ekman transport and Coriolis effects.

Contribution

The work introduces a constrained 1D model that incorporates interior return flow, enabling the simulation of rapid spin up and spin down phenomena along slopes, based on 2D dynamics.

Findings

The extended model accurately reproduces 2D mixing-generated spin up.

It provides a unified framework for Ekman arrest and spin down processes.

The model captures rapid adjustment of interior flows due to Coriolis acceleration.

Abstract

The near-bottom mixing that allows abyssal waters to upwell tilts isopycnals and spins up flow over the flanks of mid-ocean ridges. Meso- and large-scale currents along sloping topography are subjected to a delicate balance of Ekman arrest and spin down. These two seemingly disparate oceanographic phenomena share a common theory, which is based on a one-dimensional model of rotating, stratified flow over a sloping, insulated boundary. This commonly used model, however, lacks rapid adjustment of interior flows, limiting its ability to capture the full physics of spin up and spin down of along-slope flow. Motivated by two-dimensional dynamics, the present work extends the one-dimensional model by constraining the vertically integrated cross-slope transport and allowing for a barotropic cross-slope pressure gradient. This produces a closed secondary circulation by forcing Ekman transport in the bottom boundary layer to return in the interior. The extended model can thus capture Ekman spin up and spin down physics: the interior return flow is turned by the Coriolis acceleration, leading to rapid \linelabel{ll:slowdiff}rather than slow diffusive adjustment of the along-slope flow. This transport-constrained one-dimensional model accurately describes two-dimensional mixing-generated spin up over an idealized ridge and provides a unified framework for understanding the relative importance of Ekman arrest and spin down of flow along a slope.