Mixing-Driven Abyssal Ocean Circulation over Sloping Topography

The planetary-scale overturning circulation of the ocean is maintained by small-scale diapycnal mixing in the abyss. Recent theory and observations suggest that this turbulence is bottom-enhanced, confining the upwelling needed to close this circulation to thin bottom boundary layers (BLs) over sloping topography. Developing an understanding of how this mixing shapes the abyssal circulation, both locally and at the basin scale, is the unifying goal of this thesis. The local response of a water column to mixing has previously been understood using a one-dimensional model of a rotating, stratified fluid over a sloping seafloor. Canonically, this model assumes no cross- or along-slope variations of the flow, pressure, and buoyancy anomalies. At steady state, it predicts a peculiar form of the net cross-slope transport, however, failing to consider its coupling to the global circulation. For symmetric bathymetry without along-slope variations, for instance, this large-scale context implies that all cross-slope BL transport must be exactly returned in the interior. This interior downwelling is then turned by the Coriolis acceleration, rapidly spinning up along-slope flow in balance with a cross-slope barotropic pressure gradient. With these added physics, the one-dimensional model better captures the local response to mixing over an idealized ridge, for example. Using BL theory, we explicitly describe how the BL and interior communicate in this model. The up-slope transport of dense water in the bottom BL contributes a net downward flux of buoyancy, creating an effective bottom boundary condition on the interior. The coupling goes both ways, with the interior stratification at the top of the BL setting the strength of the BL transport. Variations across the slope then allow for BL--interior exchange. Ultimately, the net transport of the local response must conserve potential vorticity at the basin scale. To better understand this coupling for arbitrary topography, we develop a novel finite element model of the planetary geostrophic equations. Using a combination of simulations and BL theory, we then study the mixing-driven abyssal circulation in an idealized bowl-shaped basin. In the absence of wind forcing and the joint effect of baroclinicity and relief, the leading-order barotropic transport flows along f/H contours, where f is the Coriolis frequency and H is the depth. The local response to mixing is coupled to this barotropic circulation, simultaneously constrained by the barotropic circulation and forcing it via a bottom stress curl. For closed f/H contours, a strong along-contour barotropic circulation spins up, reminiscent of the local response described above. On the other hand, if these contours intersect the boundary, a case more typical in the real ocean, the barotropic transport is suppressed. This decouples the leading-order local response from the large-scale circulation and intensifies bottom BL upwelling. This work therefore suggests that the local abyssal stratification in the presence of bottom-enhanced mixing strongly depends on the large-scale context.