The dynamic role of ridges in a β-plane channel : towards understanding the dynamics of large scale circulation in the Southern Ocean

Abstract

In this thesis, the dynamic role of bottom topography in a β-plane channel is systematically studied in both linear homogeneous and stratified layer models in the presence of either wind stress (Chapters 2, 3, 4, and 6) or buoyancy forcing (Chapter 5). In these studies, the structure of the geostrophic contour plays a fundamental role, and the role of bottom topography is looked at from two different angles. It is shown that blocking all the geostrophic contours leads to two different physical processes in which bottom topographic form drag is generated (Chapters 2, 3 and 4) and enables geostrophic flow in a β-plane channel to support a net cross-channel volume transport (Chapters 5 and 6). It is demonstrated that by blocking all the geostrophic contours in the presence of a sufficiently high ridge, the dynamics of both source-sink and wind driven circulations in a β-plane is similar to that in a dosed basin. First, wind-driven circulation in the inviscid limit is discussed in a linear barotropic channel model in the presence of a bottom ridge. There is a critical height of the ridge, above which all geostrophic contours in the channel are blocked. In the subcritical case, the Sverdrupian balance does not apply and there is no solution in the inviscid limit. In the supercritical case, however, the Sverdrupian balance applies. The form drag is generated through two different physical processes: the through-channel recirculating flow and the Sverdrupian gyre flow. These processes are fundamentally different from the nonlinear Rossby wave drag generation. In this linear model, the presence of a supercritical high ridge is essential in the inviscid limit. With this form drag generation determined, an explicit form for the zonal transport in the channel is obtained, which shows what model parameters determine the through-channel transport. In addition, the model demonstrates that most of the potential vorticity dissipation occurs at the northern boundary where the ridge intersects. The result from the homogeneous channel model in Chapter 2 is then extended to a model whose geometry consists of a zonal channel and two partial meridional barriers along each boundary at the same longitude. Both the model transport and especially the model circulation are significantly affected by the presence of the two meridional barriers. The presence of the northern barrier always leads to a decrease in the transport. The presence of the southern barrier, however, increases the transport for a narrow ridge. The northern barrier only has a localized influence on the circulation pattern, while the southern barrier has a global influence in the channel. Then a multi-layer Q-G model is constructed by assuming that potential vorticity in all subsurface layers is homogenized. The circulation is made up of baroclinic and the barotropic part. The barotropic part is same as that in a corresponding barotropic model, and is solely determined by the wind stress, while the baroclinic part is not directly related to the wind stress. It is determined by the potential vorticity homogenization and lateral boundary conditions. The presence of the stratification does not affect the bottom topographic form drag generation. The interfacial form drag is generated by the stationary eddies. Corresponding to the circulation structure, the zonal through-channel transport associated with the barotropic circulation is determined by the wind stress and bottom topography. The other part associated with the baroclinic circulation, however, is not directly related to the wind stress and it is determined by the background stratification. Based upon the discussion on the geostrophic contour, a simple barotropic model of abyssal circulation in a circumpolar ocean basin is constructed. The presence of a supercritically high ridge is both necessary and sufficient for geostrophic flow in a β-plane channel to support a net cross-channel volume flux. In the presence of a sufficiently high ridge, the classical Stommel & Arons theory applies here, but with significant modifications. The major novelty is that a throughchannel recirculation is generated. Both its strength and direction depend critically upon the model parameters. Then, a schematic picture of the abyssal circulation in a rather idealized Southern Ocean is obtained. The most significant feature is the narrow current along the northern boundary of the circumpolar basin, which feeds the deep western boundary currents of the Indian Ocean and Pacific Ocean and connects all the oceanic basins in the Southern Ocean. Finally, the question of how the northward surface Ekman transport out of the circumpolar ocean is returned is discussed in a two-layer model with an infinitesimally thin surface Ekman layer on top of a homogeneous layer of water in a rather idealized Southern Ocean basin. First, the case with a single subtropical ocean basin is discussed. In the case with a sufficiently high ridge connecting the Antarctic and the meridional barrier, an explicit solution is found. The surface Ekman layer sucks water from the lower layer in the circumpolar basin. This same amount of water flows northward as the surface Ekman drift. It downwells in the subtropical gyre, and is carried to the western boundary layer. From there, the same amount of water flows southward as a western boundary current across the inter-gyre boundary between the circumpolar ocean and the subtropical gyre along the west coast to the southern boundary of the meridional barrier. Then, the same amount of water is carried southward and feeds the water loss to the surface Ekman layer due to the Ekman sucking in the interior circumpolar ocean. The case with multiple subtropical ocean basins such as the Southern Ocean is also discussed. It is demonstrated that the surface Ekman drift drives a strong inter-basin water mass exchange.