Several types of flows driven by outflows on the continental shelf are examined mathematically and numerically. Within a quasigeostrophic framework, a variety of vertical structures and topographies are used. Features are explained in terms of potential vorticity conservation. The combined effects of topography and anomalous vorticity of the outflow are studied. First, shelf-like topography is considered. The role of topographic wave radiation is studied using the linearised barotropic potential vorticity equation for a weak outflow with zero vorticity. Contour dynamics is used for stronger outflows with relative vorticity. Next, the effects of anomalous vorticity in driving such coastal currents are studied using 11/2-layer model and its interaction with topography. Simulations show that the strong tendency for the development of anticyclonic eddy near topographic change. Two-layer outflows and their interaction with topography are examined. Purely buoyancy driven outflows are considered in which only one of two layers enters the flow domain. Purely barotropic outflows are also considered. Simulations show the development of eddies by interaction with topography in the lower fluid. The effect of topography whose gradient lies perpendicular to the coastline on coastal currents and eddies is investigated. The formation of dipole eddies is found to be a robust feature when the coastal current interacts with the topography depending on the sign of the topographic gradient. The stability of a two-layer converging/diverging coastal jet associated with piecewise constant potential vorticity is studied numerically. Baroclinic instability is demonstrated. The origin of the instability appears first at the coast, and may explain the meandering and eddying associated with detaching western boundary currents. The final study revisits the barotropic outflow problem. Owing to boundary layer separation at the exit, the outflow may consist of a dipolar structure. The interaction of this dipole with shelf-like topography is studied numerically.

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The turbulent mixing layer has been studied extensively in many experimental undertakings. The instability that initially drives the layer produces vortex structures, and the layer grows by their successive pairings. The transition to turbulence, triggered by such a pairing, marks a change in the characteristics of the layer, with quasi-two-dimensional structures present in the turbulent flow. Experimental evidence points to a different mechanism of growth for these structures, but its details have yet to be determined. In this project a Large Eddy Simulation code has been used to simulate spatially developing mixing layers to a high degree of accuracy. Code validation has been performed with a series of test cases relevant to mixing layer flow. The transition to turbulence in mixing layers is simulated using two different inflow conditions, and excellent agreement in predicting the mean transition location against the reference experiment is found when a physically realistic inflow is applied. The mechanism of transition observed in simulations is the same as determined in previous experimental studies. Three subgrid scale models have been used to test the sensitivity of the flow to the modelling procedure. Comparisons are made between two- and three-dimensional mixing layers, demonstrating that two-dimensional simulations are wholly insufficient to capture the essential physics of the real flow. The three-dimensional simulations also show many of the features found in the real pre-transition flow. Finally, the post-transition mixing layer is studied in detail. A fundamental change in the evolutionary nature of the layer is reported, with the coherent structures present in the post-transition region interacting in a different manner to the pre-transition vortices. The post-transition structures grow in a continuous, linear fashion over their lifetime, and interact solely as a result of their growth.

In this thesis, the behaviour of oceanic boundary layers is investigated via theoretical, numerical and laboratory studies. Some of the novel features of the next generation ocean model developed at Imperial College are tested. The process of separation of the western boundary currents is not fully understood. Over the years, there have been several theories to explain this process. However, none of these are complete and lack one or the other aspect of separation of western boundary currents. The triple-deck theory is extended to oceanography to provide a theoretical understanding for the competing effects of differential rotation and curvature. It was found that the differential rotation causes the flow to accelerate, while the curvature acts to decelerate the flow. The fate of the oceanic boundary layer lies on this competition. The Imperial College Ocean Model (ICOM) is employed to undertake numerical experi- ments to investigate the separation of western boundary currents further. The study exposes the various shortcomings of the ICOM, which as a result caused the investigation to be severely constrained. The idealised wind-driven barotropic model is used to assess some of the novel features of the ICOM and to understand the instabilities and their role on the separation of the western boundary current. Another idealised model is set-up with laboratory scales to examine the role of topography and the influence of Deep Western Boundary Current on the boundary current separation. It is found that the bottom boundary condition, the width of the continental shelf and the stratification play a significant role in boundary current separation from a sloping sidewall, in the modeled laboratory analogue. A laboratory study is undertaken to explore the energetics of a shear-driven stratified fluid in a cylinder. It is found that for moderate Richardson number, about half of the external energy is spent on mixing the fluid, while the other half goes into driving the mean flow.

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