Coastal flows driven by vorticity

This thesis develops and applies simple models to investigate coastal flows driven by vorticity and compares these results to existing observations, experiments, numerical models and theory. Two main phenomena are considered: the generation of ocean eddies by flow separation along coastlines; and outflows into the coastal ocean from rivers and straits. In both of these cases, simple models in quasigeostrophic 1 1 2 -layer flow are developed, analysed and solved numerically. Eddies may be formed as flow separates at sharply varying topography, shedding vorticity into the main flow. Recent work by Dewar et al. [2015], Gula et al. [2015] and Molemaker et al. [2015] shows that vertical eddy diffusivity is sufficient on its own to introduce intense horizontal shear layers at sloping ocean margins. As the shear layer detaches it typically rolls up into a concentrated eddy. These shed eddies, or “sheddies”, may have significant oceanographic impacts. Here a point vortex model for the formation and evolution of these sheddies is developed based on the Brown and Michael [1954] model for two-dimensional vortex shedding, adapted to more realistically model mesoscale oceanic flow by including a deforming free surface. With a free surface, the streamfunction for the flow is not harmonic so the conformal mapping methods used in the standard Brown–Michael approach cannot be used and the problem must be solved numerically. A numerical scheme is developed based on a Chebyshev spectral method for the streamfunction partial differential equation and a second order implicit timestepping scheme for the vortex position ordinary differential equations. The results of the model are first tested and examined for the simple case of eddies shed from the tips of infinite wedges with various ambient flows, then are applied to a number of oceanographic examples. The model shows good qualitative agreement with observations and experimental and numerical results. It is applied to a number of well known cases of sheddy formation, including the Agulhas Cyclones, California Undercurrent and Canary Eddy Corridor, and also to investigate the effects of shed vorticity in the growth of the Cook Strait Eddy and the interaction of the North Brazil Current Rings with the islands of the Lesser Antilles. Outflows from rivers or through straits into the coastal ocean form distinct features which are highly important both dynamically and ecologically. Significant observational, experimental, numerical modelling and theoretical attention has been devoted to investigating the dynamics of coastal outflows, which can be highly complex due to non-linearity, the range of temporal and spatial scales, time-dependence and influencing effects including buoyancy, rotation, bathymetry, currents, tides, winds and mixing. Due to this complexity, theoretical investigations have typically focussed on one aspect or area of the flow in isolation or have developed scalings or qualitative representations of the dynamics. Here, a simple quasigeostrophic model representing an outflow as a source of constant potential vorticity fluid expelled into an initially quiescent ocean is presented. This focusses on the key dynamics: the rotation modified outflow velocity and the generation of vorticity as the buoyant fluid adjusts, and enables the full evolution to be investigated. The complex and varied results are explored in detail with contour dynamics simulations. Using a long wave approximation, analytical results, which accurately describe the outflow evolution, are derived, with the significant insight they offer and their relation to existing oceanographic studies discussed. These solutions give the form of variable width steady boundary profiles, showing for what parameters these exist or the outflow grows offshore indefinitely. It is shown that the unsteady heads leading the outflow are described by simple analytical expressions. The formation and evolution of shocks in the solution are accurately predicted and computed by analysing the long wave speed, and for simple source velocity profiles the full time-dependent solution is found. The model is extended to consider the effects of variable source strength, ambient alongshore currents, tides and winds using both contour dynamics and extensions to the long wave theory. A consideration of the momentum fluxes in the model is used to understand the turning of the current but also enables the momentum imbalance paradox of Pichevin and Nof [1997] to be resolved, showing that steady solutions are indeed possible. A new numerical scheme to compute steady profiles is developed.