Modelling free-surface flow with bathymetry variation using spectral methods

• Main Author: Parkinson, Steven
• Published: University of Bristol 2011
• Subjects: 551.464011
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.570859

Generation of electricity, by harnessing tidal currents with turbines, has the potential to contribute to a more sustainable future. However, knowledge of the fluid velocity, at a certain depth, is required in order to predict the available energy resource. Therefore, a modelling framework is described, which is computationally efficient, with only a few tunable parameters, and yields good results in comparison to experimental work and computational fluid dynamics. Existing approximate analysis methods, which describe fluid flow over varying topography are discussed. It is found that these theories are incapable of satisfying our objective. From field measurements of a tidal channel, a model is developed that describes turbulent free-surface flow over varying bathymetry. The flow is modelled using the steady incompressible two- dimensional shallow water equations. Turbulence closure is achieved using the eddy-viscosity model. The equations are solved using spectral methods. Convergence of the method is tested by varying the number of modes and the mixing parameterisation. A comparison with experimental work and a regional scale ocean circulation model, for free-surface flow over a ridge, is made. Close agreement is found using pseudo spectral methods. The Galerkin method does not achieve the same level of accuracy. In addition, numerical instability is found to occur on the downstream face of the ridge. However, provided the bathymetry gradients are sufficiently shallow, the solution procedure performs well. A three-dimensional model is achieved by calculating the two-dimensional depth-averaged flow through a tidal channel. Upon calculation of the streamlines from the depth-averaged flow solution, the vertical structure of the flow is calculated. The full flow profile can be obtained by piecing together outputs from each streamline. This is then compared to a one-dimensional hydraulic model where good agreement is found. Finally, flow for a real channel is computed.