Abstract
Details are presented of the application of the depth integrated k-ε turbulence model to predict tidal circulation in the lee of Rattray Island, Australia. Considerable emphasis has been focused on the finite difference representation of the k-ε equations, particularly in view of the serious numerical stability problems associated with the use of a standard second-order accurate central difference scheme. Several schemes have been tested, with the EXQUISITE scheme being found to give both numerically stable and accurate results. The tidal eddies predicted using the k-ε turbulence model were more structured and well-defined than those predicted using a simple mixing length model, with the velocity gradients at the perimeter of the eddy being larger for the k-ε model. Although the inclusion of the k-ε model did not significantly affect the depth mean velocity field, the eddy viscosity distribution across the domain was markedly different for the k-ε model in comparison with the mixing length model. The magnitude of the eddy viscosity was generally twice as large using the k-ε model, and the eddy viscosity gradients were much greater near to the Island tips - or separation points - and along the separation streamlines. This marked difference in the eddy viscosity structure could be particularly relevant in water quality modelling, where for neutrally buoyant solutes the turbulent diffusion coefficient is generally equated to the local eddy viscosity. The turbulent kinetic energy was shown to reduce considerably within the Island's wake, with the corresponding value remaining fairly constant in the main body of the free stream flow.
Published Version
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