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Harbour modelling and resonances

By Cassandra Moran

Abstract

This dissertation considers the behaviour of water waves within a harbour. The problem is motivated by both real world applications as well as being of interest from a purely abstract mathematical perspective. The harbour is modelled as a simple rectangular domain which is partially open on one side to the ocean. Techniques used in previous work on wave diffraction around a breakwater are adopted, and Partial Differential Equation and Integral Equation methods are used to formulate the equations describing the wave field within and outside of the harbour. The governing integral equation that is formed is solved numerically using Galerkin’s method, and graphical representations of the wave field are plotted. The effects of variations in the angle of the incident wave, and the wave number are analysed. In particular the phenomenon of harbour resonance is investigated, focusing on what wave numbers cause a resonant effect, but also examining the effect of changes in the incident wave angle, the size of the opening onto the ocean, and the dimensions of the harbour. i i

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Year: 2008
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