This thesis considers the scattering of small amplitude water waves, obliquely incident on a set of floating elastic plates occupying the entire water surface. The problem is twodimensional and assumes invariance in the width of the plates. All non-linear physical effects are neglected. The plates are floating on a body of water of finite depth and each plate has uniquely defined properties. The problem is formulated by imposing boundary conditions on the eigenfunction expansion of Laplace’s equation. A set of transmission and reflection coefficients is generated, which is solved by applying the edge conditions and matching at each plate boundary. We label this solution method the Matched Eigenfunction Expansion Method (MEEM). The problem is solved for a variety of edge conditions including free, clamped, sliding, springed and hinged. To verify the MEEM results, the problem is also solved using a Green Function Method. The convergence of the two methods is compared and found to be almost identical. The MEEM is used to simulate wave–ice interaction in the Marginal Ice Zone (MIZ). The model removes the resonance effects and predicts that the transmitted energy is independent of floe length, provided the wavelength is more than three times the floe length. The model predicts an exponential decay of wave energy with distance of propagation through the MIZ, which agrees with experimental findings. The results have been summarised in a graph with the attenuation coefficient expressed as a function of period for various floe thicknesses. We also provide an estimate of the attenuation coefficient using an approximation theory. The displacements of the MEEM are compared against a series of laboratory experiments performed in a two-dimensional wave-tank and show good agreement. The attenuation model results are compared against a series of field experiments carried out in the Arctic and off the West Antarctic Peninsula. Generally, the decay rates of the model agree well with the field experiments in diffuse ice. We suggest that factors other than wave scatter are relevant in models of wave-attenuation in non-diffuse ice.
| Identifer | oai:union.ndltd.org:ADTP/275509 |
| Date | January 2008 |
| Creators | Kohout, Alison L. |
| Publisher | ResearchSpace@Auckland |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
| Rights | Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated., http://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm, Copyright: The author |
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