Abstract:
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.