Abstract
The entry of ocean waves from the open sea into pack ice is a feature of the marginal ice zone which has important consequences for navigation and the construction of offshore structures in ice-infested seas. In turn it is largely the action of waves which creates the marginal ice zone as it is the wave action which is responsible for the floe size distribution within the ice cover.
In this thesis a two-dimensional model for the behaviour of a single ice floe in ocean waves is developed using a Green's function formulation. This model allows us to calculate the reflection and transmission coefficients of a single floe. It predicts that there will be frequency-dependent critical floe lengths at which the reflection is zero, analogous to electromagnetic wave propagation through a homogeneous slab. It is also found that floe bending increases as a function of floe length until a critical length is reached, above which the strain is essentially constant. The model
is successfully validated, at least for elastic sheets floating on water, by experiments performed on a polypropylene sheet. The single floe theory may also be synthesized approximately by an extension of the model developed by Fox and Squire [1990, 1991] for the interaction of waves with a semi-infinite sheet. This acts as an independent check on both theories.
The solution for a single floe may be extended to many floes as a full solution or as an approximate solution. It is shown that the approximate solution is sufficiently accurate in nearly all situations. This allows the development of a simple model for ocean wave propagation through a cover composed of many discrete floes. This model predicts that a field of pack ice will low pass filter incoming ocean waves. The model also predicts that there will be a narrowing of directional spectra with propagation through an ice cover.
Finally the model is extended so that the surge response, a frequently measured property of ice floes, may be predicted. The surge response agrees with that found by Rattier [1992] and is a strong function of floe length.
A different model for the motion of a single floe developed by Shen and Ackley [1991] is also investigated. This model is applicable to small ice floes and is related to Morrisons equation which is used extensively in problems of offshore structures. The Shen and Ackley model is shown to predict that in most physical cases all floes will tend to the same drift velocity which will be a function almost exclusively of wave amplitude.