Reflections on ice : scattering of flexural gravity waves by irregularities in Arctic and Antarctic ice sheets
Williams , Timothy D.C.
This thesis studies the scattering properties of different types of imperfections in large Arctic and Antarctic ice sheets. Such irregularities include cracks, pressure ridges and both open and refrozen leads. The scattering by a transition region between sea ice and a very thick ice shelf, for example as is found in the Ross Sea in Antarctica, is also treated. Methods of solution are based on applications of Green's theorem to the appropriate situation, which leads to either a single integral equation or a pair of coupled integral equations to be solved at the boundary between the ice and the sea water. Those equations over a finite interval are solved using numerical quadrature, while those over semi-infinite ranges are solved using the Wiener-Hopf method. Results calculated using different techniques are able to be checked against each other, giving us great confidence in their accuracy. In particular, the scattering by three ice sheets of different thicknesses is confirmed analytically by mode-matching coupled with the residue calculus technique. The scattering by the single irregularities is investigated partly for its own sake, and partly with the aim of using it to treat the scattering when large numbers of features are included in a single ice sheet. The principal objective of doing this is to observe the change in the general amounts of reflection and transmission as the background ice thickness is changed. There is enough variation in our results for us to conclude that there is definite potential for using the change in an incident wave spectrum after passing through a given ice field to estimate the background ice thickness.
Degree Name: Doctor of Philosophy
Degree Discipline: Mathematics & Statistics
Publisher: University of Otago
Research Type: Thesis