By first deriving the appropriate Green's function, a model is developed that allows the interaction of ice-coupled waves with a crack to be studied analytically. Simple formulae for the reflection and transmission coefficients emerge that have not been reported before. The coefficients are found to be strongly dependent on wave period; as period is increased the reflection coefficient drops rapidly to zero, where transmission is perfect, before rising to a low maximum and then decreasing asymptotically to zero again as period is increased further. The mathematical technique employed is amenable to other problems of this type.
Vast areas of the Arctic Ocean are covered with a continuous veneer of sea ice, broken only by cracks, leads and pressure ridges. Such features, which may stretch for tens of kilometres, form when changes in the wind especially cause divergent or convergent stresses to develop in the ice sheet. The ice will crack as it is pulled apart and, if divergent stresses persist, a lead will form that may freeze over. A wind change will then produce a pressure ridge or a shear ridge. Because waves generated in the open sea are known to penetrate far into the Arctic ice cover, there has been some interest in the possibility of using waves as a tool to "remotely sense" average ice thickness. Such an idea seems plausible now because, over the last twenty years or so, sustained effort has been put into understanding how waves and sea ice in its many forms interact. (See Squire et al, 1995 for a recent review.) However, the bulk of the theories that have been developed to model waves propagating in sea ice assume that the ice behaves as a uniform plate without flaws.
