How a region of cracked sea ice affects ice-coupled wave propagation

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Abstract
By deriving the appropriate Green’s function, a model is developed that allows the interaction of normally-incident, ice-coupled waves with any number of cracks to be studied analytically. For a single crack a simple formula for the reflection and transmission coefficients, R and T, emerges that yields identical results to the computationally intensive work of Barrett and Squire (1996) but is much easier to apply. A crack is found to behave as a steep low-pass filter, allowing long waves through while inhibiting shorter waves, although there is also some fine structure to the response curve. The introduction of more cracks is straightforward. While in that case a formula for R and T is also possible in principle, it is easier to express the result as the solution of a simple matrix equation of order 2N, where N is the number of cracks. It is found that perfect transmission (|R| = 0) occurs at a set of discrete periods, hereinafter called a comb, for N > 1 and that the comb becomes finer as period decreases. For both periodically distributed cracks and ones that are randomly spaced, the gross shape of the response curve remains similar. The results suggest that it is improbable that waves travelling through the Arctic basin can be used as a remote-sensing agent to determine mean ice thickness. The Green’s function technique employed in this paper furnishes solutions to other problems of interest.

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