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

Abstract

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 PN, where N is the number of cracks. It is found that perfect transmission (jRj 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.

Linear water wave propagation through multiple floating elastic plates of variable properties

“…Recently the crack problem has been considered by Squire and Dixon (2000) and by Williams and Squire (2002), using a Green function method applicable to infinitely deep water, and they obtained simple expressions for the reflection and transmission coefficients. Squire and Dixon (2001) extended the single crack problem to a multiple crack problem, in which the semi-infinite regions are separated by a region consisting of a finite number of plates of finite size with all plates having identical properties. This problem is very close to the one considered here, except that we allow the plate properties to be arbitrary.…”

The effect of submergence on wave scattering across a transition between two floating flexible plates

“…Interestingly, the new work has been predominantly theoretical [2], motivated by the use of more sophisticated mathematics that draws on complex variable theory, Green's functions and integral equations, and variational techniques (see, e.g., [3][4][5][6][7][8][9][10][11][12][13][14][15]). There have been no extensive field programmes to the authors' knowledge, although wave experiments have been done as parts of other programmes in both the Arctic and Antarctic and an archive of data collected in the 1980s by scientists from the Scott Polar Research Institute is also receiving some attention now that the models have become sophisticated enough to be fully tested.…”

Wave scattering by multiple floating elastic plates with spring or hinged boundary conditions

“…The method was first derived for infinite depth by Squire and Dixon [15] and for finite depth by Evans and Porter [2], both for the case of a single crack with free-edge conditions. It was extended to multiple cracks with free-edge conditions in [12].…”