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https://hdl.handle.net/2440/75109
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Type: | Journal article |
Title: | Wave scattering by ice floes and polynyas of arbitrary shape |
Author: | Bennetts, L. Williams, T. |
Citation: | Journal of Fluid Mechanics, 2010; 662:5-35 |
Publisher: | Cambridge Univ Press |
Issue Date: | 2010 |
ISSN: | 0022-1120 1469-7645 |
Statement of Responsibility: | L. G. Bennetts and T. D. Williams |
Abstract: | <jats:p>An efficient solution method is presented for linear and time-harmonic water-wave scattering by two classes of a three-dimensional hydroelastic system. In both cases, the fluid domain is of infinite horizontal extent and finite depth. The fluid surface is either open, except in a finite region where it is covered by a thin-elastic plate, which represents an ice floe, or fully covered by a plate, except in a finite region where it is open, which represents an ice polynya. The approach outlined herein permits the boundary between the ice-covered and free-surface fluid regions to be described by an arbitrary smooth curve. To solve the governing equations of the full three-dimensional linear problem, they are first projected onto the horizontal plane by using an approximation theory that combines an expansion of the vertical motion of the fluid in a finite set of judiciously chosen modes with a variational principle. This generates a system of two-dimensional partial differential equations that are converted into a set of one-dimensional integro-differential equations using matrices of Green's functions, which are solved numerically through an application of the Galerkin technique. A numerical results section justifies the consideration of an arbitrarily shaped boundary by comparing the response of differently shaped floes and polynyas over a range of relevant wavenumbers. Comparisons are made in terms of the magnitude and direction of the far-field scattering response, and also the maximum average curvature of the floe and the maximum wave elevation within the polynya.</jats:p> |
Keywords: | sea ice wave scattering |
Rights: | Copyright © Cambridge University Press 2010 |
DOI: | 10.1017/S0022112010004039 |
Published version: | http://dx.doi.org/10.1017/s0022112010004039 |
Appears in Collections: | Aurora harvest Mathematical Sciences publications |
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