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Wave scattering by ice floes and polynyas of arbitrary shape

Published online by Cambridge University Press:  28 September 2010

L. G. BENNETTS  and
T. D. WILLIAMS
L. G. BENNETTS*
Affiliation:
Department of Mathematics and Statistics, University of Otago, P.O. Box 56, Dunedin 9054, New Zealand
T. D. WILLIAMS
Affiliation:
Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
*
†Email address for correspondence: lbennetts@maths.otago.ac.nz
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Abstract

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.

JFM classification

Geophysical and Geological Flows: Sea ice Waves/Free-surface Flows: Wave scattering
Type
Papers
Information
Journal of Fluid Mechanics , Volume 662 , 10 November 2010 , pp. 5 - 35
Copyright
Copyright © Cambridge University Press 2010

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