Wave scattering by ice floes and polynyas of arbitrary shape

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...

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Bibliographic Details
Published in:Journal of fluid mechanics 2010-11, Vol.662, p.5-35
Main Authors: BENNETTS, L. G., WILLIAMS, T. D.
Format: Article
Language:English
Subjects:
Differential equations
Earth, ocean, space
Exact sciences and technology
External geophysics
Fluid mechanics
Free surfaces
Geophysics. Techniques, methods, instrumentation and models
Ice
Physical oceanography
Physics of the oceans
Sea ice
Surface waves
wave scattering
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Summary: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.
ISSN:0022-1120
1469-7645
DOI:10.1017/S0022112010004039