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IMA Journal of Applied Mathematics Advance Access originally published online on July 24, 2008
IMA Journal of Applied Mathematics 2009 74(2):273-295; doi:10.1093/imamat/hxn019
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© The Author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Wave scattering by an axisymmetric ice floe of varying thickness

Luke G. Bennetts{dagger}, Nicholas R. T. Biggs and David Porter

Department of Mathematics, The University of Reading, P.O. Box 220, Whiteknights, Reading RG6 6AX, UK

{dagger} Email: lbennetts{at}maths.otago.ac.nz

Received on January 30, 2008; Revision received January 30, 2008. Accepted on May 30, 2008

The problem of water wave scattering by a circular ice floe, floating in fluid of finite depth, is formulated and solved numerically. Unlike previous investigations of such situations, here we allow the thickness of the floe (and the fluid depth) to vary axisymmetrically and also incorporate a realistic non-zero draught. A numerical approximation to the solution of this problem is obtained to an arbitrary degree of accuracy by combining a Rayleigh–Ritz approximation of the vertical motion with an appropriate variational principle. This numerical solution procedure builds upon the work of Bennets et al. (2007, J. Fluid Mech., 579, 413–443). As part of the numerical formulation, we utilize a Fourier cosine expansion of the azimuthal motion, resulting in a system of ordinary differential equations to solve in the radial coordinate for each azimuthal mode. The displayed results concentrate on the response of the floe rather than the scattered wave field and show that the effects of introducing the new features of varying floe thickness and a realistic draught are significant.

Keywords: sea ice; wave scattering.


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