Journal Article

Wave scattering by an axisymmetric ice floe of varying thickness

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

in IMA Journal of Applied Mathematics

Published on behalf of Institute of Mathematics and its Applications

Volume 74, issue 2, pages 273-295
Published in print April 2009 | ISSN: 0272-4960
Published online July 2008 | e-ISSN: 1464-3634 | DOI: http://dx.doi.org/10.1093/imamat/hxn019
Wave scattering by an axisymmetric ice floe of varying thickness

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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

Journal Article.  0 words. 

Subjects: Applied Mathematics

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