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Wave scattering by multiple rows of circular ice floes

  • L. G. BENNETTS (a1) and V. A. SQUIRE (a1)

Abstract

A three-dimensional model of ocean-wave scattering in the marginal ice zone is constructed using linear theory under time-harmonic conditions. Individual floes are represented by circular elastic plates and are permitted to have a physically realistic draught. These floes are arranged into a finite number of parallel rows, and each row possesses an infinite number of identical floes that are evenly spaced. The floe properties may differ between rows, and the spacing between the rows is arbitrary.

The vertical dependence of the solution is expanded in a finite number of modes, and through the use of a variational principle, a finite set of two-dimensional equations is generated from which the full-linear solution may be retrieved to any desired accuracy. By dictating the periodicity in each row to be identical, the scattering properties of the individual rows are combined using transfer matrices that take account of interactions between both propagating and evanescent waves.

Numerical results are presented that investigate the differences between using the three-dimensional model and using a two-dimensional model in which the rows are replaced with strips of ice. Furthermore, Bragg resonance is identified when the rows are identical and equi-spaced, and its reduction when the inhomogeneities, that are accommodated by the model, are introduced is shown.

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Corresponding author

Email address for correspondence: lbennetts@maths.otago.ac.nz

References

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Bennetts, L. G., Biggs, N. R. T. & Porter, D. 2007 A multi-mode approximation to wave scattering by ice sheets of varying thickness. J. Fluid Mech. 579, 413443.
Bennetts, L. G., Biggs, N. R. T. & Porter, D. 2009 a The interaction of flexural-gravity waves with periodic geometries. Wave Mot. 46, 5773.
Bennetts, L. G., Biggs, N. R. T. & Porter, D. 2009 b Wave scattering by an axisymmetric ice floe of varying thickness. IMA J. Appl. Math. 74, 273295.
Bennetts, L. G. & Squire, V. A. 2009 Linear wave forcing of an array of axisymmetric ice floes. IMA J. Appl. Math. In press.
Cavalieri, D. J., Parkinson, C. L. & Vinnikov, K. Y. 2003 30-year satellite record reveals contrasting Arctic and Antarctic decadal sea ice variability. Geophy. Res. Lett. 30 (18). DOI: 10.1029/2003GL018031.
Chamberlain, P. G. & Porter, D. 1995 Decomposition methods for wave scattering by topography with application to ripple beds. Wave Mot. 22, 201214.
Chou, T. 1998 Band structure of surface flexural-gravity waves along periodic interfaces. J. Fluid Mech. 369, 333350.
Dixon, T. W. & Squire, V. A. 2001 Energy transport in the marginal ice zone. J. Geophys. Res. 106, 1991719927.
Kohout, A. L. & Meylan, M. H. 2008 An elastic plate model for wave attenuation and ice floe breaking in the marginal ice zone. J. Geophys. Res. 113, C09016. DOI: 10.1029/2007JC004434.
Kohout, A. L., Meylan, M. H., Sakai, S., Hanai, K., Leman, P. & Brossard, D. 2007 Linear water wave propagation through multiple floating elastic plates of variable properties. J. Fluids. Struct. 23 (4), 649663.
Linton, C. 1998 The Green's function for the two-dimensional Helmholtz equation in periodic domains. J. Engng Math. 33, 377402.
Linton, C. M. & Thompson, I. 2007 Resonant effects in scattering by periodic arrays. Wave Mot. 44 (3), 165175.
McPhedran, R. C., Botten, L. C., Asatryan, A. A., Nicorovici, N., Robinson, P. & Sterke, C. M. D. 1999 Calculation of electromagnetic properties of regular and random arrays of metallic and dielectric cylinders. Phys. Rev. E 60 (6), 76147617.
Meylan, M. H. & Masson, D. 2006 A linear Boltzmann equation to model wave scattering in the marginal ice zone. Ocean Model. 11, 417427.
Peter, M. A. & Meylan, M. H. 2004 Infinite depth interaction theory for arbitrary floating bodies applied to wave forcing of ice floes. J. Fluid Mech. 500, 145167.
Peter, M. A. & Meylan, M. H. 2007 Water-wave scattering by a semi-infinite periodic array of arbitrary bodies. J. Fluid Mech. 575, 473494.
Porter, R. & Porter, D. 2001 Interaction of water waves with three-dimensional periodic topography. J. Fluid Mech. 434, 301335.
Rothrock, D. A., Yu, Y. & Maykut, G. A. 1999 Thinning of the Arctic sea-ice cover. Geophys. Res. Lett. 26 (23), 34693472.
Serreze, M. C., Holland, M. M. & Stroeve, J. 2007 Perspectives on the Arctic's shrinking sea-ice cover. Science 315 (5818), 15331536. DOI: 10.1126/science.1139426.
Squire, V. A. 2007 Of ocean waves and sea-ice revisited. Cold Reg. Sci. Technol. 49, 110133.
Squire, V. A., Dugan, J. P., Wadhams, P., Rottier, P. J. & Liu, A. K. 1995 Of ocean waves and sea ice. Annu. Rev. Fluid Mech. 27, 115168.
Wadhams, P., Squire, V. A., Ewing, J. A. & Pascal, R. W. 1986 The effect of the marginal ice zone on the directional wave spectrum of the ocean. J. Phys. Oceanogr. 16 (2), 358376.
Wadhams, P., Squire, V. A., Goodman, D. J., Cowan, A. M. & Moore, S. C. 1987 The attenuation of ocean waves in the marginal ice zone. J. Geophys. Res. 93 (C6), 67996818.
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Wave scattering by multiple rows of circular ice floes

  • L. G. BENNETTS (a1) and V. A. SQUIRE (a1)

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