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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.
Bennetts et al. (2009) studied this question.