Three-dimensional time-domain scattering of waves in the marginal ice zone

• Published in: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
• Main Authors: Meylan, M. H., Bennetts, L. G.
• Other Authors: EPSRC, Simons Foundation, US Office of Naval Research, ARC Training Centre for Advanced Technologies
• Format: Article in Journal/Newspaper
• Language: English
• Published: The Royal Society 2018
• Subjects: Sea ice
• Online Access: http://dx.doi.org/10.1098/rsta.2017.0334; https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2017.0334; https://royalsocietypublishing.org/doi/full-xml/10.1098/rsta.2017.0334

Three-dimensional scattering of ocean surface waves in the marginal ice zone (MIZ) is determined in the time domain. The solution is found using spectral analysis of the linear operator for the Boltzmann equation. The method to calculate the scattering kernel that arises in the Boltzmann model from the single-floe solution is also presented along with new identities for the far-field scattering, which can be used to validate the single-floe solution. The spectrum of the operator is computed, and it is shown to have a universal structure under a special non-dimensionalization. This universal structure implies that under a scaling wave scattering in the MIZ has similar properties for a large range of ice types and wave periods. A scattering theory solution using fast Fourier transforms is given to find the solution for directional incident wave packets. A numerical solution method is also given using the split-step method and this is used to validate the spectral solution. Numerical calculations of the evolution of a typical wave field are presented. This article is part of the theme issue ‘Modelling of sea-ice phenomena’.