UBC Theses and Dissertations

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UBC Theses and Dissertations

Spectral evolution of wind generated surface gravity waves in a dispersed ice field Masson, Diane


The Marginal Ice Zone includes wide areas covered by dispersed ice floes in which wave conditions are significantly affected by the ice. When the wind blows from the solid ice pack, towards the open sea, growing waves are scattered by the floes, their spectral characteristics being modified. To further understand this problem, a model for the evolution of wind waves in a sparse field of ice floes was developed. The sea state is described by a two-dimensional discrete spectrum. Time-limited wave growth is obtained by numerical integration of the energy balance equation using the exact nonlinear transfer integral. Wave scattering by a single floe is represented in terms of far-field expressions of the diffracted and forced potentials obtained numerically by the Green's function method. The combined effect of a homogeneous field of floes on the wave spectrum is expressed in terms of the Foldy-Twersky integral equations under the assumption of single scattering. The results show a strong dependence of the spectrum amplitude and directional properties on the ratio of the ice floe diameter to the wavelength. For a certain range of this parameter, the ice cover appears to be very effective in dispersing the energy; the wave spectrum rapidly tends to isotropy, limiting its growth both for the energy content and the peak frequency. It is therefore unlikely that an offshore wind blowing over the Marginal Ice Zone would generate a significant wave field.

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