Theoretical model for predicting the breakup of ice covers due to wave ice interaction

An approximate solution for wave transmission and reflection between open water and a finite viscoelastic ice cover is developed in present study, in which both the water and the ice cover were treated as a continuum, each governed by its own equation of motion. The interface conditions included matching velocity and stresses between the two continua. The analysis is useful for modeling the wave-in-ice climate on a geophysical scale. In this study, only two modes of the dispersion relation are considered and the horizontal boundary conditions are approximated by matching the mean values. The reflection and transmission coefficients are determined for simplified cases to compare with earlier theories. Behaviors of the resonance are then obtained for a range of pure elastic ice covers. The effect of viscosity is also be investigated for viscoelastic ice covers. According to the above wave-ice interaction model, the stress and strain are calculated in the ice cover. By using the stress failure criterion, the breakup condition of ice covers with different thicknesses and lengths under the interaction of waves and sea ice is determined. Finally, a dynamic evolution model of ice floe size distribution function in the marginal ice zone is established.