Theoretical model for predicting the break-up 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 the present study, in which both the water part and the ice cover are treated as a continuum, each governed by its own equation of motion. The interface conditions include matching velocities and stresses between the two continua. In this study, only two modes of the dispersion relation are considered, and horizontal boundary conditions are approximated by matching mean values. The reflection and transmission coefficients are determined for simplified cases to compare with earlier theories. Behaviors of the resonance are obtained for pure elastic ice covers. The effect of viscosity is also 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 a stress failure criterion, the break-up condition of ice covers with different thickness and length under the interaction of waves and sea ice is determined. Finally, a dynamic evolution model of the ice floe size distribution function in the marginal ice zone is established. The present study is useful for modeling the wave-in-ice climate on a geophysical scale.