Ocean wave transmission and reflection between two connecting viscoelastic ice covers: An approximate solution

An approximate solution for wave transmission and reflection between open water and a viscoelastic ice cover was developed earlier, 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 provided a first step towards modeling the wave-in-ice climate on a geophysical scale, where properties of the ice cover change with time and location. In this study, we derive the wave transmission and reflection from one viscoelastic material to another. 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 first determined for simplified cases to compare with earlier theories. All results show reasonable agreement when the same physical parameters are used. Behaviors of the transmission and reflection coefficients are then obtained for a range of viscoelastic covers. A mode switching phenomenon with increasing ice shear modulus is found. This phenomenon was pointed out in the study of wave propagation from open water to a viscoelastic cover. For two connecting viscoelastic covers, such mode switching is found to terminate with increasing viscosity. Together with an earlier investigation of wave dispersion in a viscoelastic ice cover, the present study provides a way to implement theoretical results in a numerical model for wave propagation through a heterogeneous ice cover. In discretizing a continuously changing ice cover over the geophysical scale, on top of the energy advection, energy transmission between computational cells due to the heterogeneity can be estimated using the present method, while the attenuation and wave speed within each cell are from the previously obtained dispersion relation. In addition, on floe scales, this study provides a way to determine wave scattering from an ice floe imbedded in grease or brash ice.