Ocean wave transmission and reflection by viscoelastic ice covers

Modeling ice covers as viscoelastic continua, Zhao and Shen, (2013) applied a two-mode approximate method to determine the transmission and reflection between two different ice covers. This approximate solution considered only two modes of the dispersion relation. In addition, the horizontal boundary conditions were simplified by matching mean values over the interfaces. In this study, we employ a variational method (Fox and Squire, (1990)) to calculate the wave transmission and reflection from two connecting viscoelastic ice covers of different properties. The variational approach minimizes the overall error function at the interface of two ice covers, hence is more rigorous than the previous approximate method that minimized the difference between mean values at the interface. The effect of additional travelling and evanescent modes are also investigated. We compare results from different matching methods, as well as the effects of including additional modes. From this study, we find that additional modes do not always improve the results for our model. For all cases tested, two modes appear to be sufficient. These two modes represent the open-water-like and the elastic-pressure wave-like behavior. The two-mode approximate method and the variational method have similar results except at very short wave periods. (C) 2015 Elsevier Ltd. All rights reserved.