A collection of wet beam models for wave–ice interaction

Abstract

Theoretical models for the prediction of decay rate and dispersion process of gravity waves traveling into an integrated ice cover expanded over a long way are introduced. The term “wet beam” is chosen to refer to these models as they are developed by incorporating water-based damping and added mass forces. Presented wet beam models differ from each other according to the rheological behavior considered for the ice cover. Two-parameter viscoelastic solid models accommodating Kelvin–Voigt (KV) and Maxwell mechanisms along with a one-parameter elastic solid model are used to describe the rheological behavior of the ice layer. Quantitative comparison between the landfast ice field data and model predictions suggests that wet beam models, adopted with both KV and Maxwell mechanisms, predict the decay rate more accurately compared to a dry beam model. Furthermore, the wet beam models, adopted with both KV and Maxwell mechanisms, are found to construct decay rates of disintegrated ice fields, though they are built for a continuous ice field. Finally, it is found that wet beam models can accurately construct decay rate curves of freshwater ice, though they cannot predict the dispersion process of waves accurately. To overcome this limitation, three-parameter solid models, termed standard linear solid (SLS) mechanisms, are suggested to be used to re-formulate the dispersion relationship of wet beam models, which were seen to construct decay rates and dispersion curves of freshwater ice with an acceptable level of accuracy. Overall, the two-parameter wet beam dispersion relationships presented in this research are observed to predict decay rates and dispersion process of waves traveling into actual ice covers, though three-parameter wet beam models were seen to reconstruct the those of freshwater ice formed in a wave flume. The wet beam models presented in this research can be implemented in spectral models on a large geophysical scale.