Simplified estimation of wave attenuation in marginal ice zone using homogenized scattering model

Abstract

A theoretical model to explain the scattering process of wave attenuation in a marginal ice zone is proposed. Although many numerical methods have been developed to accurately estimate wave attenuation, it is not easy to incorporate this knowledge and results into practical use. Therefore, a simplified estimation method is developed here to explicitly and simply describe its fundamental mechanisms. We consider a periodic array of ice floes, where the floe is modeled by a vertical rigid cylinder. Using a homogenization technique, a homogenized free surface equivalent to the array is obtained. Then, we show that a dispersion relation of the homogenized free surface waves makes all wave numbers complex. As a result, the exponential energy decay in the scattering process is demonstrated. Under the deep water assumption, the wave attenuation coefficient is proportional to the open water’s wave number, ice concentration ratio, and imaginary part of the floe’s heave motion. To validate the proposed theory, a tank experiment was also conducted using cylindrical synthetic ice plates. Although our model is obtained under many simplifications, the theoretical results show the same tendency and order as the experimental results.