Homogenized scattering model of water wave attenuation in marginal ice zone

Abstract

A theoretical model to explain the scattering process of wave attenuation in a marginal ice zone is developed. Many field observations offer wave energy decay in the form of exponential function with distance, and this is justified through the complex wave number for the dissipation process. On the other hand, such a mechanism is not explicitly proven for the scattering process. To explain this, 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. Although our model is obtained using many simplifications, it reproduces consistent tendencies with both existing field observations and numerical simulations; the wave attenuation coefficient for the deep sea is proportional to the ice concentration and the wave number for open water waves, and the coefficient is bigger as the radius and draft of the floe become larger or the wave period is smaller.