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A theoretical model to explain the scattering process of wave attenuation ina marginal ice zone is developed. Many field observations offer wave energydecay in the form of exponential function with distance, and this is justifiedthrough the complex wave number for the dissipation process. On the other hand,such a mechanism is not explicitly proven for the scattering process. Toexplain this, we consider a periodic array of ice floes, where the floe ismodeled by a vertical rigid cylinder. Using a homogenization technique, ahomogenized free surface equivalent to the array is obtained. Then, we showthat a dispersion relation of the homogenized free surface waves makes all wavenumbers complex. As a result, the exponential energy decay in the scatteringprocess is demonstrated. Although our model is obtained using manysimplifications, it reproduces consistent tendencies with both existing fieldobservations and numerical simulations; the wave attenuation coefficient forthe deep sea is proportional to the ice concentration and the wave number foropen water waves, and the coefficient is bigger as the radius and draft of thefloe become larger or the wave period is smaller.

Homogenized scattering model of water wave attenuation in marginal ice zone