Homogenized scattering model of water wave attenuation in marginal ice zone

TL;DR

This paper presents a homogenized theoretical model explaining wave energy attenuation in the marginal ice zone through scattering, aligning with field observations and numerical simulations, and highlighting the influence of ice concentration and floe size.

Contribution

It introduces a homogenization approach to model wave scattering in ice-covered waters, providing a theoretical basis for exponential wave energy decay observed in the field.

Findings

Wave attenuation coefficient increases with ice concentration and wave number.

Larger floe radius and draft lead to higher wave attenuation.

The model reproduces observed tendencies in wave energy decay.

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.