# On the attenuation of waves through broken ice of randomly-varying thickness on water of finite depth

## TL;DR

This paper extends previous models of wave attenuation through broken ice to account for water of finite depth, providing explicit formulas and validating them with numerical simulations, revealing frequency-dependent attenuation behaviors.

## Contribution

It introduces a theoretical model for wave attenuation in non-shallow water with randomly-varying ice thickness, validated by numerical simulations and applicable to real-world scenarios.

## Key findings

- Attenuation proportional to frequency to the eighth power at low frequencies
- Good agreement between theoretical predictions and numerical simulations
- Identification of a roll-over effect at higher frequencies

## Abstract

The recent work of Dafydd and Porter [2024] on the attenuation of waves propagating through floating broken ice of random thickness is extended to consider water of non-shallow depth. A theoretical model of broken floating ice is analysed using a multiple scales analysis to provide an explicit expression for the attenuation of waves as they propagate from a region of constant thickness ice into a semi-infinite region of ice whose thickness is a slowly-varying random function of distance. Theoretical predictions are shown to compare well to numerical simulations of scattering over long finite regions of ice of randomly-varying thickness computed from an approximate depth-averaged model derived under a mild-slope assumption. The theory predicts a low-frequency attenuation proportional to the eighth power of frequency and a roll-over effect at higher frequencies. The relationship between the results and field measurements are discussed.