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

The work of Dafydd and Porter (Attenuation of long waves through the regions of irregular floating ice and bathymetry. J Fluid Mech 2024;996:A43) on the attenuation of waves propagating through floating broken ice of random thickness is extended to consider the water of non-shallow depth. A theoretical model of broken floating ice is analyzed using a multiple scale 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 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 is discussed.