2025/08/11 by Dafydd, Lloyd, Porter, Richard
#Analysis of PDEs (math.AP) #Atmospheric and Oceanic Physics (physics.ao-ph) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)
paper · doi:10.48550/arxiv.2508.20099
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.