Effect of small floating disks on the propagation of gravity waves

TL;DR

This paper derives a dispersion relation for gravity waves in water covered by floating disks, revealing significant effects on wave damping and dispersion, with potential applications to ice-covered oceans.

Contribution

It introduces a new macroscopic model for gravity wave propagation over disk-covered water, accounting for various regimes and providing insights into wave dynamics in icy conditions.

Findings

Dramatic increase in wave damping in the close-packing regime

Orders of magnitude change in wave dispersion due to disks

Model comparison with field data supports applicability

Abstract

A dispersion relation for gravity waves in water covered by disk-like impurities embedded in a viscous matrix is derived. The macroscopic equations are obtained by ensemble-averaging the fluid equations at the disk scale in the asymptotic limit of long waves and low disk surface fraction. Various regimes are identified depending on the disk radii and the thickness and viscosity of the top layer. Semi-quantitative analysis in the close-packing regime suggests dramatic modification of the dynamics, with orders of magnitude increase in wave damping and wave dispersion. A simplified model working in this regime is proposed. Possible applications to wave propagation in ice-covered ocean is discussed and comparison with field data is provided.