Effect of small floating disks on the propagation of gravity waves

A dispersion relation for gravity waves in water covered by disk-like impurities floating in a viscous matrix is derived. The macroscopic equations are obtained ensemble-averaging the fluid equations at the disk scale in the asymptotic limit of long waves and low disk surface fraction. Various regimes have been 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 order of magnitude increase in wave damping and wave dispersion. Possible relevance of the results to wave propagation in ice-covered ocean is discussed, and comparison with field data is provided.