Diffusion of gravity waves by random space inhomogeneities in pancake-ice fields. Theory and validation with wave buoys and synthetic aperture radar

We study the diffusion of ocean waves by ice bodies much smaller than a wavelength, such as pancakes and small ice floes. We argue that inhomogeneities in the ice cover at scales comparable to that of the wavelength significantly increase diffusion, producing a contribution to wave attenuation comparable to what is observed in the field and usually explained by viscous effects. The resulting attenuation spectrum is characterized by a peak at the scale of the inhomogeneities in the ice cover, which could explain the rollover of the attenuation profile at small wavelengths observed in field experiments. The proposed attenuation mechanism leads to the same behaviors that would be produced by a viscous wave model with effective viscosity linearly dependent on the ice thickness. This may explain recent findings that viscous wave models require a thickness-dependent viscosity to fit experimental attenuation data. Experimental validation is carried out using wave buoy attenuation data and synthetic aperture radar image analysis.Comment: 31 pages, 7 figures; minor correction to Eq. (32