Three-layer viscoelastic model with eddy viscosity effect for flexural-gravity wave propagation through ice cover

A three-layer model is presented to simulate gravity wave propagation in an ice-covered sea. Damping from a viscoelastic ice cover and the boundary layer of the water body are considered. This model is shown to converge to three previous models: viscoelastic ice over inviscid water, thin elastic plate over viscous water, and viscous ice over viscous water. The non-monotonic attenuation with respect to the wave period shown previously in the thin elastic plate over viscous water also appears in the proposed model. Sensitivity analysis indicated no significant influence of the thickness of the boundary layer modeled with an eddy viscosity on either the wave dispersion or the attenuation, but a significant effect on wave attenuation from the eddy viscosity. Based on a consistent formulation for a three-layer system, we provide a compact model that combines dissipation from the ice cover and the boundary layer underneath, as well as the associated wave dispersion.