Wave attenuation in sea ice ($a(x)=a_0{e}^{-\alpha x}$)

Wave attenuation is a reduction of a chosen wave component as it travels through sea ice. An amplitude coefficient $\alpha$ corresponds to an energy coefficient $2\alpha$. Wave scattering at a planar interface can remove energy from the forward wave without dissipating total energy; viscous dissipation, collisions and internal ice losses irreversibly convert mechanical energy to heat.

Represent disconnected frazil ice and pancake ice as an upper layer with effective density, thickness and viscosity, rather than a continuous elastic plate. Linear Navier-Stokes equations in that layer are coupled to underlying water through velocity and stress conditions. A complex wavenumber describes both dispersion and wave attenuation in sea ice. A simpler conservative limit keeps ice mass loading but removes the elastic bending term; it does not predict viscous attenuation. The suspension model's effective viscosity is a fitted property, and a compact pancake cover need not behave like dilute frazil.

Interfaces between ice floes and open water reflect and redirect surface gravity waves. The effective attenuation depends on floe thickness, diameter, spatial arrangement and wave period. For very small diameter relative to wavelength, a floe responds nearly with the water and scatters weakly. Individual-floe interference and the number of interfaces per unit distance prevent a universal monotonic diameter law.