A transport equation for flexural-gravity wave propagation under a sea ice cover of variable thickness

Wave Motion (2019)

https://www.sciencedirect.com/science/article/abs/pii/S0165212518302634?via%3Dihub

Polar waves in the presence of sea ice are observed to attenuate exponentially due to scattering and dissipative effects. Here we derive a transport equation and the associated attenuation coefficient for linear ocean wave packets in one horizontal dimension due to scattering only, assuming that the ocean is covered with ice of spatially varying thickness.Using a multiple scale expansion and a Wigner transform, we find that the resulting attenuation coefficient generally overestimates the attenuation that we expect to see in a real ice-covered ocean. We argue that this is likely due to the one-dimensional nature of our model.