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

In the polar regions, ocean wave propagation is affected by the presence of sea ice. In particular, the waves 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. This thickness variation is assumed to occur at length scales that are comparable to the wavelength but short compared to the observation scale over which the attenuation is measured. We use a multiple scale expansion and a Wigner transform to arrive at the transport equation. 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 to be due to the one-dimensional nature of our model. (C) 2019 Published by Elsevier B.V.