Ocean waves propagating through a field of sea ice floes encounter a periodic array of scatterers. Each floe reflects, transmits, and dissipates wave energy. The marginal ice zone — the transition region between open ocean and solid pack ice — behaves as a wave filter: some frequencies transmit through the floe array while others are reflected, creating a band structure analogous to electronic bands in a crystal.
The paper applies Floquet-Bloch theory — the standard framework for waves in periodic media — to freely floating rectangular ice floes. The floes are not clamped but free to heave, pitch, and roll in response to the incident wave. The coupling between wave motion and floe motion is two-way: the wave pushes the floe, the floe re-radiates waves, and the re-radiated waves interact with neighboring floes.
The band structure reveals pass bands (frequencies that propagate through the array) and stop bands (frequencies that are exponentially attenuated). The band gaps depend on floe spacing, floe size, and ice thickness — parameters that change seasonally and with climate. The wave transmission through the marginal ice zone is not a simple exponential attenuation but a frequency-dependent filter whose characteristics are set by the ice geometry.
The practical implication: predicting wave conditions in the marginal ice zone requires knowing the ice array's periodicity, not just its average concentration. Two ice fields with the same average concentration but different floe spacing produce qualitatively different wave transmission spectra. The band structure — a concept from solid-state physics — becomes the organizing principle for ocean wave propagation in ice.