Bragg scattering of surface-gravity waves by an ice shelf with rolling surface morphology

The propagation of elastic-flexural–gravity waves through an ice shelf is modeled using full three-dimensional elastic models that are coupled with a treatment of under-shelf sea-water flux: (i) finite-difference model (Model 1), (ii) finite-volume model (Model 2) and (iii) depth-integrated finite-difference model (Model 3). The sea-water flow under the ice shelf is described by a wave equation involving the pressure (the sea-water flow is treated as a “potential flow”). Numerical experiments were undertaken for an ice shelf with ‘rolling’ surface morphology, which implies a periodic structure of the ice shelf. The propagation of ocean waves through an ice shelf with rolling surface morphology is accompanied by Bragg scattering (also called Floquet band insulation). The numerical experiments reveal that band gaps resulting from this scattering occur in the dispersion spectra in frequency bands that are consistent with the Bragg’s law. Band gaps render the medium opaque to wave, that is, essentially, the abatement of the incident ocean wave by ice shelf with rolling surface morphology is observed in the models. This abatement explains the ability of preserving of ice shelves like the Ward Hunt Ice Shelf, Ellesmere Island, Canadian Arctic, from the possible resonant-like destroying impact of ocean swell.