Abatement of ocean-wave impact by an ice shelf with rolling surface morphology

The propagation of elastic-flexural waves through an ice shelf is modeled by a full 3-D finite-difference elastic model that is coupled to a treatment of under-shelf sea-water motion. The sea water motion is described by a wave equation involving the pressure, and couples to the elastic motions of the ice through the pressure at the ice/water interface. Numerical experiments show that "rolling" surface morphology of the ice shelf, a distinctive feature of Arctic ice shelves along Ellesmere Island, can have a profound effect on how elastic-flexural waves propagate through the system. The experiments show that rolling surface morphology produces Bragg scattering (also called Floquet band insulation) that is potentially effective in preventing an incident wave from entering the ice shelf and causing subsequent fracture damage. The numerical results show frequency band gaps (band insulation) that are consistent with the Bragg's law. The numerical results further show that these band gaps render the ice shelf/ocean system opaque to wave propagation with frequencies that fall within the range of the band gaps. By abating incident ocean wave activity, the rolling surface morphology inadvertently provides a fitness to the ice shelf that protects it from damage. This abatement may explain how multiyear sea ice in the Arctic Ocean along the coast of Ellesmere Island can be sufficiently stable and long-lived to evolve into the ice-shelf, once contiguous along the Ellesmere Island coast, reported by European and American explorers in the late 19th and early 20th centuries.