Triad Interactions among Surface Waves Propagating through an Ice Sheet

Abstract

We study nonlinear resonant wave-wave interactions which occur when ocean waves propagate into a thin floating ice sheet. Using multiple-scale perturbation analysis verified against regular perturbation for short distances past the ice edge, we obtain theoretical predictions of the wave amplitude evolution as a function of distance travelled past the ice edge for a semi-infinite ice sheet. We relate the amplitude evolution to ice bending strain, related to ice breakup. We show that, due to sum-frequency interactions, the maximum strain in the ice sheet can be more than twice that predicted by linearized theory. We further demonstrate that difference-frequency interactions also can result in a moderate strain increase compared to the linear result despite transferring energy to longer wave components. This work has implications to understanding the occurrence of ice breakup and the resulting ice floe size distribution.