Amplification of Maximum Ice Bending Strain and Reduction of Wave Energy Transmission due to Sum-Frequency Triad Wave Interactions in a Finite-Length Sea Ice Sheet

Floating sea ice acts as a low-pass filter of incident wave energy from open water, allowing only long waves to penetrate far past the ice boundary. However, nonlinear sum-frequency interactions among longer waves propagating through an ice sheet transfer energy to high frequency waves which are only minimally transmitted past the leading ice edge from open water. We consider leading-order triad interactions in an ice sheet of finite length through direct numerical simulations using a modified high-order spectral (HOS) method. We demonstrate that generated higher frequency waves result in more than twice the maximum bending strain predicted by linear theory, affecting the occurrence of ice breakup, as well as an appreciable decrease in transmitted wave energy flux, modifying the understanding of wave attenuation through an aggregate ice field. The extent of these nonlinear effects is shown to depend on a parameter in terms of ice length, wavelength and steepness.