On the oblique reflexion and transmission of ocean waves at shore fast sea ice

TLDR

A mathematical model describes oblique reflection and penetration of ocean waves into shore‑fast sea ice. The study aims to generalize the model to predict how shore‑fast ice affects an incoming directional wave spectrum by reporting the spreading function within the ice cover and its consequences for unimodal seas. An arbitrary‑depth model matches velocity potentials between open water and ice‑covered regions, solved via a preconditioned conjugate‑gradient technique to a specified precision. The model yields reflection and transmission coefficients, predicts a critical angle beyond which only evanescent modes penetrate, provides critical‑angle curves for various ice thicknesses, describes the induced strain field, and reports the spreading function within the ice cover.

Abstract

A mathematical model is reported describing the oblique reflexion and penetration of ocean waves into shore fast sea ice. The arbitrary depth model allows all velocity potentials occurring in the open water region to be matched precisely to their counterparts in the ice-covered region. Matching is done using a preconditioned conjugate gradient technique which allows the complete solution to be found to a predefined precision. The model enables the reflexion and transmission coefficients at the ice edge to be found, and examples are reported for ice plates of different thicknesses. A critical angle is predicted beyond which no travelling wave penetrates the ice sheet; in this case the deflexion of the ice is due only to evanescent modes. Critical angle curves are provided for various ice thicknesses on deep, intermediate and shallow water. The strain field which is set up within the ice sheet due to the incoming waves is also discussed; principal strains are provided as are the strains normal to the ice edge. Finally the spreading function within the ice cover, and some consequences of this function to unimodal seas with realistic open water spreading functions, are reported with the aim of generalizing the work to model the effect of shore fast ice on an incoming directional wave spectrum of specified structure.