Title: Ice-fast integral equations: wave dynamics in icy seas
Sea ice transmits and absorbs mechanical energy from the ocean in the form of flexural-gravity waves. The propagation of these waves is modified by the presence of polynyas, leads, and other openings in the ice cover. To study this effect, we first consider the flexural wave problem with free plate boundary conditions. Despite the complexity of these boundary conditions, it is possible to construct an integral representation that uses the Hilbert transform to cancel singularities of layer potentials, resulting in a Fredholm second kind equation. Next, we couple the plate to an infinitely deep fluid, leading to a fourth-order integro-differential equation. We derive the Green’s function and use it to tackle the problem of polynyas, which involve much lower-order boundary conditions on the ice-free part of the surface. This problem can be reduced to a Fredholm equation defined on the polynya with the help of a unique representation that uses the bilaplacian inside of a volume potential. This versatile set of techniques sheds light on ice-ocean coupling and has the potential to enhance predictive models of sea ice dynamics.