In this paper, a domain decomposition method is developed to solve the problem of wave interaction with a frozen harbour. The linearized velocity potential theory is adopted for fluid flow and the ice sheet is modelized as a thin elastic plate. The domain is divided into two subdomains. In interior harbour, the velocity potential is expanded into series of eigenfunctions, while in exterior harbour with a free surface, the velocity potential is solved by boundary element method through a modified Green function. An inner product is introduced to impose the impermeable condition on the harbour wall, together with the edge conditions on the ice sheet. Computations are carried out for a rectangular harbour for validation and discussion.
Wave motion in a harbour is very complicated due to the fluid domain is in a confined space. However, in some cold regions, the water surface in interior harbour may be covered by ice sheet or being frozen, while in exterior harbour away from the entrance the water surface still remains open and free. In such a case, the ocean surface wave may propagate into the frozen harbour, resulting a complex interaction between ice sheet and the harbour wall.
There have been many notable works on the interactions of waves with open and free-surface harbour. Mcnown derived an analytical solution for a circular and a rectangular harbour with a small entrance respectively, where the flow at the entrance is prescribed (Kravtchenko & Mcnown, 1955; Mcnown, 1952). To simulate the real flow at the entrance, the interaction of fluid flow in interior and exterior harbour shall be considered simultaneously. Therefore, such as Hwang and Tuck (1970) used the boundary integral equation both over the harbour and coastal walls. Lee (1971) constructed a domain decomposition method to remove the integral equation on coastal wall. Extensive work focused on harbour boundaries were constructed (Hamanaka, 1997; Isaacson & Qu, 1990). Kumar, Zhang, Kim, Shi, and Yuen (2015) introduced a Chebyshev point discretization into the wave scattering in a real harbour. Shi, Li, and Wu (2018) considered a problem of an arbitrary floating body floating in harbour on three-dimensional sense, in which highly oscillatory resonance of ship motion were discussed.
