![]() ![]() It depends on the interaction between flows inside and outside the harbor, which itself is part of the solution. 2 However, in the real situation, the flow into the harbor is unknown. This was later extended to a harbor with a rectangular shape by Kravtchenko and Mcnown. Mcnown 1 derived an analytical solution for a circular harbor with a small entrance at which the flow into the harbor was prescribed. When there is no ice sheet on the water surface in the harbor, there has been extensive research on interactions of external waves with internal fluid motion. Computations are first carried out for a rectangular harbor without the ice sheet to verify the methodology, and then extensive results and discussions are provided for a harbor of a more general shape covered by an ice sheet with different thicknesses and under different incident wave angles. On the interface, the orthogonal inner product is also applied to impose the continuity conditions of velocity and pressure as well as the free ice edge conditions. In the open sea outside of the harbor, through the modified Green function, the velocity potential is written in terms of an integral equation over the surface of the harbor entrance, or the interface between the two subdomains. The orthogonal inner product is adopted to impose the impermeable condition on the harbor wall, together with the edge conditions on the intersection of the harbor wall and the ice sheet. Inside the harbor, the velocity potential is expanded into a series of eigenfunctions in the vertical direction. The domain is divided into two subdomains. ![]() The linearized velocity potential theory is adopted for fluid flow, and the thin elastic plate model is applied for the ice sheet. The entrance of the harbor is open to the sea with a free surface. The shape of the horizontal plane of the harbor can be arbitrary while the sidewall is vertical. A domain decomposition method is developed to solve the problem of wave motion inside a harbor with its surface covered by an ice sheet.
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