A hybrid method for linearized wave radiation and diffraction problem by a three dimensional floating structure in a polynya

Abstract

A hybrid method is developed to solve the interaction problem of wave with a three dimensional floating structure in a polynya. The linearized velocity potential theory is used for fluid flow, and the thin elastic plate model is adopted for the infinitely extended ice sheet. Because of sudden change of the upper boundary of the computational domain, namely from the ice sheet to the free surface, the domain is divided into two sub-domains, one below free surface and the other below the ice sheet. The solution method is divided into three components. The first component is the integral equation over the structure surface and the interface of the two sub-domains. In the second component, the velocity potential is expanded into a series of eigenfunctions in the vertical directions, which avoids the numerical difficulty in calculation of the fifth derivatives. This is coupled with a series of integral equations along the edge of the ice sheet. In the third component of the method, two orthogonal inner products are used to impose the continuity conditions of the velocity and pressure on the interface, as well as the boundary conditions on the ice edge. The developed method is verified through comparison with the analytical solution for a circular cylinder. Case study is then made for a FPSO in a polynya with different shapes and floating positions. The hydrodynamic coefficients, wave exciting force and wave elevation in polynya are provided and analyzed.