Diffraction of Cnoidal Waves Around a Large Vertical Elliptical Cylinder

Abstract

Based on the cnoidal wave theory, an analytical solution for the diffraction of cnoidal incident wave around a large elliptical cylinder in shallow water is derived in elliptical coordinates. Accordingly, the analytical expressions for the pressure and wave forces are obtained. In order to validate the analytical model, a numerical model for the diffraction of cnoidal incident wave around a large cylinder with an arbitrary cross-section is also developed using finite element method, where the whole fluid domain is divided into bounded and unbounded domain. The exact artificial boundary condition is introduced to model the unbounded domain. The proposed numerical model is used to verify the present analytical solution for the cnoidal incident wave forces on the elliptical cylinder. Based on the present analytical solution, the detailed analysis on the cnoidal wave forces on elliptical cylinders are performed. It is found that the maximum dimensionless wave forces obtained by cnoidal wave theory are obviously larger than those obtained by small amplitude wave theory. Therefore, ocean engineers should consider the cnoidal wave forces in the design offshore structures with an elliptical cross-section in shallow water.