Analytical solution for the short-crested wave diffraction by an elliptical cylinder

Abstract

The diffraction of short-crested waves around an elliptical cylinder is solved using the elliptical coordinates, and an analytical solution is obtained in terms of Mathieu and modified Mathieu functions. Analytical expressions for the pressure, the water run-up and the total wave forces on an elliptical cylinder are also derived in this study. The wave run-up of short-crested waves on an elliptical cylinder is quite different from that of a plane incident wave. The maxima and location of the wave run-up as well as the total wave forces are affected significantly by the incident angle and wave phase. Moreover, the total wave forces induced by the short-crested wave on a circular cylinder is overall smaller than that induced by the plane wave with the same wave number, but in some cases the total wave forces induced by the short-crested waves on an elliptical cylinder may be larger than that induced by the plane wave. Thus, it is necessary to take the short-crested wave forces in to account in the design of an offshore structure with elliptical cross-section.