Hydrodynamic loading and wave run-up on "elliptical" breakwaters

Abstract

This paper applies a semi-analytical solution methodology for the linear hydrodynamic diffraction induced by plane breakwaters assimilated as degenerate elliptical cylinders subjected to incident waves. The solution of the Laplace equation in elliptic coordinates for both the incident and the diffracted waves is formulated analytically in terms of the even and odd periodic and radial Mathieu functions. The employment of the socalled addition theorem for Mathieu functions is properly modified and eventually expressed in terms of the even and odd periodic and radial Mathieu functions. The main contribution herein is the calculation of the exciting forces and the wave run-up in coastal structures via a robust and fast semi-analytical solution methodology. © Copyright 2016 by the International Society of Offshore and Polar Engineers (ISOPE).