Third-order wave diffraction by a truncated circular cylinder

Abstract

The diffraction problem for a truncated circular cylinder is formulated up to the third order referring to the wave slope. The problem is solved by means of eigenfunction expansion. The Green function suitable for the pressure distribution problem is used to give a special solution which satisfies the inhomogeneous free-surface condition in higher-order problems. The special solution is expressed by an integral over the free surface and the singularity contained in the integrand is discussed. A new method to improve the convergence of the solution is proposed, which has the advantage of simplicity compared with the previous approach. A convergence test also shows satisfactory results. The third-order wave forces are evaluated and compared with the previous results.