On the interaction of an infinite shallow draft cylinder oscillating at the free surface with a train of oblique waves

Abstract

This paper presents the practical and rigorous solution of the potential flow problem associated with the oscillation of a shallow-draft cylinder of infinite length on a free surface. The problem is three-dimensional to the extent that the amplitude of the cylinder oscillation is periodic along its axis as well as with time. The complementary problem associated with the interaction of the fixed cylinder with an incident wave train aligned at some oblique angle with respect to the cylinder axis is also treated. The use of a Green's function reduces the problem to an integral equation which is solved numerically. Numerical results are computed for pressure amplitude distributions, force coefficients, added mass and damping coefficients, transmission and reflexion coefficients and wave height ratios.