Linear diffraction and radiation theory of water waves by a truncated vertical circular cylinder with heave plate in deep and shallow drafts

Abstract

A first-order analytical theory on a truncated and surface-piercing vertical circular cylinder with a circular plate mounted at the bottom of the cylinder was generalized to solve the linear wave diffraction and radiation problems based on potential flow and the hypothesis of small wave and motion amplitudes. The domain was decomposed, and the linearized velocity potentials were derived in each subdomain and matched on each subdomain interface employing pressure and normal velocity continuity. The linear hydrodynamic loads obtained with the analytical method were compared with the results of linear boundary element method (BEM) solvers. Dedicated experimental campaigns were performed on fixed models with regular waves (diffraction) and then on models oscillating in surge, heave, and pitch motions without incident waves (radiation). The analytical method describes well the wave excitation loads from the experiments for small wave steepness ($H/\lambda =0.02$). The predictions of added mass and damping are shown to be applicable to the surge motion, only for small Keulegan-Carpenter numbers ($KC<1$). On the other hand, the analytically predicted radiated waves demonstrate satisfactory agreement with experiments for all motions.