A novel solution to the second-order wave radiation force on an oscillating truncated cylinder based on the application of control surfaces

Abstract

A truncated cylinder in harmonic oscillation with a small amplitude at a finite water depth is considered. A perturbation procedure is applied to analyse the wave radiation problem up to the second order in frequency domain. The technique of control surfaces is used to overcome the difficulty associated with the singularity of the fluid velocity at the corner, and a novel solution to the double-frequency wave radiation force on a surging/heaving truncated cylinder is developed. The proposed solution achieves an obvious advantage in that the calculation of the singular terms owing to the singularity of the fluid velocity at a sharp corner is avoided. After examining the convergence and validity of the proposed model, numerical studies are conducted. Numerical results reveal that the force component associated with the body-surface forcing term predominates among the various force components of the total double-frequency wave radiation force. In addition, the force component from the quadratic products of the first-order quantities is in general out-of-phase with the one associated with the body-surface forcing term.