Wave–current interaction on a vertical truncated cylinder floating in finite-depth waters

Abstract

A new method is developed for solving the diffraction problem around a fixed truncated circular cylinder which is exposed to the action of coexisting wave and current fields with a small but finite current velocity. Linear potential theory is applied and the solution is obtained by using a perturbation expansion for the diffraction potential with respect to the normalized current speed. Because of the axisymmetric geometrical configuration of the examined body, a semi-analytical formulation is used for the treatment of the inhomogeneous free-surface boundary condition involved in the hydrodynamic problem formulation for derivation of the associated perturbation potential. This method results in a Sturm–Liouville problem, which requires the construction of the appropriate Green’s function. The hydrodynamic forces are obtained after evaluation of the pressure field around the cylinder. The calculated results compare very well with numerical predictions of other investigators and existing experimental data. Finally, the mean second-order drift forces are calculated by superposing on to their zero-current values the corresponding current-dependent first-order corrections, the latter being evaluated using a ‘heuristic’ approach.