ON THE 2ND-ORDER WAVE RADIATION OF AN OSCILLATING VERTICAL CIRCULAR-CYLINDER IN FINITE-DEPTH WATER

A vertical circular cylinder which is in periodic oscillatory motion w ith small amplitudes in finite depth is considered. The usual assumpti ons necessary for the potential Row stand valid in the present study. A classical perturbation procedure is employed to solve the nonlinear problem through the second-order. According to the solution method pre sented, the fluid domain is separated into interior and exterior regio ns in which boundary-value problems (BVP) are decomposed into two BVPs each having one nonhomogeneous boundary condition. A nonhomogeneous s econd-order free-surface condition is treated by means of a modified f orm of Weber's integral theorem. Eigenfunction expansions are used for homogeneous solutions. Thus, to conclude the solution, the exterior a nd interior solutions are then matched on the common boundary. Numeric al results are given for a heaving vertical circular cylinder. Wave fi eld analysis around a vertical cylinder shows that the second-order wa ve pattern is typically dominated by the second-order wave number rela ted to the second-order dispersion relation. The procedure also satisf ies the conditions at infinity through the second-order.