Second-order wave diffraction forces on a vertical circular cylinder due to short-crested waves

Abstract A complete solution is presented in closed-form for the velocity potential, up to the second-order of wave amplitude, of the non-linear short-crested waves being diffracted by a vertical cylinder. The solution is found to consist of the forced waves generated from the nonhomogeneous free surface boundary condition and the scattered waves due to the presence of the cylinder. Non-uniform radiation conditions suggested by Kriebel [(1990), Nonlinear wave interaction with a vertical circular cylinder.—I. Diffraction theory. Ocean Engng 17, 345–377] are imposed at the second order to ensure the forced waves propagate towards infinity. The solution is expressed in the form of series, each term of which contains singular integrals to be evaluated numerically. With the adoption of the Hankel transform as well as other numerical techniques, the numerical convergence of the calculation of the singular integrals and the summation of the series can be speeded up; a presentation of the numerical results becomes possible. From our preliminary numerical results, the second-harmonic terms resulting from self-interaction of incident waves are found to play a very important role in determining the total second-order wave-induced forces. Our quantitative results also show that second-order forces induced by short-crested waves on a vertical circular cylinder can be quite large; the contribution of the second-order forces toward the total wave-induced forces is important and therefore should be taken into consideration in offshore engineering design and operation processes.