2ND-ORDER WAVE DIFFRACTION IN 2 DIMENSIONS

A method for constructing the second-order diffraction potential assoc iated with two-dimensional bodies is described. By introducing analyti c functions such as the square of the first-order complex velocity and taking their real or imaginary parts, harmonic functions are generate d which are products of first-order quantities. A particular solution for the second-order potential which satisfies the inhomogenous free s urface condition is formed from a combination of these harmonic functi ons. This particular solution is found to contain a vortex-like term w hich dominates the behavior of the second-order potential at large dep ths and high frequencies. High frequency approximations to the second- order horizontal and vertical forces are developed and compared with c omputations of the full second-order forces on a semi-circular cylinde r.