MCIVER, M., 1994. Second-order wave diffraction in two dimensions. Applied Ocean Research, 16 (1), pp.19-25.
A method for constructing the second-order diffraction potential associated with
two-dimensional bodies is described. By introducing analytic functions such as
the square of the first-order complex velocity and taking their real or imaginary
parts, harmonic functions are generated which are products of first-order
quantities. A particular solution for the second-order potential which satisfies the
inhomogeneous free surface condition is formed from a combination of these
harmonic functions. This particular solution is found to contain a vortex-like
term which dominates the behaviour of the second-order potential at large depths
and high frequencies. High frequency approximations to the second-order
horizontal and vertical forces are developed and compared with computations of
the full second-order forces on a semi-circular cylinder.