Semi-analytical formulation for second-order diffraction by a vertical cylinder in bichromatic waves

This paper extends the exact theory for second-order wave diffraction by a vertical cylinder in monochromatic waves to the case of bichromatic incident waves. On the basis of the usual assumption of an irrotational flow, the wave-diffraction problems at second-order sum-frequencies and difference-frequencies are considered. The corresponding second-order diffraction potentials are decomposed into three parts; these are associated with the second-order incident wave, the quadratic forcing terms on the free-surface due to the first-order potential, and the linearized 'free-wave' component resulting from the boundary condition on the body surface. A semi-analytical method is presented for obtaining a particular solution which exactly satisfies the inhomogeneous free-surface condition. In the case of a bottom-seated vertical circular cylinder, complete semi-analytical expressions for the second-order sum and difference frequency potentials are derived. Numerical results for the quadratic transfer functions of the second-order force components, and the nonlinear free-surface elevation complete to second-order, are given for this case. (C) 1997 Academic Press Limited.