Second-Order Wave-Diffraction by an Axisymmetric Body in Monochromatic Waves

An analysis is given for the diffraction of a plane monochromatic incident gravity wave by an axisymmetric structure. The formulation is exact to second order in the sense of a Stokes expansion where wave steepness is the perturbation parameter. The problem is defined in terms of the second-order velocity potential which satisfies Laplace's equation in the fluid domain and appropriate boundary conditions. In finding the complete solution, we have decomposed the velocity potential into a particular 'locked-wave' component and a 'free-wave' component, which satisfy the inhomogeneous and homogeneous free-surface conditions, respectively. Special attention has been paid to finding a particular locked-wave component that exactly satisfied the inhomogeneous free-surface condition, this inhomogeneity being a distinguishing feature of the second order problem. A semi-analytical expression for the particular component of the second-order diffraction potential has been derived. The homogeneous component of the second-order potential is obtained by solving a boundary integral equation, using a ring-source approach. Numerical results are given for several types of fixed bodies.