Second–order wave–diffraction by an axisymmetric body in monochromatic waves

Abstract

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 Laplace9s 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 satisfies 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.