Second-order wave diffraction by horizontal rectangular barriers

A complete second-order analytical solution for the nonlinear diffraction of waves by 2-D rectangular cylinders fixed at the free surface of finite-depth waters is presented. As a sequel to a previous linear treatment of the same problem, the present study revisits the nonlinear wave diffraction modelling in 2-D, in which a series of boundary value problems are built up by a classical perturbation expansion. Particular solution for the second-order potential is derived by means of a Fourier integral theorem, whilst the homogeneous second-order solution is obtained in a way similar to that of the linear problem. The present solution is validated by comparisons with experiments as well as with previous computational results of various researchers.