A nonlinear wave profile correction of the diffraction of a wave by a long breakwater: Fixed point approach

The authors of the present paper have suggested an iterative scheme to calculate the nonlinear wave profiles [Jang and Kwon, 2005. Application of nonlinear iteration scheme to the nonlinear water wave problem: Stokes wave. Ocean Engineering 32, 1862-1872]. The scheme was shown to be good for estimating nonlinear wave profiles. In the study, the iterative scheme is applied to the wave-diffraction problem by a long breakwater to calculate a diffracted wave by the breakwater. The iterative solution of diffraction was compared with the linear solution of Sommerfeld, 1896. [Mathematische Theoried der Diffraction. Mathematical Annals 47, 317-374]. For a small wave slope, the two solutions were in good agreement. However, the scheme enabled us to observe the nonlinear behaviors of a beating phenomenon and of wave profile such as Stokes' wave for a relatively large wave slope: as the wave slope becomes larger, we can examine the nonlinear wave characteristics of the actual shapes of waves, i.e., the crests are steeper and the troughs are flatter. (c) 2006 Elsevier Ltd. All rights reserved.