Mathematical model of wave diffraction for symmetrically arranged breakwaters

Abstract

Wave diffraction is a typical problem that is encountered in breakwater construction because knowledge of diffraction behavior has important application in the design and location of breakwaters. With the rapid development of harbor, more and more unconventional layout forms of breakwaters are often encountered in actual engineering. Therefore, this paper introduces a mathematical model of regular waves diffracted by symmetrically arranged rigid and thin breakwaters with a gap, using the conformal transformation method and Green's function method; an appropriate numerical method is described to obtain the approximate analytical solutions. Wave diffraction coefficients were calculated for cases involving different incident angles of the waves, different gap widths, and the included angles between two breakwaters, and the diffraction coefficient diagrams were plotted. The results of the present mathematical model were compared with the those of previous analytical solutions. It was found that the variation trends of the present results are consistent with those of previous studies, which proves the correctness of the model. The influence of the included angle between two breakwaters on the distribution of diffraction coefficients was also analyzed. The mathematical model is unity of the Penny and Price's [“Part I. The diffraction theory of sea waves and the shelter afforded by breakwaters,” Philos. Trans. R. Soc. London 244, 236–253 (1952)] and Kirby et al.'s (1994) [“Parabolic approximations for water waves in conformal coordinate systems,” Coastal Eng. 23, 185–213 (1994)] models; it effectively overcomes the insufficient accuracy of the superposition method for cases involving oblique incidence or gap widths of less than one wavelength. Furthermore, Lamb's [ Hydrodynamics, 6th ed. (Cambridge University Press, 1932), p. 305] solution is reproduced when the ratio of the gap width to the wavelength is very small.