The combined refraction-diffraction of water waves on a slowly varying topography was first studied by Berkhoff(1972), who derived the elliptic mild slope equation. After that, great advances have been made in the modeling of water wave propagation pr...
The combined refraction-diffraction of water waves on a slowly varying topography was first studied by Berkhoff(1972), who derived the elliptic mild slope equation. After that, great advances have been made in the modeling of water wave propagation problems using various kind of wave equation. If waves are progressive and the deviation of the wave direction from an assumed principal direction is small, the parabolic approximation, which is more efficient than the mild slope equation, may be used. Recently, Vincent and Briggs(1989) reported hydraulic model experiments for the transformation of monochromatic and directionally-spread irregular waves passing over a submerged elliptical mound. They concluded that for the case of combined refraction-diffraction of waves by a shoal, the propagation characteristics of the irregular and equivalent regular wave conditions can be vastly different. In the present paper, the parabolic approximation model is used in order to numerically simulate the hydraulic model results of Vincent and Briggs(1989). The comparison between experimental and computational results shows that the parabolic approximation model can simulate reasonably well the transformation of directional waves.