• Journal of Korean Society of Coastal and Ocean Engineers
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• v.12 no.4
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• pp.181-189
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• 2000

A weakly nonlinear mild-slope equation has been derived directly from the continuity equation with the aid of the Galerkin's method. The equation is combined with the momentum equations defined at the mean water level. A single component model has also been obtained in terms of the surface displacement. The linearized form is completely identical with the time-dependent mild-slope equation proposed by Smith and Sprinks(1975). For the verification purposes of the present nonlinear model, the degenerate forms were compared with Airy(1845)'s non-dispersive nonlinear wave equation, classical Boussinesq equation, andsecond¬order permanent Stokes waves. In this study, the present nonlinear wave equations are discretized by the approximate factorization techniques so that a tridiagonal matrix solver is used for each direction. Through the comparison with physical experiments, nonlinear wave model capacity was examined and the overall agreement was obtained.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.13 no.2
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• pp.149-157
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• 2001

From the weakly nonlinear mild-slope wave equations introduced by Nadaoka et al.(1994, 1997), a set of weakly nonlinear wave equations for rapidly varying topography are derived by including the bottom curvature and slope-squared tenns ignored in the original equations ofNadaoka et al. To solve the linear version of extended wave equations derived in this study one-dimensional finite difference numerical model is con¬structed. The perfonnance of the model is tested for the case of wave reflection from a plane slope with various inclination. The numerical results are compared with the results calculated using other numerical models reported earlier. The comparison shows that the accuracy of the numerical model is improved significantly in comparison with that of the original equations ofNadaoka et al. by including a complete set of bottom curva1w'e and slope¬squared terms for a rapidly varying topography.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.8 no.4
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• pp.297-304
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• 1996

The purpose of this study is to observe the applicability of parabolic mild-slope equations allowing relatively large angles of wave propagation based on the use of a Pade approximant or minimax approximation and also the applicability of the models with nonlinearity of diffracted waves in the shadow zone behind coastal structures. To accomplish these objectives, numerical solutions are obtained from the above parabolic models and are compared with the results from Watanabe and Maruyama's(1984) hydraulic model test on the wave field with an impermeable detached breakwater. From this study, it is found that computed wave heights increase for the nonlinear results in comparison to the linear results due to the increased diffraction effect across the geometric shadow boundary. The model with a larger aperture with respect to the principal direction was found to spread laterally to a much greater degree where spreading angle (diffraction effect) is relatively large. which causes a distortion in the overall results due to the error accumulated by the approximation of wave length.

• Journal of Navigation and Port Research
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• v.33 no.1
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• pp.65-70
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• 2009

The hybrid numerical model is developed by combining BEM that can calculate the wave motion rapidly under the potential theory and CADMAS-SURF that solves Navier-Stokes equations for the free surface variation near the structure, In the hybrid model the calculation of wave motion in a wide field of wave reflection for deep water area is conducted by BEM but for shallow water area by CADMAS-SURF. Especially the hybrid model can calculate random wave motions for long term period more rapidly with almost similar accuracy than the calculation of wave motion which was carried out by CADMAS-SURF only. In this study the coupling model was applied to the calculation of the strong nonlinear wave motion such as wave runup and overtopping at the coastal structure on the mild-slope bottom and the results of numerical model were compared with the Toyosima's experiments of regular wave runup and Goda's design diagram of ramdom wave overtopping, respectively.