• Journal of Korea Water Resources Association
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• v.32 no.4
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• pp.447-455
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• 1999

In this study, the Bragg resonant of cnoidal waves propagating over a sinusoidally varying topography lying on a uniformly sloping beach is investigated. The governing equations derived from the Boussinesq equations are numerically integrated. The effects of fast varying terms and nonlinearity in reflection coefficients are also examined. Variation of reflection coefficient for different sloping beaches is studied. It is found that reflection coefficients are not strongly dependent on slopes of beaches.

• Journal of Korea Water Resources Association
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• v.32 no.6
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• pp.649-655
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• 1999

The maximum run-up heights of periodic waves are numerically investigated in this study. Incident waves are sinusoidal and enoidal waves. The maximum run-up height of enoidal wave approaches that of sinusoidal wave as the wave length decreases, while it approaches that of solitary wave as the wave length increases. If wave height is fixed, the maximum run up heights of enoidal waves are always greater than those of sinusoidal waves but smaller than those of solitary waves.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.15 no.2
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• pp.80-85
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• 2003

This paper describes the generation and maximum run-up heights of cnoidal waves with varying periods by the numerical model. The model solves the Reynolds equations and the k-epsilon equations for the turbulent analysis. To track free surface displacements, the volume of fluid(VOF) method is employed. It is shown that profiles of the numerically generated cnoidal waves agree well with analytical solutions. The computed maximum run-up heights are compared with laboratory measurements and those of the boundary element method. The present model provides more agreeable results to laboratory measurements that the boundary element model.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.14 no.4
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• pp.274-281
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• 2002

Numerical analysis for the Bragg reflection due to a sinusoidally and a doubly-sinusoidally varying seabeds was performed by using a couple of ordinary differential equations derived from the Boussinesq equations. Incident waves are a train of cnoidal waves. The effects of the dispersion and shape of seabed were investigated. It is shown that the reflection of a sinusoidally varying seabed is enhanced by increasing the dispersion and the amplitude of a seabed. The reflection of waves over a doubly-sinusoidally varying seabed can also be enhanced by increasing the amplitude of seabed decreasing the difference of wave numbers of seabed components.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.8 no.1
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• pp.44-51
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• 1996

The accurate calculation of run-up heights of long waves along the coastline is important in the view of engineering. In this paper the run-up heights of long waves are estimated by using the cnoidal wave theory which also covers both sinusoidal and solitary waves. However, the generation and the calculation of run-up heights of cnoidal waves are difficult both in laboratory and numerical experiments. In this study, the maximum run-up heights of cnoidal waves on steep slopes are computed by using the boundary integral equation model. It has been shown that the run-up heights of cnoidal waves are less than those of solitary waves, while they are larger than those of sinusoidal waves having the same wavelengths and heights. The variation of run-up heights of cnoidal waves is not a monotonic function of the wavelength. However, the run-up heights of cnoidal waves asymptotically approach that of a solitary wave as the wavelength approaches infinity. The calculated run-up heights agreed reasonably with experimental data.