• Journal of the Korean Society for Marine Environment & Energy
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• v.3 no.2
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• pp.49-59
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• 2000

Wave distribution in Jangjeon Harbour is numerically simulated for an optimum design of the harbour facilities. A deep-water design wave is estimated based on stochastic extreme wave analysis of wind data in the vicinity of the harbour, and it is applied to the boundary condition at open sea. Boussinesq wave theory that includes effects of frequency dispersion and nonlinearity is employed for the wave simulation. The porosity and sponge layer are adapted at beach to depict partial reflection and complete absorption of waves, respectively. The design wave for breakwater is computed in global domain with coarse grids and the wave distribution inside of wharf is simulated in local domain with fine grids.

• Water Engineering Research
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• v.1 no.4
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• pp.293-298
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• 2000

Optimal values of $\alpha$ characterizing the linear dispersion property in the modified Boussinesq equations are determined by minimizing the combined relative errors of the phase and group velocities. The value of $\alpha$ is fixed in previous studies, whereas it is varying in the present study. The phase and group velocities are calculated by using variable $\alpha$ and compared to those of the linear Stokes wave theory and previous studies. It is found that the present study produces the best match to the linear Stokes theory.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.11 no.2
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• pp.77-89
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• 1991

Based on Boussinesq equation, the parabolic approximation equation is used to analyse the propagation of shallow water waves with currents over slowly varying depth. Rip currents (jet-like) occur mainly in shallow waters where the Ursell parameter significatly exceeds the range of application of Stokes wave theory. We employ the nonlinear parabolic approximation equation which is valid for waves of large Ursell parameters and small scale currents. Two types of currents are considered; relatively strong and relatively weak currents. The wave propagating over rip currents on a sloping bottom experiences a shoaling due to the variations of depth and current velocity as well as refraction and diffraction due to the vorticity of currents. Numerical analyses for a nonlinear theory are valid before the breaking point.

• Journal of the Society of Naval Architects of Korea
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• v.39 no.1
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• pp.38-48
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• 2002

Theoretical development to generate the directional extreme waves in model basin is established based on wave focusing method. The effects of associated parameters, such as the directional range, frequency width, and center frequency, are investigated in terms of wave focusing efficiency. The two different spectral models of constant wave amplitude and constant wave slope are applied to control the wave characteristics. The wave packets simulated by theory are compared with numerical results based on Boussinesq equation and FEM. Both controls of direction and frequency spectrum are essential to focus directional waves effectively. It is noticed that wave focusing ability depends on the frequency bandwidth of spectrum rather than center frequency, and both spectral models with same parameters result in the equivalent efficiency of wave focusing.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.6 no.3
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• pp.281-289
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• 1994

An equation set of nonlinear model for regular/irregular waves presented in this study can be applied to waves travelling from deep water to shallow water, which is different from the Boussinesq equations. The presented equations completely satisfy the linear dispersion relationship and when expanded, they are proven to be consistent with the Boussinesq equation of several types. In addition, the position of averaged velocity below the still water level is estimated based on the linear wave theory.

• Bulletin of the Society of Naval Architects of Korea
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• v.24 no.2
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• pp.55-61
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• 1987

The wave system due to a moving submerged body is investigated both theoretically and numerically. Boussinesq equation, which is derived under the assumption that the effects of nonlinearity and wave dispersion are of the same order, is generalized to take the forcing agency into account. Furthermore, under the more restrive assumption that the disturbance is of higher order, inhomogeneous Korteweg-de Vries equation is derived. These equations are solved numerically to obtain the generated wave system and the wave-making resistance. These results are compared with those given by the linear theory.

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 2000.09a
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• pp.103-112
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• 2000

Early efforts to model wave transformation from offshore to inshore were based on the ray theory which accounts for wave refraction due to changes in bathymetry and the diffraction effects were ignored. Prediction of nearshore waves with the combined effects of refraction and diffraction as well as reflection has taken a new dimension with the use of the mild-slope equation and the Boussinesq equation. (omitted)

• Journal of Navigation and Port Research
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• v.27 no.5
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• pp.527-537
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• 2003

The characteristics of ship induced waves caused by navigation become widely different from both ship's speed and water depth condition. The ship induced waves specially generated in coastwise routes frequently give rise to call unforeseen danger for swimmers and small boats as well as shoreline erosion or sea wall destruction in coastal zones. The main concern of ship induced wave study until now is either how to reduce ship resistance or how to manoeuvre the ship safely under a constant water depth in the view point of shipbuilding engineers. Moreover, due to the trends for appearance of the high speed ships at the shallow coastal water, we are confronted with the danger of damages from those ship induced waves. Therefore, it is necessary to examine the development of ship induced waves and the influence of their deformation effects according to its propagation ray. In present study, in order to predict the development of the ship induced waves and their propagation under the conditions of complicate and variable shallow water depth with varying ship's speed, we constructed a computer model using Boussinesq equation with a fixed coordinate system and verified the model results by comparison with experimental results. Additionally, the model was applied under the variable water depth based on actual passage and we then confirmed the importance of the variable water depth consideration.

• Journal of Environmental Science International
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• v.1 no.2
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• pp.105.2-117
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• 1992

The formation mechanism of the vortex streets in the lee of the mountain Is Investigated by a three-dimensional numerical model. The model is based upon the hydrostatic Boussinesq equations in which the vertical turbulent momentum flux is estimated by a turbulence parameterization scheme, but the horizontal viscosity is assumed to be constant. The results show that Karman vortex streets can form even without surface friction in a constant ambient flow with uniform stratification. The vortex formation is related to breaking of the mountain wave, which depends on the Froude number (Fr). In the case of a three-dimensional bell-shaped mountain, the wave breaking occurs when Fr is less than about 0.8, while a barman vortex forms when Fr is less than about 0.22. Vortex formation also depends on Reynolds number, which is estimated from the horizontal diffusivity. The vortex formation can be explained by the wave saturation theory given by Lindzen (1981) with some modification. Simulations in this study show that in the case of Karman vortex formation the momentum flux in the lower level is much larger than the saturated momentum flux, whereas it is almost equal to the saturated momentum at the upper levels as expected from the saturation theory. As a result, large flux divergence is produced in the lower layer, the mean flow is decelerated behind the mountain, and the horizontal wind shear forms between unmodified ambient wind. The momentum exchange between the mean flow and the mountain wave is produced by the turbulence within a breaking wave. From the result, well developed vortices like Karman vortex can be formed. . The results of the momentum budget calculated by the hydrostatic model are almost the same as nonhydrostatic results as long as horizontal scale of the mountain is 10 km. A well developed barman vortex similar to the hydrostatic one was simulated in the nonhydrostatic case. Therefore, we conclude that the hydrostatic assumption is adequate to investigate the origin of the Km8n vortex from the viewpoint of wave breaking.

• Environmental Sciences Bulletin of The Korean Environmental Sciences Society
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• v.1 no.2
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• pp.105-117
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• 1997

The formation mechanism of the vortex streets in the lee of the mountain is investigated by a three-dimensional numerical model. The model is based upon the hydrostatic Boussinesq equations in which the vertical turbulent momentum flux is estimated by a turbulence parameterization scheme, but the horizontal viscosity is assumed to be constant. The results show that Karman vortex streets can form even without surface friction in a constant ambient flow with uniform stratification. The vortex formation is related to breaking of the mountain wave, which depends on the Froude number (Fr). In the case of a three-dimensional bell-shaped mountain, the wave breaking occurs when Fr is less than about 0.8, while a Karman vortex forms when Fr is less than about 0.22. Vortex formation also depends on Reynolds number, which is estimated from the horizontal diffusivity. The vortex formation can be explained by the wave saturation theory given by Lindzen (1981) with some modification. Simulations in this study show that in the case of Karman vortex formation the momentum flux in the lower level is much larger than the saturated momentum flux whereas it is almost equal to the saturated momentum at the upper levels as expected from the saturation theory. As a result, large flux divergence is produced in the lower layer, the mean flow is decelerated behind the mountain, and the horizontal wind shear forms between unmodified ambient wind. The momentum exchange between the mean flow and the mountain wave is produced by the turbulence within a breaking wave. From the result, well developed vortices like Karman vortex can be formed. The results of the momentum budget calculated by the hydrostatic model are almost the same as nonhydrostatic results as long as horizontal scale of the mountain is 10 km. A well developed Karman vortex similar to the hydrostatic one was simulated in the nonhydrostatic case. Therefore, we conclude that the hydrostatic assumption is adequate to investigate the origin of the Karman vortex from the viewpoint of wave breaking.