• Journal of Korean Society of Coastal and Ocean Engineers
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• v.19 no.4
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• pp.355-360
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• 2007

The process of the nonlinear shallow water wave transformation in a basin of a constant depth is studied. Characteristics of the first breaking of the wave are analyzed in details. The Fourier spectrum and steepness of the nonlinear wave are calculated. It is shown that the spectral amplitudes can be expressed using the wave front steepness, which allows the practical estimations.

• 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 Ocean Engineering and Technology
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• v.14 no.1
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• pp.1-5
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• 2000

A numerical analysis for wave motion in the shallow water is presented. The method is based on potential theory. The fully nonlinear free surface boundary condition is assumed in an inner domain and this solution is matched along an assumed common boundary to a linear solution in outer domain. In two-dimensional problem Cauchy's integral theorem is applied to calculate the complex potential and its time derivative along boundary.

• Ocean and Polar Research
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• v.37 no.1
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• pp.1-9
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• 2015

An approach based on the combined use of a 2D shallow water model and analytical 1D long wave run-up theory is proposed which facilitates the forecasting of tsunami run-up heights in a more rapid way, compared with the statistical or empirical run-up ratio method or resorting to complicated coastal inundation models. Its application is advantageous for long-term tsunami predictions based on the modeling of many prognostic tsunami scenarios. The modeling of the Chilean tsunami on February 27, 2010 has been performed, and the estimations of run-up heights are found to be in good agreement with available observations.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1995.10a
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• pp.250-257
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• 1995

The properties of Tuned Liquid Damper are investigated theoretically. In this study, numerical model is a nonlinear model for a rectangular TLD under horizontal motion on the basis of the shallow water wave theory, where the damping of the liquid motion is included semianalytically. For TLD subjected to harmonic external force, the liquid motion of TLD is simulated. Analysis result is showed that liquid motion in TLD is strongli nonlinear even under small excitation.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.6 no.1
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• pp.61-71
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• 1994

A modified method obtained by expanding Longuet-Higgins and Stewart's method (1964) is proposed. which can easily derive the group-bountied long wave due to the irregular were group as well as the regular wave group. The result of the proposed method agree well with those of both second order nonlinear theory and radiation stress theory. Particularly in the shallow water region, three equations from the proposed method, the second order nonlinear theory and the radiation stress theory become identical.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.53-65
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• 2003

Here we present a study of small-amplitude, shallow water waves on sloping beds. The beds considered in this analysis are linear and quadratic in nature. First we start with stating the relevant governing equations and boundary conditions for the theory of water waves. Once the complete prescription of the water-wave problem is available based on some assumptions (like inviscid, irrotational flow), we normalize it by introducing a suitable set of non-dimensional variables and then we scale the variables with respect to the amplitude parameter. This helps us to characterize the various types of approximation. In the process, a summary of equations that represent different approximations of the water-wave problem is stated. All the relevant equations are presented in rectangular Cartesian coordinates. Then we derive the equations and boundary conditions for small-amplitude and shallow water waves. Two specific types of bed are considered for our calculations. One is a bed with constant slope and the other bed has a quadratic form of surface. These are solved by using separation of variables method.

• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.4_1
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• pp.137-150
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• 1992

A complete solution, exact to second-order, for wave motion forced by a hinged-wavemaker of variable-draft is presented. A solution for a piston type wavemaker is also obtained as a special case of a hinged-wavemaker. The laboratory waves generated by a plane wave board are shown to be composed of two components; viz., a Stokes second-order wave and a second-harnomic free wave which travels at a different speed. The amplitude of the second-harmonic free wave is relatively large in shallow water and decreases to less than 10% of the amplitude of the primary wave in deep water. Wavemakers with relatively deeper draft (i.e., hinged near the bottom) generate the free waves of smaller amplitude in shallow and intermediate water depths than the wavemakers with shallow draft. However, the opposite is predicted by theory in deep water.

• Journal of Ocean Engineering and Technology
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• v.17 no.6
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• pp.7-15
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• 2003

A Digital Wave Tank simulation technique, based on a finite-difference method and a modified marker-and-cell (MAC) algorithm, is applied in order to investigate the characteristics of nonlinear Tsunami propagations and their interactions with a 2D sloping beach, Ohkushiri Island, and to predict maximum wove run-up around the island. The Navier-Stokes (NS) and continuity equation are governed in the computational domain, and the boundary values are updated at each time step, by a finite-difference time-marching scheme in the frame of the rectangular coordinate system. The fully nonlinear, kinematic, free-surface condition is satisfied by the modified marker-density function technique. The near shore Tsunami is assumed to be a solitary wave, and is generated from the numerical wave-maker in the developed Digital Wave Tank. The simulation results are compared with the experiments and other numerical methods, based on the shallow-water wave theory.