• Proceedings of the KSRS Conference
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• v.1
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• pp.364-367
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• 2006

Nonlinear internal waves (NLIWs) are usually generated by nonlinear process on linear internal waves (IW). Near HengChun Ridge that links Taiwan and Luzon Islands, we found that there are linear internal waves following NLIW and they travel westward at different speed, about 1.5 m/s for IW and 2.9 m/s for NLIW. This phenomenon was observed on site with ship radar and echo sounders, and later verified with thermistor chain. West of Luzon Strait, the separation of NLIW are 5 km or more, while linear internal waves are lines of wave crests at nearly equal distance that is only a few hundred meters apart. The current hypothesis is that most of the energy of internal tide forms a beam that propagates upward from the eastern shoulder of ocean ridge and later interacts with sea surface and thermocline. The interaction with thermocline generates linear internal wave that propagate along the pycnocline at about 1.5 m/s. The interaction with sea surface scatters internal wave energy downward, ensonifies the water column and generates large nonlinear waves that propagate westward at 2.9 m/s as mode 1 in a waveguide.

• Journal of Advanced Research in Ocean Engineering
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• v.1 no.3
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• pp.157-167
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• 2015

In order to provide simple and accurate wave theory in design of offshore structure, an analytical approximation is introduced in this paper. The solution is limited to flat bottom having a constant water depth. Water is considered as inviscid, incompressible and irrotational. The solution satisfies the continuity equation, bottom boundary condition and non-linear kinematic free surface boundary condition exactly. Error for dynamic condition is quite small. The solution is suitable in description of breaking waves. The solution is presented with closed form and dispersion relation is also presented with closed form. In the last century, there have been two main approaches to the nonlinear problems. One of these is perturbation method. Stokes wave and Cnoidal wave are based on the method. The other is numerical method. Dean's stream function theory is based on the method. In this paper, power series method was considered. The power series method can be applied to certain nonlinear differential equations (initial value problems). The series coefficients are specified by a nonlinear recurrence inherited from the differential equation. Because the non-linear wave problem is a boundary value problem, the power series method cannot be applied to the problem in general. But finite number of coefficients is necessary to describe the wave profile, truncated power series is enough. Therefore the power series method can be applied to the problem. In this case, the series coefficients are specified by a set of equations instead of recurrence. By using the set of equations, the nonlinear wave problem has been solved in this paper.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.4 no.4
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• pp.219-224
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• 1992

A numerical method using the truncated Fourier series is presented to predict the wave potential and water surface profile for two dimensional nonlinear standing waves. The unknown coefficients of the series are to be determined through the Newton solution of nonlinear simultaneous equations given by the governing equation and boundary conditions of the problem. In order to prove the effectiveness of the present method. an existing Stokes-like perturbation method is considered together, and a hydraulic experiment for measuring water surface profile and wave pressure is performed as well. The results are such that the present method can generally give exact solutions even for relatively big wave stiffness regardless of the water depth condition. It also demonstrates its validity by showing double humps in the crest of temporal wave pressure profile which normally appear in strongly nonlinear standing waves.

• International Journal of Naval Architecture and Ocean Engineering
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• v.13 no.1
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• pp.526-544
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• 2021

Based on the potential flow theory, a fully nonlinear numerical procedure is developed with boundary element method to analyze the interaction between a fixed semi-submersible platform and incident waves in open water. The incident wave is separated from the scattered wave under fully nonlinear boundary conditions. The mixed Euler-Lagrangian method is used to capture the position of the disturbed wave surface in local coordinate systems. The wave forces exerted on an inverted conical frustum are used to ensure the accuracy of the present method and good agreements with published results are obtained. The hydrodynamic characteristics of the semi-submersible platform interacting with regular waves are analyzed. Pressure distribution with time and space, tension and compression of the platform under wave action are investigated. 3D behaviors of wave run-ups are predicted. Strong nonlinear phenomena such as wave upwelling and wave interference are observed and analyzed.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.381-391
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• 2012

In this paper, the formal linearization method is used to construct multisoliton solutions for three model of shallow water waves equations. The three models are completely integrable. The formal linearization method is an efficient method for obtaining exact multisoliton solutions of nonlinear partial differential equations. The method can be applied to nonintegrable equations as well as to integrable ones.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.197-208
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• 2006

This paper deals with the exact solution of surface gravity waves in an ocean with irregular bed topography. In order to obtain water surface elevation and run-up of infra-gravity waves when the bed is either wavy or exponential, closed form solutions are obtained. Numerical computations indicate that when solitary wave or sinusoidal wave conditions are applied at the boundary, water surface elevation attains near Gaussian profile.

• Journal of Ship and Ocean Technology
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• v.7 no.3
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• pp.1-12
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• 2003

The influence of nonlinear phenomena on the behavior of stationary forced flexural-gravity waves on the surface of deep water is investigated, when the perturbation of external pressure moves with near-resonant velocity. It is shown that there are three branches of bounded stationary solutions turning into asymptotic solutions of the linear problem with zero initial conditions. For the first time ice sheet destruction by turbulent fluctuations of atmosphere pressure in ice adjacent layer in wind conditions is studied.

• 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.

• Journal of Ship and Ocean Technology
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• v.5 no.2
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• pp.50-61
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• 2001

In this paper, nonlinear interactions between water waves and a horizontally submerged circular cylinder are numerically simulated. In this case, the nonlinear interactions between them generated a wave breaking phenomenon. The wave breaking phenomenon plays an important role in the wave farce. Negative drifting forces are raised at shallow submerged cylinders under waves because of the wave breaking phenomenon. For the numerical simulation, a finite difference method based on the unsteady incompressible Navier-Stokes equations and the continuity equation is adopted in the rectangular grid system. The free surface is simulated with a computational simulation method of two-layer flow by using marker density. The results are compared with some existing computational and experimental results.

• Journal of Korea Water Resources Association
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• v.30 no.3
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• pp.225-233
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• 1997

The nonlinear effects on the statistical properties of wave groups in terms of the average nomber of waves in a group and the mean number of waves in a high run is studied in this paper utilizing the complex envelope and total phase function, random variable transformation technique and perturbation method. It tures out that the phase distribution is modified significantly by nonlinearities and it show systematic excess of values near the mean phase and the corresponding symmetrical deficiency on both sides away from the mean. for the case of threshold crossing rate, it turns out that threshold crossing rate reaches its maxima just below the mean water level rather than zero and considerable amount of probability mass is shifted toward the larger values of water surface elevation as nonlinearity is getting profound. Furthermore, the mean waves in a high run associated with nonlinear wave are shown to have larger values than the linear counterpart. Similar trend can also be found in the average number of waves in a group.