• 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 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.

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 1998.09a
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• pp.72-77
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• 1998

해안에서 인류에게 기쁨과 동시에 슬픔을 안겨주는 자연현상으로 파랑의 역동적인 거동을 들 수 있겠다. 이러한 파랑의 거동에 대한 물리적인 규명은 지금까지도 계속 연구되고 있는 주제로서 파랑의 거동을 가장 정확하게 규명하는 수학적인 모형중의 하나는 Boussinesq 방정식이라고 사료된다 이는 천해에서 파랑 상호간의 비선형성과 불규칙성을 대체로 정확히 규명할 수 있다. (중략)

• Journal of Korea Water Resources Association
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• v.38 no.6 s.155
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• pp.429-438
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• 2005

In this study, a couple of ordinary differential equations which can describe random waves are derived from the Boussinesq equations. Incident random waves are generated by using the TMA(TEXEL storm, MARSEN, ARSLOE) shallow-water spectrum. The governing equations are integrated with the 4-th order Runge-Kutta method. By using newly derived wave equations, nonlinear energy interaction of propagating waves in constant depth is studied. The characteristics of random waves propagate over a sinusoidally varying topography lying on a sloping beach are also investigated numerically. Transmission and reflection of random waves are considerably affected by nonlinearity.

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 2000.09a
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• pp.95-102
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• 2000

선형분산을 가정한 Berkhoff(1972)의 완경사방정식은 단일주기파(monochromaticwave)에 대해 심해로부터 천해까지 수심에 제한 없이 파랑의 변형을 해석할 수 있으나 식의 유도과정 중 바닥이 완경사(｜∇h｜/kh≪1) 라는 가정을 도입함으로써, 바닥곡률항(∇$^2$h)과 바닥경사의 제곱항(｜∇h｜$^2$)으로 대표되는 고차수심효과를 무시하였다. (중략)

• 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 Korean Society of Coastal and Ocean Engineers
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• v.2 no.1
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• pp.51-57
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• 1990

Based on second-order Stokes wave and parabolic approximation, a refraction-diffraction model for linear and nonlinear waves is developed. With the assumption that the water depth is slowly varying, the model equation describes the forward scattered wavefield. The parabolic approximation equations account for the combined effects of refraction and diffraction, while the influences of bottom friction, current and wind have been neglected. The model is tested against laboratory experiments for the case of submerged circular shoal, when both refraction and diffraction are equally significant. Based on Boussinesq equations, the parabolic approximation eq. is applied to the propagation of shallow water waves. In the case without currents, the forward diffraction of Cnoidal waves by a straight breakwater is studied numerically. The formation of stem waves along the breakwater and the relation between the stem waves and the incident wave characteristics are discussed. Numerical experiments are carried out using different bottom slopes and different angles of incidence.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.8 no.2
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• pp.137-145
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• 1996

Effects of nonlinear terms on the generation of M$_2$ tide residual elevation and M$_4$ tide in the Yellow Sea and the East China Sea are investigated using a depth-integrated two-dimensional nonlinear M$_2$tidal model. The model domain (117$^{\circ}$E-130$^{\circ}$E, 24$^{\circ}$N-41$^{\circ}$N) covers the whole region of the Yellow Sea and the East China Sea with grid resolution of 1/6$^{\circ}$ in longitude and 1/8$^{\circ}$in latitude. A radiational boundary condition is used along the open boundaries. Calculations show that advection terms yield negative residual elevation, while shallow-water terms in continuity equation yield positive residual elevation. The contribution of both advection terms and shallow-water terms to tile generation of the M$_4$ constituent is more than 90 percents, but that of quadratic bottom friction terms to the M$_4$ constituent is comparatively small.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.4 no.3
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• pp.161-167
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• 1992

We consider the preparation of long finite amplitude nondispersive waves over a step bottom between two regions of finite different depths. Two dimensional motion is assumed. with the wave crests parallel to the step, and irrotational flow in the inviscid fluid is considered. To describe the transformation of finite amplitude waves we use the finite-amplitude shallow-water equations, the conditions of mass flow conservation and pressure continuity at the cut above the step in Riemann's variables. The equations define four families of curves-characteristics on which the values of the Riemann's invariants remain constant and a system of two nonlinear equations that relates the amplitudes of incident reflected and transmitted waves. The system obtained is difficult to analyze in common form. Thus we consider some special cases having practical usage for tsunami waves. The results obtained are compared with the long wave theory and significant nonlinear effects are found even for quite small amplitude waves.

• Journal of Ocean Engineering and Technology
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• v.16 no.5
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• pp.34-40
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• 2002

A numerical model has been developed for the permeable coastal structures to simulate hydraulic characteristics on the permeable slopes, which interact with internal four field the structures. The model includes hydraulics in the porous medium. Numerical model was calibrated using hydraulic model experiments performed in 2-D wave flume in the Institute of Ocean Hydraulics in PKNU. Better aggrements were obtained with the model which employed inertia resistance term than with the conventional model, PBREAK.