• 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 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.

• Journal of Industrial Technology
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• v.21 no.B
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• pp.175-185
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• 2001

A numerical model is represented to calculate the reflected waves, the runup of waves and the wave induced velocities on impermeable slopes for the normally incident wave trains of nonlinear monochromatic wave and solitary wave. The finite amplitude shallow water equations with the effects of bottom friction are solved numerically in time domain using an explicit dissipative Lax-Wendroff finite difference method. The numerical model is verified by comparisons with the other numerical results, the measured data and asymptotic results. It is found that the uprushing and downrushing of incident waves may be accurately predicted by the present numerical model. Therefore, the present numerical model can be applicable to swells as well as long waves.

• Proceedings of the Korea Water Resources Association Conference
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• 2003.05b
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• pp.1063-1066
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• 2003

• Journal of Ocean Engineering and Technology
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• v.21 no.1 s.74
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• pp.1-6
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• 2007

While a typhoon is traveling, characteristics of its wind fields are continuously changing, producing severe changes in local water level and wave conditions, especially, when a typhoon comes into shallow water. However, there have not been many studies related to local typhoon effects, especially, considering real time changes of wind direction related to the coastal topography. In the study, the characteristics of the wind field by typhoon and topographical characteristics in shallow water are considered, as well as conditions of wave climate estimation. These are performed by the SWAN (Simulating waves nearshore) model, in order to estimate the growth of wave energy due to the wind field. It can be strongly suggested that the wave energy of theof an inner bay should be estimated when the direction of the bay entrance and the wind direction of the typhoon are identical. The result of the numerical calculations is in better agreement with the observed data than the result of the conventional estimation techniques.

• Journal of Korean Port Research
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• v.12 no.1
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• pp.75-86
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• 1998

To design a coastal structure in the nearshore region, engineers must have means to estimate wave climate. Waves, approaching the surf zone from offshore, experience changes caused by combined effects of bathymetric variations, interference of man-made structure, and nonlinear interactions among wave trains. This paper has attempted to find out the effects of two of the more subtle phenomena involving nonlinear shallow water waves, amplitude dispersion and secondary wave generation. Boussinesq-type equations can be used to model the nonlinear transformation of surface waves in shallow water due to effect of shoaling, refraction, diffraction, and reflection. In this paper, generalized Boussinesq equations under the complex bottom condition is derived using the depth averaged velocity with the series expansion of the velocity potential as a product of powers of the depth of flow. A time stepping finite difference method is used to solve the derived equation. Numerical results are compared to hydraulic model results. The result with the non-linear dispersive wave equation can describe an interesting transformation a sinusoidal wave to one with a cnoidal aspect of a rapid degradation into modulated high frequency waves and transient secondary waves in an intermediate region. The amplitude dispersion of the primary wave crest results in a convex wave front after passing through the shoal and the secondary waves generated by the shoal diffracted in a radial manner into surrounding waters.

• Journal of Ocean Engineering and Technology
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• v.22 no.5
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• pp.69-74
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• 2008

This study performed a numerical simulation to predict the development of ship waves and their propagation in the shallow water region of Gunzang New Port and to examine the stability of taut line mooring at the sea wall using the design criteria. In order to predict the propagation of ship waves based on the speeds of various ships under complicated and shallow water depths, a computer model was constructed based on the Boussinesque equation with a fixed coordinate system. Additionally, an investigation if the stability was made by applying MOSES under the environmental loadings estimated by OCIMF.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.24 no.5
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• pp.343-351
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• 2012

In this study, shallow-water design waves are calculated for the return period of 10, 20, 30, and 50 years, based on the extreme value analysis of the wave measurement data at Gangneung beach. These values are compared with the results of SWAN simulation with the boundary condition of the deep-water design waves of the corresponding return periods at the Gangneung sea area provided by the Fisheries Agency (FA, 1988) and Korea Ocean Research & Development Institute (KORDI, 2005). It is found that the shallow-water wave heights at Gangneung beach calculated by the deep-water design waves were significantly less than the observation data. As the return period becomes higher, the significant wave heights obtained by the extreme value analysis becomes higher than those computed by SWAN with the deep-water design waves of the corresponding return periods. KORDI computed the hindcast wave data from January 2004 to August 2008 by WAM with a finer-grid mesh system than those of previous studies. Comparisons of the wave hindcast results with the wave observation show that the reproducibility of the winter-season storm wave was considerably improved compared to the hindcast data from 1979 to 2003. Hereafter, it is necessary to carry out hindcast wave data for the years before 2004 using WAM with the finer-grid mesh system and to supplement the deep-water design wave.

• Journal of Ocean Engineering and Technology
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• v.25 no.2
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• pp.21-28
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• 2011

The primary purpose of the present study was to investigate the mechanism causing scour around a pipeline placed on the seabed in a shallow water zone. Such submarine pipelines are usually exposed to currents and waves. The present experiments made estimates for each different flow type. The scour width and depth in the equilibrium scour phase were analyzed by non-dimensional parameters. The experiment in this study considered various parameters: pipe diameters, wave periods, wave heights, and current velocities. Using the experimental results, the correlations of scour width, scour depth, and main non-dimensional parameters such as the Fr number and KC number were analyzed. In the case of steady currents, the scour hole was closely related to the bottom velocity, while the scour hole in waves showed a relatively low correlation to the bottom velocity because when exposed to waves the scour hole was restricted according to the movement distance of the water particles during a wave period. However, the scour width under a steady current was not limited because vortex shedding was well developed from having enough time and distance.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.19 no.6
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• pp.511-520
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• 2007

WAM(WAve Model), deep water wave model has been extended to the region of shallow water, incorporating wave breaking, and triad wave interaction. To verify the model, numerical simulation of waves in Youngil bay, Pohang is performed and the simulated results show good agreements with measured wave data sets, one station at the mouth of bay and two stations inside the bay. As waves propagate toward the shore, wave height gradually diminishes by bottom friction and wave breaking, and wave direction, initially NE changes normal to the shore due to depth refraction.