• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1017-1031
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• 2009

The problem of interaction of surface water waves by small undulation at the bottom of a laterally unbounded sea is treated on the basis of linear water wave theory for both normal and oblique incidences. Perturbation analysis is employed to obtain the first order corrections to the reflection and transmission coefficients in terms of integrals involving the shape function c(x) representing the bottom undulation. Fourier transform method and residue theorem are applied to obtain these coefficients. As an example, a patch of sinusoidal ripples is considered in both the cases as the shape function. The principal conclusion is that the reflection coefficient is oscillatory in the ratio of twice the surface wave number to the wave number of the ripples. In particular, there is a Bragg resonance between the surface waves and the ripples, which is associated with high reflection of incident wave energy. The theoretical observations are validated computationally.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.12 no.4
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• pp.190-194
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• 2000

Dispersion coefficient influenced by the wave parameters was derived analytically using the vertical velocity distribution based on linear wave theory. It is the depth- and wave period-averaged value and shows larger values in deep water condition than in shallow water condition. It also shows the general pattern of the dispersion coefficient in the oscillatory flows, i.e. it converges the specific value as the wave period is much larger than the vertical mixing time but it approaches zcro as the wave period is much smaller than the vertical mixing time. The dispersion coefficient derived in the condition of the simple assumption have to be modified in order to consider the shallow water condition or the real condition.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.15 no.1
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• pp.51-58
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• 2003

The magnitude of evanescent modes in terms of dynamics it investigated in case that the transformation of water waves is predicted by the linear wave theory. For the waves propagating over two steps, the eigenfunction expansion method is used to predict the amplitudes of reflected and transmitted waves by the component of evanescent modes as well as propagating modes. Then. the relative importance of evanescent modes to the propagating modes is investigated. The numerical experiments find that the evanescent modes are pronounced at the relative water depth of k$_1$h$_1$＝0.11$\pi$ and the water depth ratio of h$_2$/h$_1$ close to zero.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.6 no.2
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• pp.67-75
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• 1986

This paper introduces the nonlinear Stream Function Wave Theory for design waves efficiently to compute the wave energy and energy transport quantities and to analyze the effects of nonlinearities on them. The Stream Function Wave Theory was developed by Dean for case of the observed waves with assymmetric wave profiles and of the design waves with symmetric theoretical wave profiles. Dalrymple later improved the computational procedure by adding two Lagrangian constraints so that more efficient convergence of the iterative numerical method to a specified wave height and to a zero mean free surface displacement resulted. And the Stream Function coefficients are computed numerically by the improved Marquardt algorithm developed for this study. As the result of this study the effects of nonlinearities on the wave quantities of the average potential energy density, the average kinetic energy density result in overestimation by linear wave theory compared to the Stream Function Wave Theory and increase monotonically with decreasing $L^*/L_O$ and with increasing $H/H_B$. The effects of nonlinearities on the group velocity and the wavelength quantities result in underestimation by linear wave theory and increase monotonically with increasing $H/H_B$. Finally the effect of nonlinearity on the average total energy flux results in overestimation for shallow water waves and underestimation for deep water waves by linear wave theory.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.14 no.4
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• pp.282-285
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• 2002

The magnitude of evanescent modes in terms of dynamics is investigated in case that the transformation of water waves is predicted using the linear wave theory. In other words, derivation is made of both the kinetic and potential wave energies of evanescent modes as welt as propagating modes. The evanescent modes consist of compound components of propagating and evanescent modes, those of identically equal evanescent modes, and those of identically different evanescent modes. The wave energy per a horizontal distance decreases exponentially with the distance.

• Journal of Ocean Engineering and Technology
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• v.27 no.4
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• pp.68-75
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• 2013

This paper investigates the characteristics of waves generated by a flap-type wave maker in a two-dimensional wave channel. Measurements are carried out for various water depths, wave heights, periods, and lengths capacitance-type wave height gages. The experimental results are shown to satisfy the dispersion relation of the linear wave theory. For waves with a small height and long period, the wave profiles agree well with those of the linear wave theory. However, as the wave height and period become higher and shorter, respectively, it is shown that the wave profiles measured in the present experiments are different from the linear wave profiles, and the measured wave heights are smaller than the target wave heights, which may be due to the non-linearity of the waves. As the wave progresses toward the channel end, the wave height gradually decreases. This reduction in the wave height along the wave channel is explained by the wave energy dissipation due to the friction of the side walls of the channel. The performance of the wave absorber in the channel is found to be acceptable from the results of the wave reflection tests.

• 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.

• 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.

• Ocean Systems Engineering
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• v.2 no.2
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• pp.147-158
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• 2012

A time-domain simulation of a land-based Oscillating Water Column (OWC) with various irregular waves as a form of PM spectrum is performed by using a two-dimensional fully nonlinear numerical wave tank (NWT) based on the potential theory, mixed Eulerian-Lagrangian (MEL) approach, and boundary element method. The nonlinear free-surface condition inside the OWC chamber was specially devised to describe both the pneumatic effect of the time-varying pressure and the viscous energy loss due to water column motions. The quadratic models for pneumatic pressure and viscous loss are applied to the air and free surface inside the chamber, and their numerical results are compared with those with equivalent linear ones. Various wave spectra are applied to the OWC system to predict the efficiency of wave-energy take-off for various wave conditions. The cases of regular and irregular waves are also compared.

• Journal of the Korea Safety Management & Science
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• v.11 no.4
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• pp.139-145
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• 2009

The present study is to investigate the effect of wave-structure interaction such as wave oscillation. The theoretical method is based upon the linear diffraction theory obtained by the boundary element method. The water depth and incident wave period in fluid region are assumed to be constant. To investigate the wave interaction due to offshore structures, the numerical program has been developed and the simulation has been carried out by varying the conditions of distance and width of offshore structures. This study can effectively be utilized for safety assessment to various breakwater systems and layout of offshore breakwater in the ocean and coastal field. It can give information for the safety to construct offshore structure and revetment in coastal region.