• Journal of Ocean Engineering and Technology
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• v.37 no.2
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• pp.49-57
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• 2023

Since Chappelear developed a Fourier approximation method, considerable research efforts have been made. On the other hand, Fourier approximations are unsuitable for deep water waves. The purpose of this study is to provide a Fourier approximation suitable even for deep water waves and a numerical method to determine the Fourier coefficients and the wave properties. In addition, the convergence of the solution was tested in terms of its order. This paper presents a velocity potential satisfying the Laplace equation and the bottom boundary condition (BBC) with a truncated Fourier series. Two wave profiles were derived by applying the potential to the kinematic free surface boundary condition (KFSBC) and the dynamic free surface boundary condition (DFSBC). A set of nonlinear equations was represented to determine the Fourier coefficients, which were derived so that the two profiles are identical at specified phases. The set of equations was solved using Newton's method. This study proved that there is a limit to the series order, i.e., the maximum series order is N=12, and that there is a height limitation of this method which is slightly lower than the Michell theory. The reason why the other Fourier approximations are not suitable for deep water waves is discussed.

• Journal of Ocean Engineering and Technology
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• v.36 no.2
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• pp.101-107
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• 2022

Dean (1965) proposed the use of the root mean square error (RMSE) in the dynamic free surface boundary condition (DFSBC) and kinematic free-surface boundary condition (KFSBC) as an error evaluation criterion for wave theories. There are well known wave theories with RMSE more than 1%, such as Airy theory, Stokes theory, Dean's stream function theory, Fenton's theory, and trochodial theory for deep-water waves. However, none of them can be applied for deep-water breaking waves. The purpose of this study is to provide a closed-form solution for deep-water waves with RMSE less than 1% even for breaking waves. This study is based on a previous study (Shin, 2016), and all flow fields were simplified for deep-water waves. For a closed-form solution, all Fourier series coefficients and all related parameters are presented with Newton's polynomials, which were determined by curve fitting data (Shin, 2016). For verification, a wave in Miche's limit was calculated, and, the profiles, velocities, and the accelerations were compared with those of 5^th-order Stokes theory. The results give greater velocities and acceleration than 5^th-order Stokes theory, and the wavelength depends on the wave height. The results satisfy the Laplace equation, bottom boundary condition (BBC), and KFSBC, while Stokes theory satisfies only the Laplace equation and BBC. RMSE in DFSBC less than 7.25×10^-2% was obtained. The series order of the proposed method is three, but the series order of 5^th-order Stokes theory is five. Nevertheless, this study provides less RMSE than 5^th-order Stokes theory. As a result, the method is suitable for offshore structural design.

• Journal of Advanced Research in Ocean Engineering
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• v.2 no.1
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• pp.1-11
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• 2016

The objective of this paper is to present an analytical solution in deep water waves and verify the validity of the theory (Shin, 2015). Hence this is a follow-up to Shin (2015). Instead of a variational approach, another approach was considered for a more accurate assessment in this study. The products of two coefficients were not neglected in this study. The two wave profiles from the KFSBC and DFSBC were evaluated at N discrete points on the free-surface, and the combination coefficients were determined for when the two curves pass the discrete points. Thus, the solution satisfies the differential equation (DE), bottom boundary condition (BBC), and the kinematic free surface boundary condition (KFSBC) exactly. The error in the dynamic free surface boundary condition (DFSBC) is less than 0.003%. The wave theory was simplified based on the assumption tanh $D{\approx}1$ in this paper. Unlike the perturbation method, the results are possible for steep waves and can be calculated without iteration. The result is very simple compared to the 5th Stokes' theory. Stokes' breaking-wave criterion has been checked in this study.

• Journal of Mechanical Science and Technology
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• v.20 no.11
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• pp.1950-1960
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• 2006

Based on Banach fixed point theorem, a method to calculate nonlinear superposition for three interacting Stokes' waves is proposed in this paper. A mathematical formulation for the nonlinear superposition in deep water and some numerical solutions were investigated. The authors carried out the numerical study with three progressive linear potentials of different wave numbers and succeeded in solving the nonlinear wave profiles of their three wave-interaction, that is, using only linear wave potentials, it was possible to realize the corresponding nonlinear interacting wave profiles through iteration of the method. The stability of the method for the three interacting Stokes' waves was analyzed. The calculation results, together with Fourier transform, revealed that the iteration made it possible to predict higher-order nonlinear frequencies for three Stokes' waves' interaction. The proposed method has a very fast convergence rate.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.12 no.1
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• pp.39-52
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• 2000

The triad interactions have been known to be important only for shoaling waves or finite depth wind waves. In deep water, they are insignificant compared with the quadruplet interactions in respect to the evolution of wind waves due to energy transfer among the wave components. However, the triad interactions may be important even for deep water waves because they may closely be related to the wave steepness, which definitely affects wave breaking, drag of air flow over t.'Ie sea, or navigation of ships, especially during the early stage of the development of wind waves. This study reports a series of laboratory experiments, whose data are subjected to bispectral analyses to investigate the triad interactions of deep-water wind waves. It is found that the bicoherence at the spectral peak frequency and the wave steepness are almost directly proportional, indicating that the steep waves with peaked crests and flat troughs are resulted from the triad interactions. Both bicoherence and wave steepness increase with the wave age during the early stage of wave generation and then drop off as the waves grow old. It seems that the energy of the secondary spectral peak developed by the triad interactions during the early stage of wave generation is redistributed to the neighboring frequencies by the quadruplet interactions during the later stage.

• International journal of advanced smart convergence
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• v.12 no.2
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• pp.182-186
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• 2023

In this study, we measured the power and temperature of the floating horizontal solar cell in a coastal lagoon and compared with those of ground solar cell and water platform solar cell. Because the bottom surface of the floating horizontal solar cell was contacting the water, cooling effect was expected stronger than other cells. As a result of the measurement, the power of floating horizontal cell was 11.7% higher than that of the ground cell and 15% higher than that of the water platform cell. During the measurement, it was observed that water waves were continuously flowed on the top surface of floating horizontal cell by the wind, and it could be assumed that the cooling effect occurred not only on the bottom surface of the cell but also on the top surface. In order to analyze the cooling effect and power increasing of the horizontal cell in the wave situation, we measured power and temperature of the cell while generating artificial waves in a laboratory equipped with Zenon lamp as a solar simulator. At the height of thewater surface, the power of the cell with waves was 3.7% higherthan without waves and temperature was 4.6℃ lower. At 1 cm and 2 cm below the watersurface, power of the cell with waves was decreased by 14% and 11% than without waves while temperature was same . At 3 cm below the water surface, there was no effect of waves.

• Bulletin of the Society of Naval Architects of Korea
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• v.17 no.2
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• pp.17-20
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• 1980

The shearing forces and bending moments acting on the tanker model[1] of $C_B$ 0.82 in regular oblique waves of shallow water are investigated by numerical calculations. The new strip method was adopted. It is concluded that in the shallow water shearing forces and the bending moments acting on the tanker model are higher than those of deep water waves by the present numerical investigations. The wave bending moment at the midship section is roughly twice of deep water value in the shallow of H/T less than 2. in this calculation.

• 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 Korean Society of Coastal and Ocean Engineers
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• v.12 no.4
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• pp.168-180
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• 2000

In the Part I, the three dimensional model testing with NNW deep water wave direction gave the results such that the occurrence of breaking waves over the peak of Ear-Do caused very small wave height at the structure position. But the measured wave forces were rather greater than the calculated forces based on deep water wave height. Furthermore, It was also perceived that the time series of the forces looked like corresponding to the case that waves were superimposed by an unidirectional current. In the present Part II, the current is presumed to be a flow secondly induced by breaking waves, and an extensive study to clarify the current in a quantitative sense is performed through numerical analysis and hydraulic experiment. The results showed that a strong circulation can surely occur in the vicinity of the structure due to radiation stress differentials given by the breaking waves. It was also recognized that the velocity of the induced current varied with the magnitude of energy dissipation rate introduced in the numerical analysis. The numerical analysis was tuned adjusting the dissipation rate so that the calculated wave field could closely match with the experimental results of Part I. The fluid force (in prototype) for the optimal match showed approximately 2.2% increased over the calculated value based on the deep water wave height (24.6m) whereas the force corresponding to the average of the experimental values showed the increase of about 13.0%.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.28 no.5
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• pp.292-302
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• 2016

In this study, shallow-water design waves are estimated for various return periods based on statistical analysis of extreme waves observed 13 years at four stations on the Korean east coast (Sokcho, Mukho, Hupo, Jinha). These values are compared with the results from SWAN simulation by using the deep water design waves conventionally used in Korea (KORDI, 2005). It was found that the simulated values of the shallow-water design waves are comparatively smaller than the values from the extreme value analysis, expecially below 30 years frequency, which implies possible under-estimation of the deep-water design waves on the Korean east coast.