• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.1
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• pp.203-211
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• 1993

Experiment on the instability and breaking of the initially modulated deep-water wave train (in wave amplitude or in wave frequency) is performed to investigate the effect of the initial modulation on nonlinear wave evolution. Wave amplitude and frequency modulations are developed earlier and larger than in the case of the uniform deep-water wave trains. However, for small wave steepness in the initially amplitude-modulated wave train, the wave train becomes demodulated and nearly returns to the original wave form at the end of the wave evolution far downstream from the breaking region, with energy returning to the fundamental wave frequency.

• International Journal of Naval Architecture and Ocean Engineering
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• v.12 no.1
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• pp.168-177
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• 2020

Many coastal engineering designs utilize empirical formulas containing the Equivalent Deep-water Wave Height (EDWH), which is normally given a priori. However, no studies have explicitly discussed a method for determining the EDWH and the resulting design wave heights (DEWH) under irregular wave conditions. Unfortunately, it has been the case in many design practices that the EDWH is incorrectly estimated by dividing the Shallow-water Wave Height (SWH) at the structural position with its corresponding shoaling coefficient of regular wave. The present study reexamines the relationship between the Shallow-water Wave Height (SWH) at the structural position and its corresponding EDWH. Then, a new procedure is proposed to facilitate the correct estimation of EDWH. In this procedure, the EDWH and DEWH are determined differently according to the wave propagation model used to estimate the SWH. For this, Goda's original method for nonlinear irregular wave deformation is extended to produce values for linear shoaling. Finally, exemplary calculations are performed to assess the possible errors caused by a misuse of the wave height calculation procedure. The relative errors with respect to the correct values could exceed 20%, potentially leading to a significant under-design of coastal or harbor structures in some cases.

• 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.

• International Journal of Naval Architecture and Ocean Engineering
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• v.7 no.6
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• pp.1056-1063
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• 2015

Waves can be expressed in terms of a spectrum; that is, the energy density distribution of a representative wave can be determined using statistical analysis. The JONSWAP, PM and BM spectra have been widely used for the specific target wave data set during storms. In this case, the extracted wave data are usually discontinuous and independent and cover a very short period of the total data-recording period. Previous studies on the continuous wave spectrum have focused on wave deformation in shallow water conditions and cannot be generalized for deep water conditions. In this study, the Generalized Extreme Value (GEV) function is proposed as a more-optimal function for the fitting of the continuous wave spectral shape based on long-term monitored point wave data in deep waters. The GEV function was found to be able to accurately reproduce the wave spectral shape, except for discontinuous waves of greater than 4 m in height.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.14 no.1
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• pp.34-40
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• 2002

In order to estimate the height of long period wave from character of deep water wave, field observation is carried out three wave gauge are arranged by a straight line from the seashore to offshore direction and the result is analyzed. In addition, the existing theory of the mechanism for long period wave producer is verified by field observation, and the relation between deep water wave and long period wave of shallow area is examined. Observed long period wave is coincided with the existing theory for the most part. In order to add the change of time and space of long period wave, the height of long period wave is calculated by the composition of long period wave in each position. As a result, the relation of long period wave and deep water wave is presented more clear. Estimate formula is drew through them.

• 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.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2001.10a
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• pp.117-121
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• 2001

For the effective development or preservation of Tokdo, the natural environments in the ambient sea area should be well investigated. The wave deformations and wave breaking in the vicinity have much affected the bottom morphology of Tokdo as well as its ecological environment. The present study investigates the wave deformations and wave breaking through a numerical model. The final goal is to provide the fundamental wave data for the effective development or preservation of Tokdo in future. The extended mild slope equation was applied to Tokdo sea area for three different deep water wave conditions (S, SSE, NNE directions). The results showed that for the S and SSE directions the wave heights in the area between the east island and the west island were very low with the level of 1~2m, but for the NNE direction they appeared pretty high with 3~4m, In the sea area near the northwest of west island, the wave heights were low to be 1~3m for all three directions of deep water wave.

• 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.

• Wind and Structures
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• v.16 no.2
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• pp.193-211
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• 2013

This paper presents results from a wind tunnel study that examined the drag coefficient and wind flow over an asymmetric wave train immersed in turbulent boundary layer flow. The modeled wavy surface consisted of eight replicas of a statistically-valid hurricane-generated wave, located near the coast in the shoaling wave region. For an aerodynamically rough model surface, the air flow remained attached and a pronounced speed-up region was evident over the wave crest. A wavelength-averaged drag coefficient was determined using the wind profile method, common to both field and laboratory settings. It was found that the drag coefficient was approximately 50% higher than values obtained in deep water hurricane conditions. This study suggests that nearshore wave drag is markedly higher than over deep water waves of similar size, and provides the groundwork for assessing the impact of nearshore wave conditions on storm surge modeling and coastal wind engineering.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.1
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• pp.193-201
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• 1993

Experimental investigation of nonlinear instability of deep-water wave train is performed. Two-dimensional Benjamin-Feir type wave instability and breaking are observed at wave steepness between 0.19 and 0.25 and three-dimensional instability and breaking at wave steepness greater than or equal to 0.31. At the same wave steepness, shorter waves with smaller amplitude are more unstable, with earlier occurrence of breaking, than long waves with large amplitude.