• 한국해양공학회지
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• 제37권2호
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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.

• 한국해양공학회지
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• 제36권2호
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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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• 제2권1호
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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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• 제20권11호
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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.

• 한국해안해양공학회지
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• 제12권1호
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• pp.39-52
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• 2000

3파 상호작용은 천수파 또는 유한 수심 풍파의 경우에만 중요한 것으로 알려져 왔다. 파랑 성분간의 에너지 전달에 의한 풍파의 성장 관점에서 볼 때 심해에서 3파 상호작용은 4파 상호작용에 비해 별로 중요하지 않다. 그러나, 심해에서도, 특히 풍파 성장의 초기 단계에서는, 3파 상호작용이 중요할 수 있는데, 이는 3파 상호작용이 쇄파에 결정적인 영향을 미치는 파형경사, 수면 위에서의 공기 흐름의 항력, 선박의 항해 등과 밀접한 관계를 가지고 있기 때문이다. 본 연구에서는 일련의 실험실 실험 결과를 제시하고, 이에 대한 bispectrum 분석을 통하여 심해 풍파의 3파 상호작용을 고찰한다. 스펙트럼 첨두 주파수에서의 bicoherence와 파형경사가 거의 정비례하는 것으로 나타나는데, 이는 파봉이 뽀족하고 파곡이 밋밋한, 경사가 큰 파가 3파 상호작용의 결과임을 나타낸다. Bicoherence 및 파형경사 모두가 파랑 성장의 초기 단계에서는 파령에 따라 증가하다가 파랑이 발달함에 따라 다시 작아진다. 파랑 성장의 초기 단계에서 3파 상호작용에 의하여 발달된 스펙트럽 2차 첨두의 에너지가 그 이후에는 4파 상호작용에 의해 주변의 주파수들로 재분배되는 것으로 추측된다.

• International journal of advanced smart convergence
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• 제12권2호
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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.

• 대한조선학회지
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• 제17권2호
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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.

• 한국해안·해양공학회논문집
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• 제24권5호
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• pp.343-351
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• 2012

본 연구에서는 강릉 해수욕장 전면에서 20년간 관측된 파랑자료의 극치분석을 통하여 재현빈도 10, 20, 30 및 50년의 천해설계파를 도출하였다. 이들을 수산청(1988) 및 한국해양연구원(2005)에 제시된 강릉 해역에 대한 재현빈도별 심해파 조건을 경계조건으로 천해파 모델인 SWAN을 사용하여 관측지점에서의 파고를 구한 값과 비교하였다. 그 결과 이러한 기존의 심해파 조건들로 계산한 강릉 해역의 천해파고는 관측치에 비해 상당히 작게 제시되었으며 그 차이는 재현빈도의 증가에 따라 커지는 것을 확인하였다. 한국해양연구원은 이전보다 상세한 격자와 WAM 모델을 사용하여 2004년 1월부터 2008년 8월까지의 역추산 자료를 생성하였으며, 이를 천해역의 관측 자료와 비교한 결과 1979~2003년의 자료에 비해 동계 폭풍파의 재현성이 크게 향상되었음을 확인하였다. 앞으로 2004년 이전에 대해서도 상세 격자와 WAM 모델을 사용한 역추산 자료의 생성 및 이를 사용한 심해파의 보완 작업이 필요한 것으로 사료된다.

• 한국해안해양공학회지
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• 제12권4호
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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%.

• 한국해안·해양공학회논문집
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• 제28권5호
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• pp.292-302
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• 2016

본 연구에서는 동해안의 4개 정점(속초, 묵호, 후포, 진하)에서 13년간 관측된 파랑자료를 이용하여 극치확률분석을 통해 재현빈도별로 천해설계파를 산정하였고, 이 값을 한국해양연구원(2005)에 제시된 동해안 심해설계파를 이용하여 SWAN 수치모델링로 계산된 결과와 비교하였다. 그 결과 2005년 기존 심해설계파의 수치실험 결과는 관측파랑에 의한 극치분석 결과보다 상대적으로 작은 것으로 나타났으며, 특히 30년 빈도 이하에서 동해안에서의 기존 심해설계파고가 과소산정되었을 가능성이 있음을 시사한다.