• Journal of Korean Society on Water Environment
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• v.31 no.4
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• pp.367-376
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• 2015

The momentum and kinetic turbulent energy carried by the wind to a stratified lake lead to basin-scale motions, which provide a major driving force for vertical and horizontal mixing. A three-dimensional (3D) hydrodynamic model was applied to Lake Tahoe, located between California and Nevada, USA, to simulate the dominant basin-scale internal waves in the deep lake. The results demonstrated that the model well represents the temporal and vertical variations of water temperature that allows the internal waves to be energized correctly at the basin scale. Both the model and thermistor chain (TC) data identified the presence of Kelvin modes and Poincare mode internal waves. The lake was weakly stratified during the study period, and produced large amplitude (up to 60 m) of internal oscillations after several wind events and partial upwelling near the southwestern lake. The partial upwelling and followed coastal jets could be an important feature of basin-scale internal waves because they can cause re-suspension and horizontal transport of fine particles from nearshore to offshore. The internal wave dynamics can be also associated with the distributions of water quality variables such as dissolved oxygen and nutrients in the lake. Thus, the basin-scale internal waves and horizontal circulation processes need to be accurately modeled for the correct simulation of the dissolved and particulate contaminants, and biogeochemical processes in the lake.

• 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 Korean Society of Coastal and Ocean Engineers
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• v.20 no.2
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• pp.212-218
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• 2008

A possible source of resonant problems in a harbor is long waves generated by incident wave groups. The analytical solutions of the governing equations of second-order long waves derived using a multiple-scale perturbation method consist of the locked and free long waves. The locked long waves propagate at some group velocity, whereas the free long waves propagate at the shallow-water speed. To study the resonance of free long waves, a trapezoidally varying topography is employed. With certain combinations of incident angle, water depth, and ambient current velocity, free long waves can be trapped and resonated.

• Water Engineering Research
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• v.3 no.3
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• pp.203-213
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• 2002

A wide-angle parabolic approximation equation model considering the interaction between wave and current is employed to simulate the deformation of irregular waves over a submerged shoal. It is found that the model gives qualitative agreements with experimental data for the cases of breaking waves around the shoal. Thus, the effect of breaking-induced current on the refraction-diffraction of waves is well understood.

• Computers and Concrete
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• v.18 no.2
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• pp.179-199
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• 2016

The aim of this study is to investigate arrival direction effects of travelling waves on non-linear seismic response of arch dams. It is evident that the seismic waves may reach on the dam site from any direction. Therefore, this study considers the seismic waves arrive to the dam site with different angles, ${\theta}=0^{\circ}$, $15^{\circ}$, $30^{\circ}$, $45^{\circ}$, $60^{\circ}$, $75^{\circ}$, and $90^{\circ}$ for non-linear analysis of arch dam-water-foundation interaction system. The N-S, E-W and vertical component of the Erzincan earthquake, on March 13, 1992, is used as the ground motion. Dam-water-foundation interaction is defined by Lagrangian approach in which a step-by-step integration technique is employed. The stress-strain behavior of the dam concrete is idealized using three-dimensional Drucker-Prager model based on associated flow rule assumption. The program NONSAP is employed in response calculations. The time-history of crest displacements and stresses of the dam are presented. The results obtained from non-linear analyses are compared with that of linear analyses.

• Journal of Korea Water Resources Association
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• v.32 no.6
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• pp.649-655
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• 1999

The maximum run-up heights of periodic waves are numerically investigated in this study. Incident waves are sinusoidal and enoidal waves. The maximum run-up height of enoidal wave approaches that of sinusoidal wave as the wave length decreases, while it approaches that of solitary wave as the wave length increases. If wave height is fixed, the maximum run up heights of enoidal waves are always greater than those of sinusoidal waves but smaller than those of solitary waves.

• Ocean Systems Engineering
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• v.4 no.3
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• pp.201-213
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• 2014

Wave run-up is an important issue in offshore engineering, which is tightly related to the loads on the marine structures. In this study, a series of physical experiments have been performed to investigate the wave run-up around a vertical cylinder in transitional water depth. The wave run-ups of regular waves, irregular waves and focused waves have been presented and the characteristics in frequency domain have been investigated with the FFT and wavelet transform methods. This study focuses on the nonlinear features of the wave run-up and the interaction between the wave run-up and the cylinder. The results show that the nonlinear interaction between the waves and the structures might result wave run-up components of higher frequencies. The wave run-ups of the moderate irregular waves exhibit 2nd order nonlinear characteristics. For the focused waves, the incident waves are of strong nonlinearity and the wavelet coherence analysis reveals that the wave run-up at focal moment contains combined contributions from almost all the frequency components of the focused wave sequence and the contributions of frequency components up to 4th order harmonic levels are recommended to be included.

• International Journal of Naval Architecture and Ocean Engineering
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• v.13 no.1
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• pp.278-291
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• 2021

This paper applies load variation method to predict speed-power-rpm relationship along with propulsive performances in regular head waves, and to derive overload factors (ITTC, 2018). 'Calm-water tests' and 'resistance test in waves' are used. The modified overload factors are proposed taking non-linearity into consideration, and applied to the direct powering, and resistance and thrust identity method. These indirect methods are evaluated through comparing the speed-power-rpm relationships with those obtained from the resistance and self-propulsion tests in calm water and in waves. The objective ship is KVLCC2. The load variation method predicts well the speed-power-rpm relationship and propulsion performances in waves. The direct powering method with modified overload factors also predicts well. The resistance and thrust identity method with modified overload factor predicts with a little difference. The direct powering method with overload factors predicts with a relatively larger difference.