• Water for future
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• v.27 no.2
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• pp.147-154
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• 1994

The occurrence condition of debris fiow due to rainfall is given by solving the equations for fiow on a slope. The solution shows that a debris fiow will occur on a slope when the accumulated rainfall within the time of concentration exceeds a certain value determined by the properties of the slope. To estimate this critical value, the system analysis technique would be commendable. In this study, a procedure to fine the critical rainfall from the rainfall data whith and without debris flows is proposed. Reliability of this method is verified by applying to the debris flows in Unzen Volcano which recently began to erupt. Discharge of debris flow in a stream is obtained by solving the equation of continuity using the kinematic wave theory and assuming the cross sectional area to be a function of discharge. The computed hydrographs agree weel with the ones observed at the rivers in Sakurajima and Unzen Volcanos. It is found from the derived equation that the runoff intensity of debris flow is in proportion to the rainfall intensity and accumulated rainfall, jointly. This gives a theoretical basis to the conventional method which has been widely used.

• Journal of Advanced Research in Ocean Engineering
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• v.1 no.3
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• pp.157-167
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• 2015

In order to provide simple and accurate wave theory in design of offshore structure, an analytical approximation is introduced in this paper. The solution is limited to flat bottom having a constant water depth. Water is considered as inviscid, incompressible and irrotational. The solution satisfies the continuity equation, bottom boundary condition and non-linear kinematic free surface boundary condition exactly. Error for dynamic condition is quite small. The solution is suitable in description of breaking waves. The solution is presented with closed form and dispersion relation is also presented with closed form. In the last century, there have been two main approaches to the nonlinear problems. One of these is perturbation method. Stokes wave and Cnoidal wave are based on the method. The other is numerical method. Dean's stream function theory is based on the method. In this paper, power series method was considered. The power series method can be applied to certain nonlinear differential equations (initial value problems). The series coefficients are specified by a nonlinear recurrence inherited from the differential equation. Because the non-linear wave problem is a boundary value problem, the power series method cannot be applied to the problem in general. But finite number of coefficients is necessary to describe the wave profile, truncated power series is enough. Therefore the power series method can be applied to the problem. In this case, the series coefficients are specified by a set of equations instead of recurrence. By using the set of equations, the nonlinear wave problem has been solved in this paper.

• 한국전산유체공학회:학술대회논문집
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• 2004.03a
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• pp.119-125
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• 2004

Unsteady nonlinear wave motions on the free surface over a plane beach of constant slope are numerically simulated using a finite difference method in rectangular grid system. Two-dimensional Navier-Stokes equations and the continuity equation are used for the computations. Irregular leg lengths and stars are employed near the boundaries of body and free surface to satisfy the boundary conditions. Also, the free surface which consists of markers or segments is determined every time step with the satisfaction of kinematic and dynamic free surface conditions. Moreover, marker-density method is also adopted to allow plunging jets impinging on the free surface. The second-order Stokes wave theory and solitary wave theory are employed for the generation of waves on the inflow boundary. For the simulation of wave breaking phenomena, the computations are carried out with the plane beach of constant slope in surf zone. The results are compared with each other. The marker-density method is better then the hybrid method. Also they are compared with other existing experimental results. The Agreement between the experimental data and the computation results is good.

• 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.

• Water Engineering Research
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• v.2 no.1
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• pp.49-61
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• 2001

A grid-based KIneMatic wave soil-water EROsion and deposition Model(KIMEROM) that predicts temporal variation and spatial distribution of sediment transport in a watershed was developed. This model uses ASCII-formatted map data supported from the regular gridded map of GRASS (U.S. Army CERL, 1993)-GIS(Geographic Information Systems), and generates the distributed results by ASCII-formatted map data. For hydrologic process, the kinematic wave equation and Darcy equation were used to simulated surface and subsurface flow, respectively (Kim, 1998; Kim et al., 1998). For soil erosion process, the physically-based soil erosion concept by Rose and Hairsine (1988) was used to simulate soil-water erosion and deposition. The model adopts single overland flowpath algorithm and simulates surface and subsurface water depth, and sediment concentration at each grid element for a given time increment. The model was tested to a 162.3 $\textrm{km}^2$ watershed located in the tideland reclaimed ares of South Korea. After the hydrologic calibration for two storm events in 1999, the results of sediment transport were presented for the same storm events. The results of temporal variation and spatial distribution of overland flow and sediment areas are shown using GRASS.

• Proceedings of the Korea Water Resources Association Conference
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• 2001.05a
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• pp.25-34
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• 2001

A grid-based KIneMatic wave soil-water EROsion and deposition Model (KIMEROM) that predicts temporal variation and spatial distribution of sediment transport in a watershed was developed. This model uses ASCII-formatted map data supported from the regular gridded map of GRASS (U.S. Army CERL, 1993)-GIS (Geographic Information Systems), and generates the distributed results by ASCIIl-formatted map data. For hydrologic process, the kinematic wave equation and Darcy equation were used to simulate surface and subsurface flow, respectively (Kim, 1798; Kim et al., 1993). For soil erosion process, the physically-based soil erosion concept by Rose and Hairsine (1988) was used to simulate soil-water erosion and deposition. The model adopts sing1e overland flowpath algorithm and simulates surface and subsurface water depth, and sediment concentration at each grid element (or a given time increment. The model was tested to a 162.3 km$^2$ watershed located in the tideland reclaimed area of South Korea. After the hydrologic calibration for two storm events in 1999, the results of sediment transport were presented for the same storm events. The results of temporal variation and spatial distribution of overland flow and sediment areas are shown using GRASS.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 2001.10a
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• pp.45-50
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• 2001

The purpose of this study was to estimate of soil loss form hillslope using WEPP(Water Erosion Prediction Project) model. WEPP model was developed for predicting soil erosion and deposition, fundamentally based on soil erosion prediction technology. The model for predicting sediment yields from single storms was applied to a tested watershed. Surface runoff is calculated by kinematic wave equation and infiltration is based on the Green and Ampt equation. Governing equations for sediment continuity, detachment, deposition, shear stress in rills, and transport capacity are presented. Tested watershed has an area of 0.6ha, where the runoff and sediment data were collected. The relative error between predicted and measured runoff was $-16.6{\sim}2.2%$, peak runoff was $-15.6{\sim}2.2%$ and soil loss was $-23.9{\sim}356.5%$.

• 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 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 Ship and Ocean Technology
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• v.8 no.2
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• pp.61-69
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• 2004

Unsteady nonlinear wave motions on the free surface over a plane beach of constant slope are numerically simulated using a finite difference method in rectangular grid system. Two-dimensional Navier-Stokes equations and the continuity equation are used for the computations. Irregular leg lengths and stars are employed near the boundaries of body and free surface to satisfy the boundary conditions. Also, the free surface which consists of markers or segments is determined every time step with the satisfaction of kinematic and dynamic free surface conditions. Moreover, marker-density method is also adopted to allow plunging jets impinging on the free surface. The second-order Stokes wave theory is employed for the generation of waves on the inflow boundary. For the simulation of wave breaking phenomena, the computations are carried out with the plane beach of constant slope in surf zone. The results are compared with other existing experimental results. Agreement between the experimental data and the computation results is good.