• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.28 no.1B
• /
• pp.111-114
• /
• 2008

Explicit solutions of the wave dispersion equation are developed using the recursive relation in terms of the relative water depth. We use the solutions of Eckart (1951), Hunt (1979), and the deep-water and shallow-water solutions for initial values of the solution. All the recursive solutions converge to the exact one except that with the initial value of deep-water solution. The solution with the initial value by Hunt converged much faster than the others. The recursive solutions may be obtained quickly and simply by a hand calculator. For the transformation of linear water waves in whole water depth, the use of the recursive solutions will yield more accurate analytical solutions than use of previously developed explicit solutions.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.26 no.5
• /
• pp.314-326
• /
• 2014

On 31 March 2007, the abnormal wave occurred along the western coast of Korea. In order to investigate the generation mechanism of abnormal waves and to understand the amplification process of the abnormal waves, the observed data were analyzed and one-dimensional numerical model experiments were performed by using both the linear shallow water equation and the linear Boussinesq equation models. Various types of pressure jump for the abnormal waves previously proposed by other researchers were reviewed. As a result, it was not possible to reproduce the abnormal waves from the previously proposed pressure jumps. In this study, we proposed a new form of pressure jump, and numerical simulations were performed in order to check the validity of the proposed pressure jump. The numerical results showed that the calculated period of abnormal waves and the maximum water elevations agreed reasonably well with those of the observations.

• International Journal of Ocean System Engineering
• /
• v.3 no.2
• /
• pp.68-76
• /
• 2013

In this study, a 3D numerical model was used to predict nonlinear wave forces on a cylindrical pile installed in a shallow water region. The model was based on solving the viscous and incompressible Navier-Stokes equations for a two-phase flow (water and air) model and the volume of fluid method for treating the free surface of water. A new application was developed based on the cut-cell method to allow easy installation of complicated obstacles (e.g., bottom geometry and cylindrical pile) in a computational domain. Free-surface elevation, water particle velocities, and inline wave forces were calculated, and the results show good agreement with experimental data obtained by the Danish Hydraulic Institute. The simulation results revealed that the proposed model can, without the use of empirical formulas (i.e., Morison equation) and additional wave analysis models, reliably predict non-linear wave forces on an offshore wind turbine foundation installed in a shallow water region.

• Journal of the Society of Naval Architects of Korea
• /
• v.31 no.3
• /
• pp.47-58
• /
• 1994

Theoretical calculations are carried out for the estimation of linear maneuvering coefficients of a ship moving in shallow water region. Hydrodynamic forces and moments acting on a maneuvering ship are modelled based on a slender body theory, from which integro-differential equation for the unknown inner stream velocity is derived. Numerical algorithms fur solving this equation are described in detail. By considering water depth effects in the mathematical model, variations of maneuvering coefficients with water depth are studied. Programs are developed according to this method and calculations are done for Mariner, Series 60 and Wigley hull forms. For the verification of the programs, calculated results are compared with some analytic solutions and with published experimental results, which show good agreements in spite of many assumptions included in the mathematical model. It is expected that this method can be used as a preliminary tool for the estimation of maneuverability coefficients of a ship in shallow water region at its initial design stage.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
• /
• 2003.04a
• /
• pp.163-167
• /
• 2003

Based on the transient finite difference solution of Richards' equation, an infiltration model is developed to analyze temporal variation of precipitation recharge in the region of monsoon climates. Simulation results obtained by using time series data of 20-year daily precipitation and pan evaporation indicate that a linear relationship between the annual precipitation and the annual recharge holds for the soils under the monsoon climates with varying degrees of the correlation coefficient depending on the soil types. A sensitivity analysis reveals that the water table depth has little effects on the recharge for the sandy soil, whereas, for the loamy and silty soils, rise of the water table at shallow depths causes increase of evaporation by approximately 100㎜/yr and a corresponding decrease in recharge. A series of simulations for two-layered soils illustrate that the amount of recharge is dominantly determined by the soil properties of the upper layer, although the temporal variation of recharge is affected by both layers.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.6 no.4
• /
• pp.389-396
• /
• 1994

We analyze existing time-dependent mild-slope equations, which were developed by Smith and Sprinks (1975) (or, equivalently, Radder and Dingemans (1985)) and Kubo et al. (1992), in terms of the dispersion relation and energy transport. One-dimensionally in the horizontal direction, we compare the modulation of wave amplitudes for the time-dependent mild-slope equations against the linear Scrodinger equation. In view of the dispersion relation and modulation of wave amplitudes, Smith and Sprinks' model is more accurate in shallower water (kh$\leq$0.2$\pi$) and satisfies the linear Scrodinger equation in very shallow water (kh>0.2$\pi$) and satisfies the linear Scrodinger equation at a point of intermediate water depth (kh=0.3$\pi$). In view of the energy transport, Kubo et al.'s model is more accurate but yields singular solutions at some higher frequency range.

• Water for future
• /
• v.18 no.1
• /
• pp.67-73
• /
• 1985

Tidal propagation in the Keum River has been routinely handled by numerical integration of the long fravity wave equation by Dronkers. The dynamic equations include non-linear terms thereby reproducing the shallow water tides. The model was used to compute tidal distribution of the Kum River for aveage spring, mean, neap tidal conditions and further utilised to investigate the waterlevel response within tidal reaches by combined tide and flood discharge effects. The objective of this initial study is to investigate the tidal dynamics of the lower reaches of the Keum River under the condition of before-cross-channel barrage construction.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.5 no.4
• /
• pp.350-356
• /
• 1993

We carry out a numerical calculation to understand the nonlinear wave deformation around breakwaters using the Boussinesq equation, which is weakly nonlinear and weakly dispersive shallow water equation. A numerical method based on a finite element scheme and fourth order Runge-Kutta algorithm is employed to investigate the diffraction of incident waves by the breakwater. As a computational model, two-dimensional wave flume is treated. The breakwaters is perpendicular to the side wall of a channel. From the numerical results, the wave deformations according to the change of the length and the thickness of breakwaters are investigated. We also investigate the effect of the nonlinearity by comparing the results with the linear solutions.

• Korean Journal of Environmental Agriculture
• /
• v.8 no.1
• /
• pp.37-46
• /
• 1989

A 2-dimensional pollutant transport phenomenon in shallow reservoirs was analyzed by using a finite element method. The Galerkin's weighted residual method, based on linear interpolation, was used and a triangle was adopted as an element. The two dimensional Stock's equation and the advection-diffusion equation integrated over depth were used as governing equations. Also the Newton-Raphson method was introduced to solve the non-linear terms of the equation. The results calculated by the model are in good agreement with the analytical solution for a simplified channel where a known solution is avaiable. An actual application of the model is attempted for Sapkyo Lake with a consideration of the influx of the Sapkyo Chun, the Muhan Chun and kogkyo Chun. Further refined research is needed to evaluate the water quality in the other reservoirs.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.5 no.3
• /
• pp.212-220
• /
• 1993

A numerical model for the transformation of irregular waves in a coastal area is developed, which takes account of shoaling, refraction, diffraction, bottom friction and wave breaking. The governing equations are the usual energy conservation equation and kinematic conservation equations, but to consider the diffraction effects additional terms are included in the usual kinematic conservation or wave number equations. A linear superposition technique is used to represent the spectral formation. and an explicit formula is developed for the estimation of friction factor of irregular waves. A breaking criterion of component waves, which is the modified form of the Kitaigorodskii saturation relation, is employed to restrict the growth of shoaling waves in very shallow waters. The model was applied to a laboratory test and satisfactory agreement was obtained between the computation and measurement.