• Title/Summary/Keyword: Shallow-Water Equations

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Propagation Analysis of Dam Break Wave using Approximate Riemann solver (Riemann 해법을 이용한 댐 붕괴파의 전파 해석)

  • Kim, Byung Hyun;Han, Kun Yeon;Ahn, Ki Hong
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.29 no.5B
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    • pp.429-439
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    • 2009
  • When Catastrophic extreme flood occurs due to dam break, the response time for flood warning is much shorter than for natural floods. Numerical models can be powerful tools to predict behaviors in flood wave propagation and to provide the information about the flooded area, wave front arrival time and water depth and so on. But flood wave propagation due to dam break can be a process of difficult mathematical characterization since the flood wave includes discontinuous flow and dry bed propagation. Nevertheless, a lot of numerical models using finite volume method have been recently developed to simulate flood inundation due to dam break. As Finite volume methods are based on the integral form of the conservation equations, finite volume model can easily capture discontinuous flows and shock wave. In this study the numerical model using Riemann approximate solvers and finite volume method applied to the conservative form for two-dimensional shallow water equation was developed. The MUSCL scheme with surface gradient method for reconstruction of conservation variables in continuity and momentum equations is used in the predictor-corrector procedure and the scheme is second order accurate both in space and time. The developed finite volume model is applied to 2D partial dam break flows and dam break flows with triangular bump and validated by comparing numerical solution with laboratory measurements data and other researcher's data.

Probability Distribution of Nonlinear Random Wave Heights Using Maximum Entropy Method (최대 엔트로피 방법을 이용한 비선형 불규칙 파고의 확률분포함수)

  • 안경모
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.10 no.4
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    • pp.204-210
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    • 1998
  • This paper presents the development of the probability density function applicable for wave heights (peak-to-trough excursions) in finite water depth including shallow water depth. The probability distribution applicable to wave heights of a non-Gaussian random process is derived based on the concept of the maximum entropy method. When wave heights are limited by breaking wave heights (or water depth) and only first and second moments of wave heights are given, the probability density function developed is closed form and expressed in terms of wave parameters such as $H_m$(mean wave height), $H_{rms}$(root-mean-square wave height), $H_b$(breaking wave height). When higher than third moment of wave heights are given, it is necessary to solve the system of nonlinear integral equations numerically using Newton-Raphson method to obtain the parameters of probability density function which is maximizing the entropy function. The probability density function thusly derived agrees very well with the histogram of wave heights in finite water depth obtained during storm. The probability density function of wave heights developed using maximum entropy method appears to be useful in estimating extreme values and statistical properties of wave heights for the design of coastal structures.

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Generation and Growth of Long Ocean Waves along the West Coast of Korea in March 2007 (2007년 3월 한국 서해안에 발생한 해양장파의 형성과 성장과정)

  • Choi, Byoung-Ju;Park, Yong-Woo;Kwon, Kyung-Man
    • Ocean and Polar Research
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    • v.30 no.4
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    • pp.453-466
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    • 2008
  • In order to examine the generation mechanism of long ocean waves along the west coast of Korea and to understand the amplification process of the long ocean waves, sea level, atmospheric pressure and wind data observed every minute from 2007 March 29 to 2007 April 1 were analyzed and onedimensional numerical ocean model experiments were performed. An atmospheric pressure jump propagated southeastward from Backryungdo to Yeonggwang along the west coast of Korea with speed of $13{\sim}27\;m/s$ between 2007 March 30 23:00 and 2007 April 1 1:30. Average magnitude of pressure jump was 4.2 hPa. As a moving atmospheric jump propagated from north to south along the coast, long ocean waves were generated and the sea level abnormally rose or fell at Anheung, Kunsan, Wido and Yeonggwang. Average amplitude of sea level rise (or fall) was about 113.6 cm. In a one-dimensional numerical ocean model, nonlinear shallow water equations were numerically integrated and a moving atmospheric pressure jump with traveling speed of 24 m/s was used as an external force. While the atmospheric pressure jump travels over 60 m depth ocean, a long ocean wave is generated. Because the propagation speed of the atmospheric jump is almost equal to that of the long ocean wave, Proudman resonance occurs and the long ocean wave amplifies. As the atmospheric pressure jump moves into the coastal area shallower than 60 m, the speed of the long ocean wave decreases and Proudman resonance effect decreases. However, the amplitude of the long ocean wave increases and wave length becomes shorter because of shoaling effect. When the long ocean wave hits the land boundary, amplitude of the long ocean wave drastically amplifies due to reflection. Data analysis and numerical experiments suggest that the southeastward propagation of an atmospheric pressure jump over the shallow ocean, which is a necessary condition for Proudaman resonance, generated the long ocean waves along the west coast of Korea on 2007 March 31 and the ocean waves amplified due to shoaling effect in the coastal area and reflection at the shore.

Estimation of Volume-Area-Depth Relationship for Shallow Wetland (습지의 체적-면적-깊이에 대한 관계식 추정)

  • Kim, Jun-Gwon;Kim, Hyeong-Su;Jeong, Sang-Man
    • Journal of Korea Water Resources Association
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    • v.35 no.2
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    • pp.231-240
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    • 2002
  • The wetland has very important functions in hydrologic and ecological aspects and the research of wetland functions requires the basic hydrological properties such as water quantity. However, we do not have a research work on the hydrological properties for a wetland study in Korea. Therefore, this study is to estimate the relations between the volume(V), the area(A), and the depth(h) of water in the wetland which might be the basis for the wetland research in Korea. To estimate the relations, we derive the basic equations, obtain the surveyed data and do modelling, and estimate the relations of A-h and V-h using the Surfer program. The estimated and observed volumes for 5-wetland are compared and the errors are in the range of 2 % to 11 % for 4-wetland and 34 % for the rest. The wetlands in small errors showed the similar ones with the profile of the wetted perimeter which is assumed for the derivation of the equation but the wetland of large error has much different profile with the assumed one. We re-estimate the volumes for 3-wetland(W3, W4, W5) which showed the large errors due to the bended profiles of the wetland slopes. say, after the slopes was divided into two parts of upper and lower ones, the volumes were estimated. From our re-estimation, we obtained very good results ranged from 1 % to 8 % in their errors. We conjecture that the procedure suggested in this study might be useful as a reference for the future research on the relations of V-A-h in Korea.

Coastal Currents Driven by Irregular Waves (불규칙파에 의한 연안류)

  • Yoo, Dong Hoon
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.10 no.4
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    • pp.151-158
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    • 1990
  • Various factors may contribute on the mixing processes in the surf zone formed by irregular waves. The turbulence motion driven by wave breaking may be one of the major causes, the effect due to spatial variation on current velocity be a secondary one, and the additional process may result from the irregular superposition of radiation stresses or wave breaking dissipation incurred by random breaking waves in a broadened surf zone. In the present study a numerical model of spectral waves and induced currents was developed using a superposition technique with ${\kappa}-{\varepsilon}$ closure for mixing process and applied to a field situation of longshore current generated by spectral waves on a uniform beach. It was found from the application that the surf-zone mixing processes formed by irregular waves can be well described by using ${\kappa}-{\varepsilon}$ equations if the source of ${\kappa}$ is properly represented. The nonlinear energy transfer was also found to have some influence on the velocity profile of longshore current particularly in very shallow water region near coast.

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Anumerical model study on tide-induced residual currents around Chejudo Island (제주도 주변의 조석 잔차류에 대한 수치 모델 연구)

  • 박용향;김성일
    • 한국해양학회지
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    • v.22 no.1
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    • pp.9-18
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    • 1987
  • A number of hydrographic studies and some recent current measurements around Chejudo Island suggest an existence of a clockwise residual flow in the west and north coasts of the island all the year round. On the eastern side of the island the Tsushinma Current flows northward and northeastward. The contribution of tide-induced residual currents to the observed residual. flow around the island was examined here through numerical solution of the two-dimensional nonlinear shallow-water equations. The calculated tide-induced residual currents show a clockwise circulation around the island. Significant residuals of 2-4cms$\^$-1/are confined over sloping bottom topography around t he island and the far-field residuals are negligibly small. The inclusion of a permanent current into the model was also attempted in order to see the effects of the Tsushima Current system on the residual circulation around the is land. It was found that combined effects of tide-induced residuals and the permanent current field associatedwith the Tsushima Current explain qualitatively not only the observed clock wise residuals in the west and north coasts but also the northward flow on the eastern side of the island.

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Application of Oil Spill Model to the South Sea of Korea (누유확산 모델의 남해안 적용)

  • Hong Keyyong;Lee Moonjin
    • Journal of the Korean Society for Marine Environment & Energy
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    • v.1 no.1
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    • pp.56-65
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    • 1998
  • An oil spill model, Green Sea Ranger(GSR) based on trajectory and fate modeling of spilt oil behavior is introduced. The various physical models on weathering processes are reviewed and those adopted by GSR are described. A database for currents, which is necessary for the real-time simulation of oil spill, is generated on the south sea of Korea. The real-time prediction of tidal currents in the South Sea of Korea is carried out. Four major constituents (M₂, S₂, K₁, O₁ tide) are employed in the prediction, and those angular speeds and phases are determined from the astronomical arguments. The harmonic constants of the constituents are computed by solving shallow-water tide equations. The GSR has user-freiendly GUI and flexible framework which makes it easy to expand the database for sea environments in Korean coastal waters. The GSR is validated by the simulation of O-Sung oil spill caused by a grounded oil tanker in coastal sea near Maemol-do. The simulated trajectory is compared with observed one and it is shown that the GSR gives reasonable estimation on spilt oil bahavior.

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Simulation of Tsunamis in the East Sea Using Dynamically-Interfaced Multi-Grid Model (동적결합둥지형 모형에 의한 동해안 쓰나미 시뮬레이션)

  • Choi, Byung-Ho;Efim, Pelinovsky;Woo, Seung-Buhm;Lee, Jong-Woong;Mun, Jong-Yoon
    • Journal of the Earthquake Engineering Society of Korea
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    • v.7 no.1
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    • pp.41-55
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    • 2003
  • A dynamically-interfaced multi-grid finite difference model for simulation of tsunamis in the East Sea(Choi et al.) was established and further applied to produce detailed feature of coastal inundations along the whole eastern coast of Korea. The computational domain is composed of several sub-regions with different grid sizes connected in parallel of inclined directions with 16 innermost nested models. The innermost sub-region represents the coastal alignment reasonably well and has a grid size of about 30 meters. Numerical simulations have been performed in the framework of shallow-water equations(linear, as well as nonlinear) over the plane or spherical coordinate system, depending on the dimensions of the sub-region. Results of simulations show the general agreements with the observed data of run-up height for both tsunamis. The evolution of the distribution function of tsunami heights is studied numerically and it is shown that it tends to the log-normal curve for long distance from the source.

A Numerical Analysis of Gravity and Free Surface Effects on a Two-Dimensional Supercavitating Flow (2차원 초공동 유동의 중력과 자유표면 효과에 대한 수치해석)

  • Kim, Hyoung-Tae;Lee, Hyun-Bae
    • Journal of the Society of Naval Architects of Korea
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    • v.51 no.5
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    • pp.435-449
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    • 2014
  • The effects of the gravity field and the free surface on the cavity shape and the drag are investigated through a numerical analysis for the steady supercavitating flow past a simple two-dimensional body underneath the free surface. The continuity and the RANS equations are numerically solved for an incompressible fluid using a $k-{\epsilon}$ turbulence model and a mixture fluid model has been applied for calculating the multiphase flow of air, water and vapor using the method of volume of fluid and the Schnerr-Sauer cavitation model. Numerical solutions have been obtained for the supercavitating flow about a two-dimensional $30^{\circ}$ wedge in wide range of depths of submergence and inflow velocities. The results are presented for the cavity shape, especially the length and the width, and the drag of the wedge in comparison with those of the case for the infinite fluid flow neglecting the gravity and the free surface. The influences of the gravity field and the free surface on the aforementioned quantities are discussed. The length and the width of the supercavity are reduced and the centerline of the cavity rises toward the free surface due to the effects of the gravity field and the free surface. The drag coefficient of the wedge, however, is about the same except for shallow depths of submergence. As the supercavitating wedge is approaching very close to the free surface, it is found the length and the width of a cavity are shorten even though the cavitation number is reduced. Also the present result suggests that, under the influence of the gravity field and the free surface, the length of the supercavity for a certain cavitation number varies and moreover is proportional to the inverse of the submergence depth Froude number.

A Review on the Photochemical Oxidant Modeling as Applied to Air Quality Studies in Complex Terrain

  • Lee Hwa-Woon;Kim Yoo-Keun;Won Gyeong-Mee;Park Jong-Kil
    • Environmental Sciences Bulletin of The Korean Environmental Sciences Society
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    • v.1 no.1
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    • pp.19-33
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    • 1997
  • The high oxidants, which occur the daily maximum concentrations in the afternoon, are transported into the other region via long range transport mechanisms or trapped within the shallow mixing boundary layer and then removed physically (deposition, transport by mountain wind, etc.) and chemically (reaction with local sources). Therefore, modeling formation of photochemical oxidants requires a complex description of both chemical and meteorological processes. In this study, as a part of air quality studies, we reviewed various aspects of photochemical modeling on the basis of currently available literature. The result of the review shows that the model is based on a set of coupled continuity equations describing advection, diffusion, transport, deposition, chemistry, emission. Also photochemical oxidant models require a large amount of input data concerned with all aspects of the ozone life cycle. First, emission inventories of hydrocarbon and nitrogen oxides, with appropriate spatial and temporal resolution. Second, chemical and photochemical data allowing the quantitative description of the formation of ozone and other photochemically-generated secondary pollutants. Third, dry deposition mechanisms particularly for ozone, PAN and hydrogen peroxide to account for their removal by absorption on the ground, crops, natural vegetation, man-made and water surfaces. Finally, meteorological data describing the transport of primary pollutants away from their sources and of secondary pollutants towards the sensitive receptors where environmental damage may occur. In order to improve our present study, shortcomings and limitation of existing models are pointed out and verification process through observation is emphasized.

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