• Title/Summary/Keyword: shallow water waves equations

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Estimation of Tsunami Run-up Heights with Parameters (매개변수에 따른 지진해일의 처오름높이 예측)

  • Ahn, Young-Chang;Hwang, Kyu-Nam;Cho, Yong-Sik
    • Journal of Korea Water Resources Association
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    • v.36 no.3 s.134
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    • pp.437-445
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    • 2003
  • Since many islands are located in the South Sea, unexpected damage by tsunamis could be caused by mutual interferences between adjacent islands. In this study, the variation of run-up heights is investigated by using different crest lengths of incident waves and different distances between two adjacent islands. The run-up height sharply increases when the crest length of Incident waves is greater than the distance bewteen outer boundaries of two islands. The run-up height also increases as the distance between two adjacent islands decreases.

Active Dispersion-Correction Scheme of 2-D Finite Element Model for Simulation of Tsunami Propagation (지진해일 전파 수치모의를 위한 2차원 유한요소모형의 능동적 분산보정기법)

  • Yoon Sung Bum;Lim Chae Ho
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.17 no.1
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    • pp.1-8
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    • 2005
  • For the simulation of tsunami propagation an active dispersion-correction two-dimensional finite element model has been developed based on a shallow-water wave equation. This model employs an arbitrary triangular mesh and an explicit time integration scheme. However, the physical dispersion effects as included in the Boussinesq equations can be taken into account in the computation. The validity of the dispersion-correction scheme developed in this study is verified through the comparison of numerical solutions calculated using the new scheme with analytical ones considering dispersion effect of waves. As a result, the present model is shown to be considerably accurate.

Higher Harmonic Generation by Nonlinear Interaction between Monochromatic Waves and a Horizontal Plate (규칙파와 수평판의 비선형 상호작용에 의한 고차 조화항 발생)

  • Koh, Hyeok-Jun;Cho, Il-Hyoung
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.19 no.5
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    • pp.484-491
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    • 2007
  • Numerical experiments using a numerical wave tank have been performed to verier the nonlinear interaction between monochromatic waves and a submerged horizontal plate. As a model for numerical wave tank, we used a higher-order Boundary Element Method(BEM) based on fully nonlinear potential flow theory and CADMAS-SURF for solving Navier Stokes equations and exact free surface conditions. Both nonlinear models are able to predict the higher harmonic generation in the shallow water region over a submerged horizontal plate. CADMAS-SURF, which involves the viscous effect, can evaluate the higher harmonic generation by flow separation and vortices at the each ends of plate. The comparison of reflection and transmission coefficients with experimental results(Patarapanich and Cheong, 1989) at different lengths and submergence depths of a horizontal plate are presented with a good agreement. It is found that the transfer of energy from the incident fundamental waves to higher harmonics becomes larger as the submergence depth ratio decreases and the length ratio increases.

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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Analytic Solution to Mild Slope Equation for Transformation of Waves Propagating over an Axi-symmetric Pit (축대칭 함몰지형 위를 진행하는 파의 변형에 관한 완경사 방정식의 해석 해)

  • Jung, Tae-Hwa;Suh, Kyung-Duck
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.18 no.4
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    • pp.308-320
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    • 2006
  • An analytic solution to the mild-slope equation is derived for waves propagating over an axi-symmetric pit. The water depth inside the pit varies in proportion to a power of radial distance from the pit center. The governing equation is transformed into ordinary differential equations by using separation of variables, and the coefficients of the equations are transformed into explicit forms by using Hunt's (1979) approximate solution. Finally, by using the Frobenius series, the analytic solution is derived. Due to the feature of Hunt's equation, the present analytic solution is accurate in shallow and deep waters, while it is less accurate in intermediate depth water. The validity of the analytic solution is demonstrated by comparison with numerical solutions. The analytic solution is also used to examine the effects of pit geometry and relative depth on wave transformation.

Decomposition of Reflecting Waves by Hyperbolic Model (쌍곡선형 모델에 의한 반사파 성분 분해)

    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.10 no.4
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    • pp.197-203
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    • 1998
  • An approach of decomposing the reflecting components is proposed by using the mild-slope equation of hyperbolic type which has the similar form to the shallow water equations. The approach is verified on Booij's problem and sinusoidally varying ripples. Inclusion of higher-order bottom effect given by chamberlain and Porter(1995) yields even more satisfactory results than the Berkhoff's mild-slope equation when compared with finite element solution or experiments.

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A Numerical Study on Characteristics of Flood Wave Passing through Urban Areas (2) : Application and Analysis (도시지역을 관통하는 홍수파의 특성에 관한 수치적 연구 (2) : 적용 및 분석)

  • Jeong, Woo-Chang;Cho, Yong-Sik;Lee, Jin-Woo
    • Journal of the Korean Society of Hazard Mitigation
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    • v.10 no.1
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    • pp.65-72
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    • 2010
  • In this study, the effects of urban areas against flood waves due to a dam failure were numerically investigated based on the two laboratory experiments and the predicted water surface elevations at specific points showed good agreement with available measurements. In the first experiment, a relatively high water depth and the delay effect of flow at the front of urban areas are observed. The urban areas may become a large obstacle against smooth propagation of flood wave. In the second one, as the inflow increases, moreover, the water surface elevations can be classified into abruptly decreasing portion and slowly decreasing portion, and the first arrival time to the front of urban area is decreasing with the increasing inflow.

A Study on Simulation of Dam-break Wave Using Two-dimensional Finite Volume Model (2차원 유한체적모형을 이용한 댐 붕괴파 모의에 관한 연구)

  • Jeong, Woo-Chang;Park, Young-Jin
    • Journal of Korea Water Resources Association
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    • v.44 no.3
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    • pp.249-262
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    • 2011
  • In this study, in order to reduce the numerical oscillation due to the unbalance between source and flux terms as the HLLC scheme is applied to the flow analysis on the irregular bed topography, a unstructured finite volume model based on the well-balanced HLLC scheme and the shallow water equations is developed and applied to problems of dam-break waves. The well-balanced HLLC scheme considers directly the gradient of bed topography as the flux terms is calculated. This scheme provides the good numerical balance between the source and flux terms in the case of the application to the steady-state transcritical flow. To verify the numerical model developed in this study, it is applied to three cases of hydraulic model experiments and a field case study of Mapasset dam failure (France). As a result of the verification, the predicted numerical results agree relatively well with available laboratory and field measurements. The model provides slightly more accurate results compared with the existing models.

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.

Numerical Simulation of Depth-Averaged Flow with a CDG Finite Element Method (CDG 유한요소법을 이용한 수심적분 흐름의 수치모의)

  • Kim, Tae Beom;Choi, Sung-Uk;Min, Kyung Duck
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.26 no.5B
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    • pp.447-457
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    • 2006
  • This paper presents a numerical model for the simulations of 2D depth-averaged flows. The shallow water equations are solved numerically by the Characteristic Dissipative Galerkin (CDG) finite element method. For validation, the developed model is applied to the hydraulic jump. The computed results are compared with the analytical solution, revealing good agreement. In addition, flow in a contracting channel showing standing waves is simulated. The calculated water surface profile appears to be qualitatively consistent with the observed data. The foregoing results indicate that the model is capable of simulating the abrupt change in flow field. Next, the model is applied to the flow in a $180^{\circ}$ curved channel. The simulated results show that the velocity near the inner bank is faster than that near the outer bank and the water depth near the inner bank is shallower than that near the outer bank. However, the simulated results show that the velocity distribution across the channel is almost uniform in the bend except the reach close to the end of the bend. This is due to the limitation of the governing equations in which the transverse convection of momentum by the secondary flows along a channel bend is not taken into account.