• Title/Summary/Keyword: 비선형천해방정식

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Tidal Propagation in the Keum River (금강 感趙구간의 조석전파)

  • 최병호;안원식
    • Water for future
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    • v.18 no.1
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    • pp.67-73
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    • 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.

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An analytical and numerical study of a vertically-discretized wavemaker (수직다열화된 조파장치의 해석해 개발 및 수치모형 실험)

  • Son, Sangyoung;Kim, Yeulwoo;Jung, Taehwa
    • Proceedings of the Korea Water Resources Association Conference
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    • 2021.06a
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    • pp.103-103
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    • 2021
  • 실험실에서의 파랑생성에 흔히 사용되는 피스톤형 조파장치는 수심에 따라 유속이 동일하게 생성된다는 제약이 있어 주로 천해파의 생성에 적합한 것으로 알려져 있다. 본 연구에서는 이러한 제약조건 없이 다양한 유속분포의 파형을 생성하는 수직 다열화된 조파장치가 개발되었다. 우선, 수심방향으로 이산화된 각 패들(paddle)의 스트로크에 대해 선형해석해가 유도되었다. 개발된 해석해는 패들의 수 및 유속분포에 따라 기존의 피스톤형 혹은 플랩형 조파장치 해석해로 근사함이 밝혀짐으로써 포괄적으로 활용될 수 있음이 확인되었다. 즉 개발된 해석해를 활용하면 선택적으로 피스톤형 및 플랩형 조파성능이 구현될 수 있다. 더불어 개발된 해석해는 다상유체의 내부파 생성에도 확정되어 적용가능함이 확인되었다. 다음으로, 개발된 조파장치를 수치적으로 구현하였다. 오픈소스 3차원 수치모형인 OpenFOAM 중, 두 개 이상의 불연속 및 비압축 유체에 대한 Navier-Stokes 방정식을 해결하는 수치 모듈을 사용하여 제안된 수직다열화된 조파장치의 성능이 평가되었다. 이때 동적격자모델(olaDyMFlow)을 결합함으로써 개발된 조파장치 움직임이 물리적 조파장치와 흡사하도록 수치적으로 구현하였다. 모의결과, 여러 개의 다열화된 패들이 층류 흐름 조건에서 심해파를 효율적으로 생성시키고, 중간수심 파랑조건에서는 제안된 조파장치가 상대적으로 덜 유리함을 확인할 수 있었다. 마지막으로 공기, 기름 및 물 등 3상의 흐름조건에서 단 두 개의 패들을 활용하여 각각 내부파 및 표면파를 생성하되었으며, 모의 결과는 해석해과 비교됨으로써 개발된 조파장치의 성능이 검증되었다.

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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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On numerical analysis for tsunami run-up on slope beach (경사 해빈에서 지진해일 처오름에 관한 수치적 고찰)

  • Lee, Woo-Dong;Kim, Taeyoon;Hwang, Taegeon;Ko, Chanhyun
    • Proceedings of the Korea Water Resources Association Conference
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    • 2022.05a
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    • pp.83-83
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    • 2022
  • 여러 분야의 연구자들이 지진해일의 위험에 대한 경각심을 가지고, 지진해일의 발생, 전파 그리고 수리현상을 해석하기 위해 많은 노력을 기울이고 있다. 해안지역에서 직접적인 피해를 입히는 지진해일의 충격파, 처오름, 월파, 침수 등에 관한 연구에 유사한 파형 특성을 가진 고립파를 많이 사용한다. 고립파는 비선형성과 분산이 균형을 이루는 가정에서 Korteweg-de Vries(KdV) 방정식을 만족하는 안정적인 이론파이다. 고립파의 파형분포는 수심에 의해 결정되고, 일정 수심 이상에서는 지진해일을 대신해 사용할 수 있다. 그러나 수심이 낮은 천해에서는 주기와 파장이 비현실적으로 짧아짐으로 지진해일을 대신하기에는 무리가 있다. 본 연구에서는 지진해일의 처오름 특성을 분석하기 위한 1:20 불투과성 경사면이 포함된 수치파동수조를 구성한다. 먼저, 일본 NOWPHAS(Nationwide Ocean Wave information network for Ports and HArbourS)의 관측자료를 이용하여 2011 동일본 지진해일과 고립파의 파형분포를 비교한다. 그리고 다양한 파형의 지진해일 생성할 수 있게 개발된 조파방법을 수치파동수조에 도입하여 수치해석을 수행한다. 수치해석결과, 지진해일의 처오름 높이가 고립파에 비해 최대 1.8배, 최소 1.13배, 평균 1.56배 증가한다.

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A Parabolic Approximation Model for Wave Deformation Combined Refraction, Diffraction, and Breaking (파랑(波浪)의 굴절(屈折), 회절(回折) 및 쇄파변형(碎波變形)에 관한 포물형근사모형(抛物形近似模型))

  • Lee, Dong Soo;Lee, Jong Sup;Park, II Heum
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.14 no.3
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    • pp.619-633
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    • 1994
  • A wave deformation model for general purpose combined refraction, diffraction, and breaking is developed in the shallow water. A parabolic approximation equation considered a higher order diffraction term is derived from the previous mild slope equation. A wave energy dissipation term due to bottom friction and breaking is introduced from the turbulence model. The Crank-Nicoloson implicit scheme is used in the numerical calculation, then the solutions are compared with the various hydraulic experiment data in the circular, the elliptic shoal, and the surf zone. The wave height decay in the surf zone is sensitively affected by the incident wave steepness, and the wave height variation around the elliptic shoal is well explained by the non-linear dispersion relation and the wave energy dissipation term. The model is also applied to a field coastal area and reasonable results are obtained.

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A Three-dimensional Spectral Model for the Computation of Wind-induced Flows in a Homogeneous Shelf Sea (취송류 재현을 위한 3차원 스펙트랄모형 개발)

  • So, Jae-Kwi;Jung, Kyung-Tae;Lee, Kwang-Soo;Seung, Young-Ho
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.4 no.2
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    • pp.91-107
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    • 1992
  • A numerical formulation is developed to solve the linear three-dimensional hydrodynamic equations which describes wind induced flows in a homogeneous shelf sea. The hydmdynamic equations are at the outset separated into two systems. namely, an equation containing the gradient of sea surface elevation and the mean flow (external mode) and an equation describing the deviation from the mean flow (internal mode). The Galerkin method is then applied to the internal mode equation. The eigenvalues are determined from the eigenvalue problem involving the vertical eddy viscosity subject to a homogeneous boundary condition at the surface and a sheared boundary condition at the sea bed. The model is tested in a one-dimensional channel with uniform depth under a steady, uniform wind. The analytical velocity profile by Cooper and Pearce (1977) using a constant vertical eddy viscosity in channels of infinite and finite length is chosen as a benchmark solution. The model is also tested in a homogeneous, rectangular basin with constant depth under a steady, uniform wind field (the Heaps' Basin of the North Sea scale).

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Applicability of the Korteweg-de Vries Equation for Description of the Statistics of Freak Waves (최극해파통계분석을 위한 Korteweg-de Vries식의 적용성 검토)

  • Anna Kokorina;Efim Pelinovsky
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.14 no.4
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    • pp.308-318
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    • 2002
  • The requirements to the numerical model of wind-generated waves in shallow water are discussed in the framework of the Korteweg-de Vries equation. The weakness of nonlinearity and dispersion required for the Korteweg-de Vries equation applicability is considered for fully developed sea, non-stationary wind waves and swell, including some experimental data. We note for sufficient evaluation of the freak wave statistics it is necessary to consider more than about 10,000 waves in the wave record, and this leads to the limitation of the numerical domain and number of realizations. The numerical modelling of irregular water waves is made to demonstrate the possibility of effective evaluation of the statistical properties of freak waves with heights equal to 2-2.3 significant wave height.

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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Numerical Prediction of Ship Induced Wave and its Propagation Using Nonlinear Dispersive Wave Model (비선형분산파랑모형을 이용한 항주파의 발생과 전파에 관한 수치예측모형 개발)

  • Shin, Seung-Ho;Jeong, Dae-Deug
    • Journal of Navigation and Port Research
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    • v.27 no.5
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    • pp.527-537
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    • 2003
  • The characteristics of ship induced waves caused by navigation become widely different from both ship's speed and water depth condition. The ship induced waves specially generated in coastwise routes frequently give rise to call unforeseen danger for swimmers and small boats as well as shoreline erosion or sea wall destruction in coastal zones. The main concern of ship induced wave study until now is either how to reduce ship resistance or how to manoeuvre the ship safely under a constant water depth in the view point of shipbuilding engineers. Moreover, due to the trends for appearance of the high speed ships at the shallow coastal water, we are confronted with the danger of damages from those ship induced waves. Therefore, it is necessary to examine the development of ship induced waves and the influence of their deformation effects according to its propagation ray. In present study, in order to predict the development of the ship induced waves and their propagation under the conditions of complicate and variable shallow water depth with varying ship's speed, we constructed a computer model using Boussinesq equation with a fixed coordinate system and verified the model results by comparison with experimental results. Additionally, the model was applied under the variable water depth based on actual passage and we then confirmed the importance of the variable water depth consideration.