• Title/Summary/Keyword: Boussinesq equation model

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A Practical Application of Multiple Wave Models to the Small Fishery Harbor Entrance

  • Jung, Jae-Hyun;Lee, Joong-Woo;Jeon, Min-Su;Kang, Seok-Jin
    • Journal of Navigation and Port Research
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    • v.31 no.7
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    • pp.579-587
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    • 2007
  • Samchunpo(Sin Hyang) Harbor is located in the bay of Sa Chun, the central south coast of Korean peninsula. The harbor and coastal boundaries have been protecting by natural coastal islands and shoals. Currently, The Sin Hyang harbor needs maintenance and renovation of the sheltered structures against the weather deterioration and typhoon damages. Consequently to support this, the calculation of accurate design wave through the typhoon wave attack is necessary. In this study, calculation of incident wave condition is simulated using steady state spectrum energy wave model(wide area wave model) from 50 years return wave condition. And this simulation results in wide offshore area were used for the input of the extended mild slope wave model at the narrow coastal area. Finally, the calculation of design wave at Sin Hyang harbor entrance was induced by Boussinesq wave model(detail area wave model) simulation. The numerical model system was able to simulate wave transformations from generation scale to shoreline or harbor impact. We hope these results will be helpful to the engineers doing placement, design, orientation, and evaluation of a wide range of potential solutions in this area.

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.

Numerical Analysis of Nonlinear Effect of Wave on Refraction and Diffraction (파의 굴절 및 회절에 미치는 비선형 효과에 대한 수치해석)

  • 이정규;이종인
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.2 no.1
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    • pp.51-57
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    • 1990
  • Based on second-order Stokes wave and parabolic approximation, a refraction-diffraction model for linear and nonlinear waves is developed. With the assumption that the water depth is slowly varying, the model equation describes the forward scattered wavefield. The parabolic approximation equations account for the combined effects of refraction and diffraction, while the influences of bottom friction, current and wind have been neglected. The model is tested against laboratory experiments for the case of submerged circular shoal, when both refraction and diffraction are equally significant. Based on Boussinesq equations, the parabolic approximation eq. is applied to the propagation of shallow water waves. In the case without currents, the forward diffraction of Cnoidal waves by a straight breakwater is studied numerically. The formation of stem waves along the breakwater and the relation between the stem waves and the incident wave characteristics are discussed. Numerical experiments are carried out using different bottom slopes and different angles of incidence.

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A Study on Wave Transformation Analysis using Higher-Order Finite Element (고차유한요소의 파랑변형해석에의 적용에 관한 소고)

  • Jung, Tae-Hwa;Lee, Jong-In;Kim, Young-Taek;Ryu, Yong-Uk
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.21 no.2
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    • pp.108-116
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    • 2009
  • The present study introduces a Legendre interpolation function which is capable of analyzing wave transformation effectively in a finite element method. A Lagrangian interpolation function has been mostly used for a finite element method with a higher-order interpolation function. Although this function has an advantage of giving an accurate result with less number of elements, simulation time increases. Calculation time can be reduced by mass lumping, whereas the accuracy of solution is lowered. In this study, we introduce a modified Lagrangian interpolation function, Legendre cardinal interpolation, which can reduce simulation time with keeping up favorable accuracy. Through various numerical simulations using a Boussinesq equations model, the superiority of the Legendre cardinal interpolation function to a Lagrangian interpolation function was shown.

Analytic solution for the interaction between a viscoelastic Bernoulli-Navier beam and a winkler medium

  • Floris, Claudio;Lamacchia, Francesco Paolo
    • Structural Engineering and Mechanics
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    • v.38 no.5
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    • pp.593-618
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    • 2011
  • This paper deals with the problem of the determination of the response of a viscoelastic Bernoulli-Navier beam, which is resting on an elastic medium. Assuming uniaxial bending, the displacement of the beam axis is governed by an integro-differential equation. The compatibility of the displacements between the beam and the elastic medium is imposed through an integral equation. In general and in particular in the case of a Boussinesq medium, the solution has to be pursued numerically. On the contrary, in the case of a Winkler's medium the compatibility equation becomes a linear finite relationship, which allows finding an original analytical solution of the problem for both hereditary and aging behavior of the beam. Some numerical examples complete the paper, in which a comparison is made between the hereditary and the aging model for the creep of the beam.

Numerical Study on a Dominant Mechanism of Rip Current at Haeundae Beach: Honeycomb Pattern of Waves (수치모의를 통한 해운대 이안류의 주요 메커니즘 연구: 파랑의 벌집구조)

  • Choi, Junwoo;Park, Won Kyung;Bae, Jae Seok;Yoon, Sung Bum
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.32 no.5B
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    • pp.321-329
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    • 2012
  • Two regular progressive wave trains, the directions of which are slightly different from each other, develop a honeycomb pattern of wave crests due to their nonlinear interaction. In the honeycomb pattern of wave crest, the nodal line area, which has very low wave energy, is formed. When the honeycomb pattern is developed near the beach area, rip current evolves through the nodal line area formed in the cross shore direction. In this study, to confirm that the formation of honeycomb pattern of waves near the beach area is a dominant mechanism of rip current occurred at Haeundae beach, we performed a numerical simulation of nearshore circulation at Haeundae beach under an unidirectional and monochromatic wave condition by using a nonlinear Boussinesq equation model. As a result, wave refraction due to topographical characteristics (i.e., submerged shoal) of Haeundae gave rise to several wave trains propagating with slightly different directions toward the beach, and consequently rip currents well developed through the nodal line area of honeycomb patterns of wave crest. In addition, we found that a narrow-banded spectral wave condition (i.e., a swell spectrum) increases more likelihood of rip current than a broad-banded spectral wave condtion based on the simulations employing various wave spectra with an equivalent wave height and period.

Theoretical Study on the Generation of Directional Extreme Waves (다방향 극한파 생성의 이론적 연구)

  • Key-Yong Hong;Shuxue Liu;Seok-Won Hong
    • Journal of the Society of Naval Architects of Korea
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    • v.39 no.1
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    • pp.38-48
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    • 2002
  • Theoretical development to generate the directional extreme waves in model basin is established based on wave focusing method. The effects of associated parameters, such as the directional range, frequency width, and center frequency, are investigated in terms of wave focusing efficiency. The two different spectral models of constant wave amplitude and constant wave slope are applied to control the wave characteristics. The wave packets simulated by theory are compared with numerical results based on Boussinesq equation and FEM. Both controls of direction and frequency spectrum are essential to focus directional waves effectively. It is noticed that wave focusing ability depends on the frequency bandwidth of spectrum rather than center frequency, and both spectral models with same parameters result in the equivalent efficiency of wave focusing.

The Prediction of Wave Groups within a Harbor to Assist Ship Operation at the Entrance

  • Cho Ik-Soon
    • Journal of Navigation and Port Research
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    • v.30 no.2
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    • pp.125-130
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    • 2006
  • Waves, which are the main source of ship motions in a seaway, considerably affect the performance of a ship. The study of waves and their impact on ship motions within harbors is an important aspect of the design and operation of harbors. The prediction of incoming groups of waves is particularly important for evaluating ship motion within a harbor. Such a prediction makes it possible to evaluate ship safety more accurately. The wave transformation model reported here is applied to actual ports based on Boussinesq wave equations both non-linear and dispersive wave processes be considered in order to capture physical effects such as wave shoaling, refractions, reflection and diffraction in variable depth environments. The prediction of incoming groups of waves is particularly important for evaluating ship motion within a harbor, Such a prediction makes it possible to evaluate ship safety more accurately and provide safe wave informations for navigation. Furthermore, a wave information support system is proposed for entering ships as one technique for improving the safety of ship operations. This system predicts the run of waves and reduces the danger by identifying the most dangerous point near the harbor entrance at the small wave groups.

Numerical analysis of 3-dimensional buoyant turbulent flow in a stairwell model with three different finite differencing schemes (유한차분 도식에 따른 건물 계단통에서의 3차원 부력 난류유동 수치해석)

  • Myong, H.K.
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.11 no.1
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    • pp.73-80
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    • 1999
  • This paper describes a numerical study of three-dimensional buoyant turbulent flow in a stairwell model with three convective differencing schemes, which include the upwind differencing scheme, the hybrid scheme and QUICK scheme. The Reynolds-averaged Navier-Stokes and energy equations are solved with a two-equation turbulence model. The Boussinesq approximation is used to model buoyancy terms in the governing equations. Three-dimensional predictions of the velocity and temperature fields are presented and are compared with experimental data. Three-dimensional simulations with each scheme have predicted the overall features of the flow fairly satisfactorily. A better agreement with experimental is achieved with QUICK scheme.

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Analysis of Turbulent Flow in a Square Duct with a $180^{\circ}$ Bend ($180^{\circ}$곡관을 갖는 정사각 단면 덕트에서의 란류류동 해석)

  • Launder, B. E.;Kim, Myung-Ho;Moon, Chan;Choi, Young-Don
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.12 no.3
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    • pp.607-621
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    • 1988
  • The paper describes the incorporation of an algebraic stress model(ASM) of turbulence in to a semi-elliptic solution procedure for the prediction of turbulent flow in passage around a 180.deg. square sectioned bend. The numerical results are obtained from a finite-volume discretization with applications of QUICK scheme and full find grid system without PSL approximation. Results show that the better agreements in velocity profiles with experimental data than those from k, $\varepsilon$ equation model with wall function and PSL are obtained. Predictions of Reynolds stresses also show good agreements with the experimental data.