• Title/Summary/Keyword: Nonlinear Mild-Slope Equation

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Calculation of Wave Deformation and Wave Induced Current around an Underwater Shoal by Boussinesq Equation (Boussinesq 방정식을 이용한 수중 천퇴에서의 파랑변형 및 파랑류 계산)

  • Chun Insik;Seong Sangbong;Kim Guidong;Sim Jaeseol
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.17 no.3
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    • pp.202-212
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    • 2005
  • In the design of an of offshore structure located near an underwater shoal, the same amount of attention given to the wave height may have to be put to the wave induced current as well since some of the wave energy translates to the current. In the present study, two numerical models each based on the nonlinear Boussinesq equation and the linear mild slope equation are applied to calculate the wave deformation and secondly induced current around a shoal. The underwater shoal in Vincent and briggs' experiment (1989) is used here, and all non-breaking wave conditions of the experiment with various monochromatic and unidirectional or multidirectional spectral wave incidences are concerned. Both numerical models clearly showed wave induced currents symmetrically farmed along the centerline over the shoal. The calculated wave heights along a preset line also generally showed very nice agreements with the experimental values.

Estimation of Harbor Responses due to Construction of a New Port in Ulsan Bay

  • Lee, Joong-Woo;Lee, Hoon;Lee, Hak-Seung;Jeon, Min-Su
    • Journal of Navigation and Port Research
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    • v.28 no.7
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    • pp.619-627
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    • 2004
  • Introduction of wave model, considered the effect of shoaling, refraction, diffraction, partial reflection, bottom friction, breaking at the coastal waters of complex bathymetry, is a very important factor for most coastal engineering design and disaster prevention problems. As waves move from deeper waters to shallow coastal waters, the fundamental wave parameters will change and the wave energy is redistributed along wave crests due to the depth variation, the presence of islands, coastal protection structures, irregularities of the enclosing shore boundaries, and other geological features. Moreover, waves undergo severe change inside the surf zone where wave breaking occurs and in the regions where reflected waves from coastline and structural boundaries interact with the incident waves. Therefore, the application of mild-slope equation model in this field would help for understanding of wave transformation mechanism where many other models could not deal with up to now. The purpose of this study is to form a extended mild-slope equation wave model and make comparison and analysis on variation of harbor responses in the vicinities of Ulsan Harbor and Ulsan New Port, etc. due to construction of New Port in Ulsan Bay. We also considered the increase of water depth at the entrance channel by dredging work up to 15 meters depth in order to see the dredging effect. Among several model analyses, the nonlinear and breaking wave conditions are showed the most applicable results. This type of trial might be a milestone for port development in macro scale, where the induced impact analysis in the existing port due to the development could be easily neglected.

The Analysis of Wave Height Distribution in the Jumunjin Fishery Port with Seawater-Exchange Breakwater (해수교환방파제가 설치된 주문진항에서의 파고분포 해석)

  • Kim, Nam-Hyeong;Yun, Hyeon-Cheol;Koo, Bon-Soo
    • Journal of Navigation and Port Research
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    • v.34 no.1
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    • pp.51-57
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    • 2010
  • When estimating the calmness in a harbor, it is important that diffraction and reflection of irregular waves should be exactly calculated. The basic equation of the numerical model in this study was used Mild-slope equation, which has the advantage of which non-linearity with great influence for the wave behavior can be considered, and a triangular mesh was generated by using finite element method. So as to verify the nonlinear effects, the results of the numerical model developed in this study are compared with the experimental and numerical results by other researchers. As a result, it is shown that the results in case of considering nonlinear wave are more exact for wave analysis than in case of not considering nonlinear wave. In order to apply this model, wave height distributions in Jumunjin fishery port installed a seawater-exchange breakwater are computed. From the results of this numerical analysis, when abnormal waves are intruded through the seawater-exchange breakwater, the results of the wave height distributions in the harbor are highly presented. Therefore, in order to get wave height low in the harbor, it is considered that the facility with the ability to protect the inflow of abnormal waves is needed.

Characteristics of Wave Trasnformation in Gamcheon Harbor (감천항내의 파랑변형 특성)

  • 김재중;김기철;이정만
    • Journal of Korean Port Research
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    • v.13 no.2
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    • pp.399-408
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    • 1999
  • Copeland’s(1985) hyperbolic mild-slope equation including diffraction refraction and reflection in the wave field is used as a governing equation in this study. The result of Maruyama & Kajima(1985) is used to calculate wave direction and that of Watanabe & Maruyama(1986) is used as a energy dissipation formula. Numerical solutions are obtained by the Leap-Frog scheme and compared with Watanabe & Maruyama’s (1984) hydraulic experimental results and numerical simulation results for the detached breakwater. This wave model is applied to a detached breakwater and compared with Watanabe and Maruyama’s (1984) hydraulic model results to check the characteristics of reflected wave field around a detached breakwater. The distribution of wave height and we phase in front of a detached breakwater is more accurate than the Watanabe and Maruyama’s numerical results. The results from our wave model show good agreements with the others and also show nonlinear effects around the detached breakwater. This model is applied to the Gamcheon harbor of pusan. the field observations were carried out at Pusan harbor wave station in 1986-1995 and the results were accepted as a design wave condition in this study. The wave height and wave period was measured by Dong-A university at one station in the Gamcheon harbor in 1996-1997 and used as a calibration criterion. The measured data were used as input data for the numerical simulation and also compared with simulated results. The numerical simulation shows a fairly good results which considering the effect of topographic characteristics and effect of narrow entrance due to two separated breakwaters in Gamcheon harbor. The wave distribution characteristics inside Gamcheon harbor is quite different with the offshore wave direction and wave period.

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A Runoff Model based on the Stream Magnitude (수로망(水路綱)크기를 이용한 유출모형(流出模型))

  • Lee, Won Hwan;Jun, Min Woo
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.9 no.2
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    • pp.83-90
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    • 1989
  • A runoff model was estabilished for the direct runoff hydrograph at each subareas by obtaining the storage coefficient based on stream magnitudes of geomorphic parameters. For this, the relationship between flowsection and channel distance from the outlet of each subareas was assumed as nonlinear equation, and compared with linear one. The applicability of the runoff model to the real watershed was tested for the Bochung river basin. The results of the analysis show that the model was approved to be used for the prediction of small watershed having no runoff records and a linear equation between flowsection and channel distance from the outlet of each subareas was more similar to the observed data for the upper subarea with a steep slope and small area, on the other hand, nonlinear equation for the lower subarea with mild slope and relatively large area.

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Simulation of Wave-Induced Currents by Nonlinear Mild-Slope Equation and Comparison with PIV Measurements (비선형 완경사 방정식에 의한 연안류의 모의 및 PIV 관측결과와의 비교)

  • Lee, Jung-Lyul;Park, Chan-Sung;Han, Sang-Woo
    • Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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    • 2000.09a
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    • pp.140-148
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    • 2000
  • The nearshore currents are required for the preservation of coastal areas and the more pressing environmental problems since they cause sediments to be in suspension and transport the sediments into tranquil regions. Numerical models are often used to calculate current patterns formed around man-made or naturally caused changes around the coastal area. (omitted)

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Application of Boussinesq Equation Model for the Breaking Wave Behavior around Underwater Shoals (수중 천퇴에서의 쇄파거동 예측을 위한 Boussinesq 방정식 모델의 적용)

  • Chun, In-Sik;Kim, Gui-Dong;Sim, Jae-Seol
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.18 no.2
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    • pp.154-165
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    • 2006
  • In the present study, a numerical model using Boussinesq equation is set up to predict the interacted equilibrium between waves and their induced currents in the occurrence of breaking waves over an underwater shoal, and the numerical results are compared with results of existing hydraulic experiments. A sensitivity analysis has been done to find out appropriate values of breaking wave parameters with the result (regular wave case) of Vincent and Briggs (1989)’ experiment. Then the numerical model is applied to the irregular wave cases of the experiment and the hydraulic model test of Ieodo which is a natural undersea shoal. The results show that a strong current forms in the wave direction at the downstream side of the shoals, causing the attenuation of wave heights there. The calculated wave heights generally show a similar pattern with the measured data.