• Title/Summary/Keyword: Mild-slope Equation

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Analysis of Wave Transmission Characteristics on the TTP Submerged Breakwater Using a Parabolic-Type Linear Wave Deformation Model

  • Jeong, Jin-Hwan;Kim, Jin-Hoon;Lee, Jung-Lyul
    • Journal of Ocean Engineering and Technology
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    • v.35 no.1
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    • pp.82-90
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    • 2021
  • Owing to the advantages of assuring the best views and seawater exchange, submerged breakwaters have been widely installed along the eastern coast of Korea in recent years. It significantly contributes to promoting the advancement of shorelines by partially inhibiting incident wave energy. Observations were carried out by a pressure-type wave gauge in the Bongpo Beach to evaluate the coefficients of wave transmission via a submerged breakwater, and the results obtained were compared with those of existing conventional equations on the transmission coefficient derived from hydraulic experiments. After reviewing the existing equations, we proposed a transmission coefficient equation in terms of an error function. Although it exhibited robust relationships with the crest height and breaking coefficient, deviations from the observed data were evident and considered to be triggered by the difference in the incident wave climate. Therefore, in this study, we conducted a numerical experiment to verify the influence of wave period on the coefficients of wave transmission, in which we adopted a parabolic-type mild-slope equation model. Consequently, the deviation from calculated results appears to practically cover all deviation range in the observed data. The wave period and direction of the incident wave increased, the transmission coefficient decreased, and the wave direction was determined to demonstrate a relatively significant influence on the transmission coefficient. It was inferred that this numerical study is expected to be used practically in evaluating the design achievement of the submerged breakwater, which is adopted as a countermeasure to coastal beach erosion.

Wave Attenuation due to Water-Front Vegetation (수변식생에 의한 파랑감쇠 특성)

  • Lee, Seong-Dae
    • Journal of Navigation and Port Research
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    • v.32 no.5
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    • pp.341-347
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    • 2008
  • Recently, it has been widely recognized that water-front and coastal vegetations may have great value in supporting fisheries, protecting from wave attack, stabilizing the sea bed and maintaining good scenery. Hydrodynamic factors playa major role in the functions of water quality and ecosystems. However, the studies on numerical and analytical process of wave propagation are few and far behind compared to those on the hydrodynamic roles of water-front vegetations. In this study, in order to express wave attenuation into water-front vegetation, a numerical model based on the unsteady mild slope equation is developed. This result is compared with an analytical model for describing the wave attenuation by assumed simple long wave condition. Based on both the analytical and numerical results, the physical properties of the wave attenuation are examined under various wave, geometric and vegetation conditions. Through comparisons between the analytical and numerical results, the effects of the vegetation properties, wave properties and model parameters such as the momentum exchange coefficient have been clarified.

Effectiveness of Wave Resonator for Secondary Undulation under Real Sea Conditions (실해역에서 공진장치를 이용한 부진동의 제어)

  • Jeong, Jin-Woo;Kim, Do-Sam;Park, Jong-Bae;An, Sung-Wook
    • Journal of Ocean Engineering and Technology
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    • v.24 no.6
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    • pp.51-60
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    • 2010
  • In this study, the performance evaluation of a conventional wave resonator at the entrance of a port or a pier against secondary undulation has been performed using 2D hydrodynamic modeling within port. A wave resonator has been designed for the attenuation of the secondary undulation induced by the long-periodic waves. The controlled performance of the wave resonator has been numerically investigated for CGWAVE MODULE of finite-element model of SMS (Surface water Modeling System) based on the elliptic mild-slope wave equation. SMS was verified though the comparisons with analytical solution performed by Ippen and Goda (1963). Also, It was confirmed that a wave resonator of a rectangular model harbor is effective enough to control the secondary undulation when it compares variation of water level with the case of no resonance system. From the above results, amplification phenomenon induced by long-period waves transferred from 1900 sec to 2100 sec when it applied a wave resonator in Busan Gamcheon Port which is a deep-sea. And it was confirmed that a wave resonator of Pohang New Port attenuates largely long-period waves which are within the range of 300 sec induced by long-period motion of the moored ship.

A Mathematical Model of Undertow in the Surf Zone (쇄파대(碎波帶)에서 undertow에 관한 수학적(數學的) 모형(模型))

  • Lee, Jong Sup;Park, Il Heum
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.13 no.3
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    • pp.193-206
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    • 1993
  • An analytical model of undertow is presented in the surf zone. Each term of the derived governing equation is evaluated by the ordering methods. Then the turbulent normal stresses and the streaming velocity terms are neglected. The driving force of undertow is derived from the wave profile which is approximated by the 4th order Chebyshev polynomials. The three types of vertical distribution of eddy viscosity are assumed and the coefficient of eddy viscosity is decided from the new boundary condition. So the input parameters for the calculation of undertow become very simple. The theoretical solutions of the present model are compared with the various experimental results. This model shows a good agreement with the experimental results in the case of mild slope and linear type eddy viscosity.

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Investigation on the Design Wave Forces for Ear-do Ocean Research Station II: Fluid Force in the Breaking Wave Field (이어도 종합해양과학기지에 대한 설계파력의 검토 II: 쇄파역에서의 유체력)

  • 전인식;심재설;최성진
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.12 no.4
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    • pp.168-180
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    • 2000
  • In the Part I, the three dimensional model testing with NNW deep water wave direction gave the results such that the occurrence of breaking waves over the peak of Ear-Do caused very small wave height at the structure position. But the measured wave forces were rather greater than the calculated forces based on deep water wave height. Furthermore, It was also perceived that the time series of the forces looked like corresponding to the case that waves were superimposed by an unidirectional current. In the present Part II, the current is presumed to be a flow secondly induced by breaking waves, and an extensive study to clarify the current in a quantitative sense is performed through numerical analysis and hydraulic experiment. The results showed that a strong circulation can surely occur in the vicinity of the structure due to radiation stress differentials given by the breaking waves. It was also recognized that the velocity of the induced current varied with the magnitude of energy dissipation rate introduced in the numerical analysis. The numerical analysis was tuned adjusting the dissipation rate so that the calculated wave field could closely match with the experimental results of Part I. The fluid force (in prototype) for the optimal match showed approximately 2.2% increased over the calculated value based on the deep water wave height (24.6m) whereas the force corresponding to the average of the experimental values showed the increase of about 13.0%.

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Infinite Element for the Analysis of Harbor Resonances (항만 부진동 해석을 위한 무한요소)

  • Park, Woo-Sun;Chun, In-Sik;Jeong, Weon-Mu
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.6 no.2
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    • pp.139-149
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    • 1994
  • In this paper, a finite element technique is applied to the prediction of the wave resonance phenomena in harbors. The mild-slope equation is used with a partial reflection boundary condition introduced to model the energy dissipating effects on the solid boundary. For an efficient modeling of the radiation condition at infinity, a new infinite element is developed. The shape function of the infinite element is derived from the asymptotic behavior of the first kind of the Hankel's function in the analytical boundary series solutions. For the computational efficiency, the system matrices of the element are constructed by performing the relevant integrations in the infinite direction analytically. Comparisons with the results from experiments and other solution methods show that the present model gives fairly good results. Numerical experiments are also carried out to determine the proper distance to the infinite elements from the mouth of the halter, which directly affect the accuracy and efficiency of the solution.

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Resonant Characteristics in Rectangular Harbor with Narrow Entrance (2.Effects of Entrance Energy Loss) (개구부가 좁은 직사각형 항만의 공진 특성 (2.항입구 에너지 손실의 영향))

  • 정원무;박우선;서경덕;채장원
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.11 no.4
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    • pp.216-230
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    • 1999
  • A Galerkin finite element model for the analysis of harbor oscillation has been developed based on the extended mild-slope equation. Infinite elements are used to accomodate the radiation condition at infinity and joint elements to treat the matching conditions at the harbor entrance which include the energy loss due to flow separation. The numerical tests for rectangular harbors with fully or partially open entrances show that the energy loss at the harbor entrance considerably reduces the the amplification ratios at the innermost parts of the harbors and that the amplification ratios decrease considerably with increasing incident wave heights and jet lengths at the harbor entrance. Application of the model to the Gamcheon harbor show that when the incident wave amplitude is small the amplification ratios rather increase when the entrance energy loss is included than when ignored because of the shift of the resonance periods. Even though the entrance energy loss was insignificant for the measured long-period incident waves, it would be of great importance if the incident waves were large as in the attack of tsunamis. The resonance period of the Helmholtz mode at the Gamcheon Harbor was calculated to be 31 minutes, which agrees well with the measured one between 27 and 33.3 minutes. The measured resonance periods between 9.4 and 12.1 minutes and 5.2 and 6.2 minutes were also calculated by the numerical model as 10.4 minutes and 6.6 or 5.6 minutes, indicating good performance of the model. On the other hand, it was shown that a variety of oscillation modes exists in the Gamcheon Harbor and lateral resonances of considerable amplification ratios also exist at the periods of 3.6 and 1.6 minutes as in the Young-II Bay.

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Application of Wave Resonator to the Field for Controlling Secondary Undulation (부진동의 제어를 위한 공진장치의 현장적용)

  • Lee, Kwang-Ho;Beom, Seong-Sim;Kim, Do-Sam;Choi, Nack-Hoon;Park, Jong-Bae;An, Seong-Wook
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.24 no.1
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    • pp.58-65
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    • 2012
  • In this study, to reduce the motion of the vessels resulting from resonance and secondary undulation by long-period waves, numerical review on the control performance of resonator was carried out by attaching the resonator to the established harbor of real waters. In the numerical analysis, CGWAVE MODULE of commercial software SMS(Surface water Modeling System), a finite element model based on 2-dimensional elliptical mild slope equation was applied, and through comparative analysis of the existing experiments and analysis results on the rectangular model ports, the validity of the friction coefficients in which validity and effectiveness of SMS on the secondary undulation analysis is applied was verified. Based on this, the control performance of resonator was confirmed through comparative review of the secondary undulation according to whether or not to attach the resonator to rectangular harbor. In addition, to reduce long-period motion of the moored vessels and the secondary undulation which may occur in Pohang new port, the method to move the resonant period which causes abnormal motion of the vessels to long-term one was discussed through application of the resonators with various sizes, thereby identifying the availability.

Vegetation and flora of Hibiscus hamabo inhabited naturally in Soan Island

  • Ahn, Young-Hee;Chung, Kyu-Hwan;Park, Hee-Seung
    • Journal of Environmental Science International
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    • v.12 no.11
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    • pp.1181-1187
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    • 2003
  • Hibiscus hamabo, called "Hwang-geun", growing about 3m in height is a deciduous shrub or subtree of Malvaceae. Because the number of these species is very limited in the world, the Ministry of Environment has designated H. hamabo as a preserved plant. The Korea Forest Service also protects it strictly by law since H. hamabo is an out-of-the-way plant and possibly may be exterminated soon in Korea. Investigation for distribution and ecological characteristics of the habitat for H. hamabo was carried out on Soan Island. Two wild H. hamabo were found at the forest edge (equation omitted) along the sea coast located in the southern part of Soan Island and this was the first report in the Korean academic world. These two wild H. hamabos were growing in a naturally inhibited area. The diameters at the base were 12cm and 15cm. The Tree heights were 150cm and 210cm and the number of branches of each wild H. hamabo was 4 and 7. However, the present condition of these plants was not good. Environmental conditions of the naturally inhibited area of H. hamabo were very mild because it is located at the edge of the forest and is always sunny during the daytime since the slope of the inhibited area is facing South. The ground drained very well since the soil was made of gravels and sand. Because the percent of vegetation of the subtree layer where H. hamabo was growing was 40%, the cover degree and sociability of flex crenata trees and Eurya japonica were found to be high. In the naturally inhibited area of H. hamabo, a dominant value of Rubus parvifolius in the lower part of the herb layer was very high and many plants in Compositae, such as Artemisia princeps var. orientalis and Erigeron annuus, were also present. A dominant value of liana, such as Vitis thunbergii var. sinuata, Rosa multiflora, Clematis terniflora and Hedera rhombea, and Gramineae plants that rhizomes were well developed and aggressively propagated, such as Miscanthus sinensis var. purpurascens, Phragmites communis, Spodiopogon cotulifer and Oplismenus undulatifolius which were surveyed as high, too. These results imply that H. hamabo might be exterminated soon through a natural selection if the proper management of the naturally inhibited area of H. hamabo is not conducted continually.

Regression Modeling of Water-balance in Watershed (유역(流域) 물 수지(收支)의 회귀모형화(回歸模型化))

  • Kim, Tai Cheol
    • Korean Journal of Agricultural Science
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    • v.10 no.2
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    • pp.324-333
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    • 1983
  • Modeling of longterm runoff is theoritically based on waterbalance analysis. Simplified equation of water balance with rainfall, evapotranspiration and soil moisture storage could be formulated into regression model with variables of rainfall, pan evaporation and previous-month streamflow. The hydrologic response of water shed could be represented lumpedly, qualitatively and deductively by regression coefficients of water-balance regression model. Characteristics of regression modeling of water-balance were summarized as follows; 1. Regression coefficient $b_1$ represents the rate of direct runoff component of precipitation. The bigger the drainage area, the less $b_1$ value. This means that there are more losses of interception, surface detension and transmission in the downstream watershed. 2. Regression coefficient $b_2$ represents the rate of baseflow due to changes of soil moisture storage. The bigger the drainage area and the milder the watershed slope, the bigger b, value. This means that there are more storage capacity of watershed in mild downstream watershed. 3. Regression coefficient $b_3$ represents the rate of watershed evaporation. This depends on the s oil type, soil coverage and soil moisture status. The bigger the drainage area, the bigger $b_3$ value. This means that there are more watershed evaporation loss since more storage of surface and subsurface water would be in down stream watershed. 4. It was possible to explain the seasonal variation of streamflow reasonably through regress ion coefficients. 5. Percentages of beta coefficients what is a relative measure of the importance of rainfall, evaporation and soil moisture storage to month streamflow are approximately 89%, 9% and 11% respectively.

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