• Journal of Korean Society of Coastal and Ocean Engineers
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• v.10 no.4
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• pp.174-186
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• 1998

A Galerkin's finite element model incorporating infinite elements for modeling of radiation condition at infinity has been developed, which is based on an extended mild-slope equation. To illustrate the validity and applicability of the present model, the example analyses were carried out for a resonance problem in the rectangular harbor of Ippen and Goda (1963) and for wave transformations over circular shoals of Sharp (1968) and Chandrasekera and Cheung (1997). Comparisons with the results obtained by hydraulic experiments and hybrid element method showed that the present model gives very good results in spite of the rapidly varying topography. Numerical experiments were also performed for wave transformations over a circular concave well which may be an alternative to conventional wave barriers.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.209-212
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• 2002

Since Berkhoff proposed the mild-slope equation in 1972, it has widely been used for calculation of shallow water wave transformation. Recently, it was extended to give an extended mild-slope equation, which includes the bottom slope squared term and bottom curvature term so as to be capable of modeling wave transformation on rapidly varying topography. These equations were derived by integrating the Laplace equation vertically. In the present study, we develop a finite element model to solve the Laplace equation directly while keeping the same computational efficiency as the mild-slope equation. This model assumes the vertical variation of wave potential as a cosine hyperbolic function as done in the derivation of the mild-slope equation, and the Galerkin method is used to discretize . The computational domain was discretized with proper finite elements, while the radiation condition at infinity was treated by introducing the concept of an infinite element. The upper boundary condition can be either free surface or a solid structure. The applicability of the developed model was verified through example analyses of two-dimensional wave reflection and transmission. .

• 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.

• 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.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2001.10a
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• pp.117-121
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• 2001

For the effective development or preservation of Tokdo, the natural environments in the ambient sea area should be well investigated. The wave deformations and wave breaking in the vicinity have much affected the bottom morphology of Tokdo as well as its ecological environment. The present study investigates the wave deformations and wave breaking through a numerical model. The final goal is to provide the fundamental wave data for the effective development or preservation of Tokdo in future. The extended mild slope equation was applied to Tokdo sea area for three different deep water wave conditions (S, SSE, NNE directions). The results showed that for the S and SSE directions the wave heights in the area between the east island and the west island were very low with the level of 1~2m, but for the NNE direction they appeared pretty high with 3~4m, In the sea area near the northwest of west island, the wave heights were low to be 1~3m for all three directions of deep water wave.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2004.08a
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• pp.217-225
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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. 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.

• Journal of Korean Port Research
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• v.7 no.1
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• pp.79-88
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• 1993

This study deals with the case of a fixed floating structure(FFS) at the mouth of a rectangular harbor under the action of waves represented by the linear wave theory. Modified forms of the mild-slope equation is applied to the propagation of regular wave over constant water depth. The model is extended to include bottom friction and boundary absorption. A hybrid element approximation is used for calculation of linear wave oscillation in and near coastal harbor. Modification of the model was necessary for the FFS. For the conditions tested, the results of laboratory experiments by Ippen and Goda(1963), and Lee (1969) are compared with the calculated one from this model. The cases of flat cylinderical structures, both fixed and floating, were taken to be in an intermediate water depth.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.13 no.2
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• pp.149-157
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• 2001

From the weakly nonlinear mild-slope wave equations introduced by Nadaoka et al.(1994, 1997), a set of weakly nonlinear wave equations for rapidly varying topography are derived by including the bottom curvature and slope-squared tenns ignored in the original equations ofNadaoka et al. To solve the linear version of extended wave equations derived in this study one-dimensional finite difference numerical model is con¬structed. The perfonnance of the model is tested for the case of wave reflection from a plane slope with various inclination. The numerical results are compared with the results calculated using other numerical models reported earlier. The comparison shows that the accuracy of the numerical model is improved significantly in comparison with that of the original equations ofNadaoka et al. by including a complete set of bottom curva1w'e and slope¬squared terms for a rapidly varying topography.

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 2003.08a
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• pp.44-52
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• 2003

항만 및 해안의 이용과 개발 그리고 연안해역공간에서 발생하는 각종 재해를 예방하는 측면에서 볼 때 해안에서 형성되는 여러 물리적인 현상들을 정확하게 이해하고 해석하여 필요에 따라 적절히 활용할 수 있는 것이 무엇보다도 중요한 과제이다. (중략)

• Journal of Korea Water Resources Association
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• v.31 no.6
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• pp.845-854
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• 1998

Following the approach of Ebersole (1985), water wave transformation is predicted using the eikonal equation and transport equation for wave energy which are reduced from the extended mild-slope equation of Massel (1993), and also the irrotationality of wave number vectors. The higher-order bottom effect terms, i.e., squared bottom slope and bottom curvature, are neglected in the study of Ebersole but are included in the present study. It was expected that, if these terms are included in this study, the approach would give more accurate solution in the case of rapidly varying topography. But, the expectation was frustrated. It is probably because, in the case of rapidly varying topography, the diffraction effect which is included in the eikonal equation does not work well and thus the solution is deteriorated.