• Journal of Korean Society of Coastal and Ocean Engineers
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• v.19 no.3
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• pp.228-236
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• 2007

An analytical solution for long waves propagating over an asymmetric trench is derived. The water depth inside the trench varies in proportion to a power of distance from the center of the trench. The mild-slope equation, governing equation, is transformed into second order ordinary differential equation with variable coefficients by using the long wave assumption and then the analytical solution is obtained by using the power series technique. The analytical solution is confirmed by comparison with the numerical solution. After calculating the analytical solution under various conditions, the results are analyzed.

• Journal of the Korean Society for Marine Environment & Energy
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• v.12 no.3
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• pp.165-172
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• 2009

A set of equations for description of transformation of harmonic waves is proposed here. Velocity potential function and separation of variables are introduced for the derivation. The continuity equation is in a vertical plane is integrated through the water so that a horizontal one-dimensional wave equation is produced. The new equation composed of the complex velocity potential function, further be modified into. A set up of equations composed of the wave amplitude and wave phase gradient. The horizontally one-dimensional equations on the wave amplitude and wave phase gradient are the first and second-order ordinary differential equations. They are solved in a one-way marching manner starting from a side where boundary values are supplied, i.e. the wave amplitude, the wave amplitude gradient, and the wave phase gradient. Simple spatially-centered finite difference schemes are adopted for the present set of equations. The equations set is applied to three test cases, Booij's inclined plane slope profile, Massel's smooth bed profile, and Bragg's wavy bed profile. The present equations set is satisfactorily verified against existing theories including Massel's modified mild-slope equation, Berkhoff's mild-slope equation, and the full linear equation.

• 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 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 Society of Coastal and Ocean Engineers
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• v.6 no.4
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• pp.389-396
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• 1994

We analyze existing time-dependent mild-slope equations, which were developed by Smith and Sprinks (1975) (or, equivalently, Radder and Dingemans (1985)) and Kubo et al. (1992), in terms of the dispersion relation and energy transport. One-dimensionally in the horizontal direction, we compare the modulation of wave amplitudes for the time-dependent mild-slope equations against the linear Scrodinger equation. In view of the dispersion relation and modulation of wave amplitudes, Smith and Sprinks' model is more accurate in shallower water (kh$\leq$0.2$\pi$) and satisfies the linear Scrodinger equation in very shallow water (kh>0.2$\pi$) and satisfies the linear Scrodinger equation at a point of intermediate water depth (kh=0.3$\pi$). In view of the energy transport, Kubo et al.'s model is more accurate but yields singular solutions at some higher frequency range.

• Journal of the Korean Society of Hazard Mitigation
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• v.8 no.1
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• pp.133-138
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• 2008

To analyze incident waves traveling from the deep ocean is very important in that it is based on resolving problems occurred in coastal areas. In general, numerical models and analytical solutions are used to analyze wave transformation. Although a numerical model can be applied to various bottoms and wave conditions, it may have some cumbersome numerical errors. On the other hand, an analytical solution has an advantage of obtaining the solution quickly and accurately without numerical errors. The analytical solution can, however, be utilized only for specific conditions. In this study, the analytical solution of the mild-slope equation has been developed. It can be applied to various conditions combing a numerical technique and an analytical approach while minimizing the numerical errors. As a result of comparing the obtained solutions in this study with those of the previously developed numerical model, A good agreement was observed.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.7 no.2
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• pp.141-147
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• 1995

Various numerical models for predicting wave deformation have been proposed. Among them a time-dependent mild-slope equation based on the line discharges and surface-elevation changes has been widely used in the wave fields with reflective waves. If applying this model to the case of obliquely-incident waves, not only the open-sea boundary but also one of the lateral boundaries should be treated as incident boundaries. In this study, Maruyama and Kajima (1985), Copeland (1985) and Ohnaka and Watanabe (1987)'s method are reviewed and the characteristics of these methods are analyzed using e normalized wave heights, wave angels and phases obtained from the numerical experiments. It is shown that Ohnaka and Watanabe(1987)'s method provides the most adequate driving boundary is the most suitable in e wave field with a general bottom slope.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.18 no.1
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• pp.84-96
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• 2006

This paper presents a simplified numerical method that can be used to incorporate the partial reflection and transmission of water waves in the hyperbolic mild-slope equation. For given reflection and transmission coefficients, wave fields around a porous breakwater including reflection, transmission, and diffraction can be simulated accurately. For the verification of the proposed method, numerical experiments have been carried out and compared with analytic solutions given by Yu(1995) and McIver(1999). The proposed method is easy to implement and is computationally efficient. It is demonstrated that the method performs well with a sloping bottom bathymetry and varying incident wave angles.

• 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)

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 1994.07a
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• pp.19-25
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• 1994