• Journal of Korean Society of Coastal and Ocean Engineers
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• v.15 no.3
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• pp.159-166
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• 2003

In this study, we develop a finite element model to directly solve the Laplace equation while keeping the same computational efficiency as the models based on the extended mild-slope equation which has been widely used for calculation of wave transformation in shallow water. For this, the computational domain is discretized into finite elements with a single layer in the vertical direction. The velocity potential in the element is then expressed in terms of the potentials at the nodes located at water surface, and the Galerkin method is used to construct the numerical model. A common shape function is adopted in horizontal direction, and the cosine hyperbolic function in vertical direction, which describes the vertical behavior of progressive waves. The model was developed for vertical two-dimensional problems. In order to verify the developed model, it is applied to vertical two-dimensional problems of wave reflection and transmission. It is shown that the present finite element model is comparable to the models based on extended mild-slope equations in both computational efficiency and accuracy.

• Journal of Navigation and Port Research
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• v.28 no.5
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• pp.421-428
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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 Pohang Old Harbor and Pohang New Port, etc. due to construction of New Port in Youngil Bay. This type of trial might be a milestone for port development in macroscale, 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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• 2004.04a
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• pp.179-186
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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 Pohang Old Harbor and Pohang New Port, etc. due to construction of New Port in Youngil Bay. This type of trial might be a milestone for port development in macroscale, where the induced impact analysis in the existing port due to the developemnt could be easily neglected.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.13 no.3
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• pp.254-261
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• 2001

It is well known that when long waves propagate from deep ocean onto a continental shelf with a very steep continental slope, the waves reflected from the shore can not propagate offshore and are re-reflected from the continental slope so that large water level fluctuations are induced near the shore. Liu(1986) has analyzed this phenomenon by assuming a topography which has a depth discontinuity along a semicircular offshore boundary, but his solution is erroneous. In the present paper, we correct his analytical solutions for a straight shoreline and a rectangular harbor. The corrected solution is then compared with the numerical results of the Galerkin finite element model of Jeong et al.(1998), which is based on the extended mild-slope equation.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• v.1
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• pp.57-62
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• 2006

Busan New Port, under construction aiming for the hub of Northeast Asia and Partly in operation, had damaged up to 48 billion Won due to Typhoon 'maemi' in 2003. The present criteria of domestic harbor design only describes about the critical wave height with respect to the size of vessel for harbor tranquility. The berth operation ratio which represents the annual available berthing days is depending on the efficiency of cargo handling work and this depends on the motion of the moored vessel due to the wave action and the characteristics of cargo gears. The motion of moored vessel might be related not only to the wave height but also to wave period. Furthermore, the berth operation ratio relies on external forces such as currents and winds, including the characteristics of mooring system and the specification of the moored vessel. In this study we only deal with berth operation ratio in normal sea state, considering wave and current by measured data and numerical calculation. Especially we tried to evaluate the berth operation ratio for each berth adopting the variation of dredging and reclamation plan and the change of wave environment during the process of the new port construction. For better understanding and analysis of wave transformation process, we applied the steady state spectral wave model and extended mild-slope wave model to the related site. This study summarizes comparisons of harbor responses predicted by two numerical predictions obtained at Busan New port site. Field and numerical model analysis was conducted for the original port plan and the final corrected plan.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.13 no.3
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• pp.189-194
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• 2001

The present study describes the Bragg reflection of monochromatic water waves propagating over a train of doubly-sinusoidally varying topographies. A numerical model based on the boundary element method is firstly verified by calculating reflection and transmission coefficients of waves over a trench. Calculated solutions are compared with those of the eigenfunction expansion method. The model is then used to simulated reflection of monochromatic water waves propagating over doubly-sinusoidally varying bottom topographies. Obtained reflection coefficients are compared with those of available laboratory measurements, those of the eigenfunction expansion method and the extended mild-slope equation. A reasonable agreement is shown.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.13 no.2
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• pp.122-138
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• 2001

It is well known that whcn waves propagating on a shallow water suddenly encounter a much deeper water they do not propagate further but are reflected. If we apply this phenomenon to a harbor by making the harbor depth much greater than outside, we could improve the harbor tranquillity by making the waves impinging into the harbor be reflected at the harbor entrance. In the present paper, first we apply the numerical models based' on the mild-slope equation and extended mild-slope equation to calculate the long wave resonances in a rectangular harbor with a very large depth discontinuity at its entrance to find that the difference between the models is almost negligible. By applying the numerical model to a realistic model harbor whose inside is entirely dredged, it is found that the effect of dredging is insignificant when the inside depth is twice the outside one but tripled inside depth significantly reduces the long waves of period of one to five minutes whieh may exert a bad influence on ship motion. Moreover, even when only a portion of the harbor basin is dredged, the cffect of dredging in the dredged area is found to be comparable to that of entire dredging, showing that the dredging of harbor basin can be a countenncasure for harbor resonance.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.21 no.2
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• pp.127-135
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• 2009

Reid and Kajiura(1957) has studied on the wave damping rate over a permeable bed of infinite depth. In this study, wave damping rate over a permeable bed of finite depth is derived by linear wave theory. It is then extended to derive wave damping rates over a double or triple layer, each of which consist of different material. Applying the wave damping rate to the mild slope equation, the wave transmission coefficient over a permeable bed has been calculated. The model has been certificated by comparing with the result of Flaten and Rygg(1991)'s integral equation method in the case of a single-layer bed.

• Journal of Korean Port Research
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• v.8 no.2
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• pp.37-56
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• 1994

The effects of wave energy focusing by a submerged berm type of structure is examined. The fundamental idea is based on the phenomenon of refraction by a lens-shaped crescent structure which results in the focusing of wave energy on the center line of the structure. The shape of the submerged structure is a complex curve combining circular with elliptical elements. Based on the design procedure, a special configuration of structure(termed herein as a triple crescent structure) is introduced. Next, some hydraulic model tests are performed to confirm the wave focusing effect in laboratory. In addition, in order to interpret the wave focusing performance behind the structure, a numerical procedure by the hybrid element method is used on the basis of the conventional mild slope equation but modified and extended to allow for steeper bottom slopes and higher curvature. The modified refraction and diffraction provide additional mechanism for wave height amplification and the maximum amplification for triple crescent structure is presented. It also allows for the possibility of wave energy scattering with the change of the incident wave direction. Comparisons with previous theoretical results involving a submerged crescent shape structure are described.

• 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.