• Journal of Korean Society of Coastal and Ocean Engineers
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• v.10 no.4
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• pp.197-203
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• 1998

An approach of decomposing the reflecting components is proposed by using the mild-slope equation of hyperbolic type which has the similar form to the shallow water equations. The approach is verified on Booij's problem and sinusoidally varying ripples. Inclusion of higher-order bottom effect given by chamberlain and Porter(1995) yields even more satisfactory results than the Berkhoff's mild-slope equation when compared with finite element solution or experiments.

• 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. .

• Proceedings of the Korea Water Resources Association Conference
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• 2006.05a
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• pp.567-573
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• 2006

An efficient typhoon wave-generating model is applied to northeast Asia sea zone presented that can be used by civil defense agencies for real-time prediction and fast warnings on typhoon-generated wind wave and storm surge. Instead of using commercialized wave models such as WAM, SWAN, the wind waves are simulated by using a new concept of wavelength modulation to enhance broader application of the hyperbolic wave model of the mild-slope equation type. The results simulated along the Korean coasts during Typhoon Nabi (2005) showed reasonable agreement with the recorded wind waves.

• Proceedings of the Korea Water Resources Association Conference
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• 2006.05a
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• pp.574-578
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• 2006

Tidal amplification by construction of the sea-dike and sea-walls had been detected not only near Mokpo Harbor but also at Chungkye Bay which is connected with Mokpo Harbor by a narrow channel. This brings about increase of tidal flat area and in particular increase of surge-wave combined runup during storms. The purpose of this study is to examine an efficient operational model that can be used by civil defense agencies for real-time prediction and fast warnings on wind waves and storm surges. Instead of using commercialized wave models such as WAM, SWAN, the wind waves are simulated by using a new concept of wavelength modulation to enhance broader application of the hyperbolic wave model of the mild-slope equation type. Furthermore, The predicting system is composed of easy and economical tools for inputting depth data of complex bathymetry and enormous tidal flats such as Mokpo coastal zone. The method is applied to Chungkye Bay, and possible inundation features at Mokpo Harbor are analyzed.

• 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.

• Journal of Ocean Engineering and Technology
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• v.15 no.2
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• pp.6-10
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• 2001

Water waves propagate over irregular bottom bathymetry are transformed by refraction, diffraction, shoaling, reflection etc. Principal factor of wave transform is bottom bathymetry, but in case of current field, current is another important factor which effect wave transformation. The governing equation of this study is develope as wave-current equation type to investigate the effect of wave-current interaction. It starts from Berkhoff's(1972) mild slope equation and is transformed to time-dependent hyperbolic type equation by using variational principal. Finally the governing equation is shown as a parabolic type equation by splitting method. This wave-current model was applied to the kwangan beach which is located at Pusan. The numerical simulation results of this model show the characteristics of wave transformation and flow pattern around the Kwangan beach fairly well.

• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.3
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• pp.231-238
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• 1992

Error vector propagation method is applied to the elliptic mild slope equation in order to reduce the computation time. Results from the elliptic, parabolic, and hyperbolic models are compared with experimental data for an elliptic shoal. Also, results of the elliptic and hyperbolic models are compared with experimental data for a detached breakwater. As a result of applying this model. it is concluded that the present model satisfactorily reduces the computation time compared with other numerical models. In the accuracy of solutions, there are some oscillations but the trend compares well with other models.

• 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 Ocean Engineering and Technology
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• v.9 no.2
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• pp.41-52
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• 1995

the necessity of development of the Nearshore zone greatly emphasis in recent years. In the wave deformation model, we can get the wave height and wave direction using the hyperbolic mild slope equation considered the reflection wave. Radiation Stress the driving force of flow was calculated by the Watanabe and Maruyama who proposed on the partial standing wave. In the surf zone, applying the Izumiya and Horikawa's turbulent model considered the bottom friction and energy dissipation, we compared and examined with the Numerical model and Hydraulic test result of Watanabe and Maruyama. This model results obtained for Jin-ha Beach agreed well with the Numerical results. This model is expected so helpful to solve the prediction of the wave deformation problems in the development of the Nearshore zone in the future.