• Wind and Structures
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• v.29 no.1
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• pp.33-41
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• 2019

The interaction of head waves with an infinite row of identical, equally spaced, rectangular breakwaters is investigated in the presence of uneven bottom topography. Using linear water wave theory and matched eigenfunction expansion method, the boundary value problem is transformed into a system of linear algebraic equations which are numerically solved to know the velocity potentials completely. Utilizing this method, reflected and transmitted wave energy are computed for different physical parameters along with the wave field in the vicinity of breakwaters. It is observed that the wave field becomes more complicated when the incoming wavelength becomes smaller than the channel width. A critical ratio of the gap width to the channel width, corresponding to the inflection point of the transmitted energy variation, is identified for which 1/3 of the total energy is transmitted. Similarly, depending on the incident wavelength, there is a critical breakwater width for which a minimum energy is transmitted. Further, the accuracy of the computed results is verified by using the derived energy relation.

• Korean Chemical Engineering Research
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• v.57 no.5
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• pp.652-665
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• 2019

Analytical solutions of the reactant concentration inside porous spherical catalytic particles were obtained from unsteady reaction-diffusion equation by applying eigenfunction expansion method. Various surface concentrations as exponentially decaying or oscillating function were considered as boundary conditions to solve the unsteady partial differential equation as a function of radial distance and time. Dirac delta function was also used for the instantaneous injection of the reactant as the surface boundary condition to calculate average reactant concentration inside the particles as a function of time by Laplace transform. Besides spherical morphology, other geometries of particles, such as cylinder or slab, were considered to obtain the solution of the reaction-diffusion equation, and the results were compared with the solution in spherical coordinate. The concentration inside the particles based on calculation was compared with the bulk concentration of the reactant molecules measured by photocatalytic decomposition as a function of time.

• International Journal of Naval Architecture and Ocean Engineering
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• v.12 no.1
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• pp.468-478
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• 2020

The wave interaction problem with a vertical slotted breakwater, consisting of impermeable upper, lower parts and a permeable middle part, has been studied theoretically. An analytical model was presented for the estimation of reflection and transmission of monochromatic waves by a slotted breakwater. The far-field solution of the wave scattering involving nonlinear porous boundary condition was obtained using eigenfunction expansion method. The empirical formula for drag coefficient in the near-field, representing energy dissipation across the slotted barrier, was determined by curve fitting of the numerical solutions of 2-D channel flow using CFD code StarCCM+. The theoretical model was validated with laboratory experiments for various configurations of a slotted barrier. It showed that the developed analytical model can correctly predict the energy dissipation caused by turbulent eddies due to sudden contraction and expansion of a slotted barrier. The present paper provides a synergetic approach of the analytical and numerical modelling with minimum CPU time, for better estimation of the hydrodynamic performance of slotted breakwater.

• Journal of Ocean Engineering and Technology
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• v.35 no.3
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• pp.216-228
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• 2021

In the present study, the performance of a floating oscillating water column (OWC) device has been studied in regular waves. The OWC model has the shape of a hollow cylinder. The linear potential theory is assumed, and a matched eigenfunction expansion method(MEEM) is applied for solving the diffraction and radiation problems. The radiation problem involves the radiation of waves by the heaving motion of a floating OWC device and the oscillating pressure in the air chamber. The characteristics of the exciting forces, hydrodynamic forces, flow rate, air pressure in the chamber, and heave motion response are investigated with various system parameters, such as the inner radius, draft of an OWC, and turbine constant. The efficiency of a floating OWC device is estimated in connection with the extracted wave power and capture width. Specifically, the piston-mode resonance in an internal fluid region plays an important role in the performance of a floating OWC device, along with the heave motion resonance. The developed prediction tool will help determine the various design parameters affecting the performance of a floating OWC device in waves.

• Journal of the Korean Society of Marine Environment & Safety
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• v.18 no.3
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• pp.199-205
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• 2012

In this study, wave transformation by damping due to the permeable bed of finite depth is investigated. The relationship between wave damping rate and relative water depth are presented. The damping rate is used in the eigenfunction expansion method to calculate the wave dissipation over the permeable bed. For a permeable shoal, the eigenfunction expansion model result is compared with that of the integral equation method to show good agreement. The model is also used to examine the wave reflection over the permeable planar slope of various frequency. It has been found that in general relatively short waves are more influenced by the permeability of the permeable seabed than relatively long waves unless the water depth is so large that the influence of permeable bed on surface water waves disappears.

• Kyungpook Mathematical Journal
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• v.28 no.2
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• pp.221-226
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• 1988

Using the method of eigenfunction expantion of self adjoint operators, we establish the necessary and sufficient conditions for a reflection positive generalized matrix kernel to be represented in an integral form. This integral converges in the cosidered spaces.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2004.05a
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• pp.241-248
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• 2004

In general, the salient features if the floating breakwater have excellent regulation of sea-water keeping the marine a1ways clean, up and dorm free movement with the incoming and outgoing tides, capable of being installed without considering the geological condition of sea-bed at any water depth, This study discusses the three dimensional wave transformation of the floating breakwater moored by catenary. Numerical method is based at the Green function method and eigenfunction expansion method. The validity of the present is confirmed by comparing it with the result of Ijima et a1.(1975) fer tensile maxed floating breakwater. According to the numerical results, drift and width of the floating breakwater affect at the wave transformation greatly, and incident wave of long period is well transmitted to the rear of the floating breakwater.

• Journal of Ocean Engineering and Technology
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• v.28 no.5
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• pp.474-483
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• 2014

The majority of existing WECs (wave energy converters) are designed to achieve maximum power at a resonance condition. In the case of a single WEC, its size must be large enough for tuning, and it has high efficiency only within a limited frequency band. Recently, wave power extraction by deploying many small buoys in a compact array has been studied under the assumption that the buoy's size and separation distance are much smaller than the water depth, wave length, and size of the array. A boundary value problem involving the macro-scale boundary condition on the mean surface covered by an infinite strip of buoys is solved using the eigenfunction expansion method. The energy extraction efficiency (${\varepsilon}=1-R^2_f-T^2_r$), where $R_f$ and $T_r$ are the reflection and transmission coefficients for a strip array of buoys, is assessed for various combinations of packing ratio, strip width, and PTO damping coefficient.

• Journal of Ocean Engineering and Technology
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• v.31 no.3
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• pp.208-218
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• 2017

The performance of a wave energy converter (WEC) that uses the rolling motion of a partially submerged pendulum plate in front of a quay wall was analyzed. The wave exciting moment and hydrodynamic moment were obtained using a matched eigenfunction expansion method (MEEM) based on the linear potential theory, and then the roll motion response of a pendulum plate, time averaged extracted power, and efficiency were investigated. The optimal PTO damping coefficient was suggested to give the optimal extracted power. The peak value of the optimal extracted power occurs at the resonant frequency. The resonant peak and its width increase as the submergence depth of the pendulum plate decreases and thickness of the pendulum plate increases. An increase in the wave incidence angle reduces the efficiency of the wave energy converter. In addition, the WEC using a rolling pendulum plate contributes not only to the extraction of the wave energy, but also to a reduction in the waves reflected from the quay wall, which helps to stabilize ships going near the quay wall.

• Journal of Korea Water Resources Association
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• v.33 no.6
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• pp.805-814
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• 2000

A numerical model based on the boundary element method is employed to describe diffraction of monochromatic water waves due to varying topographies. The model is firstly verified by comparing obtained reflection and transmission coefficients of waves over a trench to those of the eigenfunction expansion method. The model is then used to investigate the Bragg reflection of waves over sinusoidally varying topographies. Calculated reflection coefficients are compared to available laboratory measurements and semi-theoretical results. A reasonably good agreement is observed.served.