• Journal of Korea Water Resources Association
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• v.36 no.3 s.134
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• pp.447-454
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• 2003

The Bragg reflection of monochromatic waves propagating over a rectangular-typed impermeable submerged breakwaters is numerically investigated by using the finite element method. The reflection coefficients calculated from the present model are compared with those of laboratory measurements and the eigenfunction expansion method. A good agreement is observed. The finite element model is also applied to calculate reflection coefficients according to variations of length and width of submerged breakwater.

• Journal of Ocean Engineering and Technology
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• v.21 no.4
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• pp.1-7
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• 2007

Based on the eigenfunction expansion method, the wave-absorbing performance of a square or circular pile breakwater was investigated. Flow separation resulting from sudden contraction and expansion is generated and is the main cause of significant energy loss. Therefore, evaluation of an exact energy loss coefficient is critical to enhancing the reliability of the mathematical model. To obtain the energy loss coefficient, 2-dimensional turbulent flow is analyzed using the FLUENT commercial code, and the energy loss coefficient can be obtained from the pressure difference between upstream and downstream. It was found that energy loss coefficient of circular pile is 20% that of a square pile. To validate the fitting equation for the energy loss coefficient, comparison between the analytical results and the experimental results (Kakuno and Liu, 1993) was made for square and circular piles with good agreement. The array of square piles also provides better wave-absorbing efficiency than the circular piles, and the optimal porosity value is near P=0.1.

• Journal of Ocean Engineering and Technology
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• v.25 no.6
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• pp.9-16
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• 2011

The feasibility of wave energy extraction from a heaving truncated cylinder and the corresponding response of the linear electric generator (LEG) composed of spring, magnet, and coil has been investigated in the frame of three-dimensional linear potential theory. The heaving motion of a circular cylinder is calculated by means of the matched eigenfunction expansion method. Further, the analytical results are validated by numerical results using the ANSYS AQWA commercial code. By the action of a heaving circular cylinder, the magnet suspended by a spring can slide vertically inside the heaving cylinder. The mechanical power is extracted from the magnet motion relative to the coil/stator which is attached to the cylinder. The coupled ODE of a heaving cylinder and LEG system in waves is derived to obtain the magnet motion relative to a cylinder. To maximize the relative motion of the magnet, both the buoy draft and the LEG system parameters (spring stiffness, damping) should be selected properly for generating the double resonance considering the peak frequency of the target spectrum.

• Journal of computational fluids engineering
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• v.21 no.4
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• pp.96-101
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• 2016

A two-dimensional Stokes flow past a circular disk in a circular tube is analyzed. The circular disk is located coaxially with the circular tube and the Hagen-Poiseuille flow exists at upstream and downstream far from the circular disk. The Stokes approximation is used and the flow is investigated analytically by using the method of eigenfunction expansion and the method of least square. From the analysis, the stream function and the pressure of the flow field are obtained, and the streamlines and pressure distribution are shown. Also, the pressure and shear stress distributions on the circular disk and circular tube wall are calculated, and shown for some typical radii of the circular disk. The additional pressure drop induced by the disk and the drag force exerted on the disk are compared as functions of the radius of the circular disk, and it is shown that the shear force on the wall of the tube increases due to the disk.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.15 no.3
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• pp.143-150
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• 2003

Based on the eigenfunction expansion method, the interaction between monochromatic waves and a partially immersed slotted plate with a back wall has been investigated. Analytical results show that the reflection coefficients by a partially immersed slotted plate depend on the porosity, immersed depth, chamber width, incidence angle and wave frequency. It is found that the reflection coefficient has minimum value within entire frequency range when the porosity has optimal value 0.1. Comparison between the analytical results and the experimental results(Zhu,2001) of reflection coefficients is made for various chamber widths, immersed depths and wave periods with good agreement. The present analytic method can account adequately for energy dissipation caused by flow separation behind a slotted plate and provide the design informations for the construction of slit caisson breakwater.

• Ocean Systems Engineering
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• v.4 no.3
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• pp.169-183
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• 2014

For the reliable design of substructure supporting offshore wind turbines it is very important to reduce the effects of wave forces. Since the substructure is strongly influenced by the effects of wave forces as the size of substructure increases. In the present study, the hybrid substructure with multi-cylinder is newly suggested to reduce the effects of wave forces. Using diffraction theory the scattering waves in a fluid region are expressed by an Eigenfunction expansion method with three dimensional potential theory to calculate the wave force acting on the hybrid substructure. The wave force and wave run-up acting on the hybrid substructure is presented to examine the water wave interaction according to the variation of cylindrical size and the distance among cylinders. It is found that the suggested hybrid substructure with multi-cylinder is very useful to reduce the effects of wave forces acting on the substructure for offshore wind turbines.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.36D no.4
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• pp.18-24
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• 1999

The design method of a wave absorber for a perfectly conducting sphere is presented. The backscattered field from a coated sphere can be represented as the sum of the reflected field and the creeping wave. The wave absorber for a curved surface has been designed from that the reflection coefficient of the reflected field is zero. For the design of wave absorber for a small sized conducting sphere, the creeping wave should be considered as well as the reflected field. The perfect absorbing conditions are numerically searched using the Newton-Raphson method from the backscattered field of the eigenfunction series solution from a coated sphere. The wave absorber designed by this method exhibits a superior performance of absorption to that designed from the plate type absorbing condition.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.721-745
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• 2020

In this paper we study fractional Sobolev spaces characterized by a norm based on eigenfunction expansions. The goal of this paper is twofold. The first one is to define fractional Sobolev spaces of order -1 ≤ s ≤ 2 equipped with a norm defined in terms of Neumann eigenfunction expansions. Due to the zero Neumann trace of Neumann eigenfunctions on a boundary, fractional Sobolev spaces of order 3/2 ≤ s ≤ 2 characterized by the norm are the spaces of functions with zero Neumann trace on a boundary. The spaces equipped with the norm are useful for studying cross-sectional traces of solutions to the Helmholtz equation in waveguides with a homogeneous Neumann boundary condition. The second one is to define fractional Sobolev spaces of order -1 ≤ s ≤ 1 for vector-valued functions in a simply-connected, bounded and smooth domain in ℝ². These spaces are defined by a norm based on series expansions in terms of eigenfunctions of the vector Laplacian with boundary conditions of zero tangential component or zero normal component. The spaces defined by the norm are important for analyzing cross-sectional traces of time-harmonic electromagnetic fields in perfectly conducting waveguides.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.21 no.2
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• pp.117-126
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• 2009

In order to test the accuracy between the modified mild slope equation (MMSE) without evanescent modes and the plane-wave approximation (PA) of eigenfunction expansion method, various numerical results from both models are presented. In this study, analytical solutions of two models are employed, one based on the MMSE derived by Porter (2003) and the other on the scatterer method of PA by Seo (2008a). Judging from direct comparisons against existing results of rapidly varying topography, the PA model gives better predictions of the wave propagation than the MMSE model.

• Journal of the Korean Society for Marine Environment & Energy
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• v.5 no.3
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• pp.35-44
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• 2002

In this paper, the analytic studies on the wave control performance of moored pontoon-type floating breakwater are presented. A two-dimensional eigenfunction expansion method is adopted to study the motion responses and the transmission coefficients of pontoon-type floating breakwater in beam waves. The stiffness coefficients of mooring line are idealized as linear elastic spring. Comparison of the analytical results with a numerical results (FEM) shows good agreement over a wide range of frequencies. The performance of mooed pontoon-type floating breakwater is tested with various design parameters such as sectional geometry, mooring line characteristics and wave frequencies. It is found that the properly designed floating breakwater can be an effective wave control structure.