• Journal of Korean Society of Coastal and Ocean Engineers
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• v.32 no.5
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• pp.307-321
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• 2020

The design and the construction are carried out by installation of new caissons on the back or the front of old caissons to increase the stability of old caisson breakwater. In this study, we use the eigenfunction expansion method to analyze the effects of wave structure interaction when new circular caissons are installed on the back or the front of old caissons. The comparison of numerical results between present method and Williams and Li is made, and the wave force and the wave run-up acting on each circular caisson are calculated for various parameters by considering the wave structure interaction.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.15 no.1
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• pp.51-58
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• 2003

The magnitude of evanescent modes in terms of dynamics it investigated in case that the transformation of water waves is predicted by the linear wave theory. For the waves propagating over two steps, the eigenfunction expansion method is used to predict the amplitudes of reflected and transmitted waves by the component of evanescent modes as well as propagating modes. Then. the relative importance of evanescent modes to the propagating modes is investigated. The numerical experiments find that the evanescent modes are pronounced at the relative water depth of k$_1$h$_1$＝0.11$\pi$ and the water depth ratio of h$_2$/h$_1$ close to zero.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.19 no.1
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• pp.29-37
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• 2007

In this study, transmission and reflection of multi-directional random waves propagating over impermeable submerged breakwaters are calculated by using eigenfunction expansion method. A series of mutiderectional random waves is generated by using the Bretschneider-Mitsuyasu frequency and Mitsuyasu type directional spectrum. Strong reflection is occurred at the Bragg reflection condition of the peak frequency. If the row of breakwaters is fixed at 3 and the relative height of breakwater is fixed at 0.6, more than 25% of incident wave energy is reflected to offshore. It is also found that the reflection of directionally spreading random waves increases as the maximum spreading parameter $s_{max}$ increases.

• Journal of Korea Water Resources Association
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• v.32 no.6
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• pp.675-683
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• 1999

The reflection coefficients of monochromatic waves propagating over a shelf with varying dimensions are theoretically calculated. The diffraction of waves by an abrupt depth change is formulated by the eigenfunction expansion method. Not only propagating mode but also evanescent modes are considered in formulation. The role of evanescent modes in reflection coefficients is investigated in detail. Water waves are obliquely as well as normally incident to the region. The obtained reflection coefficients are verified by checking conservation of wave energy.

• Journal of Ocean Engineering and Technology
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• v.27 no.5
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• pp.43-50
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• 2013

In the present investigation, the hydrodynamic characteristics of a vertically floating hollow cylinder in regular waves have been studied. The potential theory for solving the diffraction and radiation problem was employed by assuming that the heave response motion was linear. By using the matched eigenfunction expansion method, the characteristics of the exciting forces, hydrodynamic coefficients, and heave motion responses were investigated with various system parameters such as the radius and draft of a hollow cylinder. In the present analytical model, two resonances are identified: the system resonance of a hollow cylinder and the piston-mode resonance in the confined inner fluid region. The piston resonance mode is especially important in the motion response of a hollow circular cylinder. In many cases, the heave response at the piston resonance mode is large, and its resonant frequency can be predicted using the empirical formula of Fukuda (1977). The present design tool can be applied to analyze the motion response of a spar offshore structure with a moon pool.

• Journal of Ocean Engineering and Technology
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• v.27 no.5
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• pp.51-62
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• 2013

The water wave interactions on any three-dimensional structure of arbitrary geometry can be calculated numerically through the use of source distribution or Green's function techniques. However, such a method can be computationally expensive. In the present study, the water wave interactions in floating circular cylinder arrays were investigated numerically using the eigenfunction expansion method with the three- dimensional potential theory to reduce the computational expense. The wave excitation force, added mass coefficient, radiation damping coefficient, and wave run-up are presented with the water wave interactions in an array of 5 or 9 cylinders. The effects of the number of cylinders and the spacing between them are examined because the water wave interactions in floating circular cylinder arrays are significantly dependent upon these.

• International Journal of Naval Architecture and Ocean Engineering
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• v.13 no.1
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• pp.833-847
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• 2021

The horizontal porous baffle and its effect as an anti-slosh device have been investigated intensively in a swaying and rolling rectangular tank. To accurately assess the level at which porous baffles reduce liquid sloshing, the Matched Eigenfunction Expansion Method (MEEM) has been utilized as an analytical tool. The velocity potentials in the horizontal baffle-covered fluid region are expressed by the sum of the homogeneous and particular solutions to avoid solving the complex dispersion equation. By applying an equivalent linearized quadratic loss model, the nonlinear algebraic equation is derived and solved by implementing the Newton-Raphson iterative scheme. To prove the validity of the present theoretical model, a series of experiments have been conducted with different centered horizontal porous baffles with varying porosities and submerged depths in a swaying and rolling rectangular tank. Reasonably good agreements are obtained regarding the analytical solutions and the experiment's findings. The influence of porosity, submerged depth, and length of a centered horizontal porous baffle on anti-slosh performance have been analyzed, especially at resonance modes. The developed predictive tool can potentially provide guidelines for optimal design of the horizontal porous baffle.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.2 no.4
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• pp.190-199
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• 1990

The solution for wind drift current in a three-layered open sea region is derived using the Galerkin-Eigenfunction mothod. The presence of discontinuities in the vertical eddy viscosity required a definition of a scalar product which involves the summation of integrals defined over each layer. The expansion of fourth-order B-spline functions is used in determining eigenvalues and corresponding eigenfunctions. In a three-layered system a low value of eddy viscosity is prescribed within the pycnocline to represent the suppression of turburent intensity at the thermocline level. A high concentration of knots within the pycnocline is important in determining eigenfunctions and the associated eigenvalues accurately. Due to the global property of eigenfunctions nonphysical oscillations appear in the current profiles below the surface layer, particularly within the pycnocline.

• 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 the Society of Naval Architects of Korea
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• v.41 no.5
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• pp.34-40
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• 2004

Very Large Floating Structure(VLFS) is regarded as one of promising candidates for the future utilization of ocean space. VLFS has the merits of small environmental effect. short construction term, easiness for extension and removal. It is well known that hydroelastic response is one of major design concerns of such a huge structure. Most of studies on the hydroelastic analysis of VLFS assumed uniform mass and bending stiffness. In case of a floating hotel where noticeable change of mass and stiffness at the hotel part is expected. it is necessary to investigate the effect of nonuniform mass and bending stiffness on the hydroelastic response. A model test of a pontoon type VLFS with nonuniform bending stiffness carried out for performance evaluation of a floating marina-hotel-convention center is described in this paper. Through investigation of model test results and comparison with numerical analysis using eigenfunction method, effect of the variation of bending stiffness is discussed.