• Journal of Korean Society of Coastal and Ocean Engineers
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• v.21 no.2
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• pp.91-107
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• 2009

In order to compute linear wave transformation over a single step bottom, both variational approximation and eigenfunction expansion method are used. Both numerical results are in good agreement for reflection and transmission coefficients, surface displacement respectively. However x velocity profiles at the boundary of step are seen to be different to each other even though x velocity matching condition is used.

• Water Engineering Research
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• v.1 no.1
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• pp.75-81
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• 2000

The bragg reflection of obliquely incident monochromatic water waves propagating over a sinusoidally varying topography is theoretically investigated in this study. The eigenfunction expansion method is first employed to calculate reflection coefficients of water waves due to depth changes. A reasonable agreement is observed. Obtained reflection coefficients of normally incident waves are compared with laboratory measurements. Reflection coefficients of obliquely incident waves are then calculated. The wavenumber providing the Bragg reflection agrees well with analytical predictions.

• Computational Structural Engineering
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• v.8 no.1
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• pp.173-186
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• 1995

It is well known that structures constructed by bonding two or more materials and then subjected to temperature change experience thermal stress. This stress results from thermal expansion mismatch of materials. The present paper derives formulas for the stresses in a bimaterial axisymmetric disk which is subjected to a uniform temperature change. First, an approximate solution following strength-of-materials principles is developed. However, the strength-of-materials solution has difficulty in predicting both the peak value of interfacial stresses and its associated distribution. Next, a solution consistent with the theory of elasticity is developed by way of an eigenfunction expansion approach. The eigenfunction analysis is compared with finite element stress analysis results for a specific numerical example. Finite element analysis results show that the interfacial stresses are adequately predicted by eigenfunction solution. Therefore, the method developed in this paper will be useful in determination of the interfacial stress state.

• Journal of Korea Water Resources Association
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• v.42 no.12
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• pp.1125-1133
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• 2009

Evanescent modes which are the other solutions of the Laplace equation for the linear dispersion equation may affect the wave transformation especially when a water depth varies abruptly. In this study, the effects of evanescent modes for a three-dimensional depression of seabed are investigated by using the eigenfunction expansion method. A convergence test is first carried out by changing numbers of domains and evanescent modes. The wave transformation for various depressions of seabed is then calculated under condition that the solution of the eigenfunction expansion method is converged.

• 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.15 no.3
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• pp.167-175
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• 2003

In this study, reflection of regular waves over a train of submerged breakwaters is experimentally investigated. Wave reflection from various-shaped submerged breakwaters is examined by using laboratory experiment and eigenfunction expansion method. Shapes of submerged breakwaters are rectangular, triangular, trapezoidal and semi-circular. Laboratory measurements are compared with predicted coefficients obtained from the eigenfunction expansion method. Although measured coefficients are slightly smaller than predicted ones, the overall agreement is very good. The present study can provide a criterion for the proper choice of a shape of submerged breakwaters in practical situation.

• Journal of Korea Water Resources Association
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• v.37 no.9
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• pp.729-736
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• 2004

Analysis of reflection of random waves propagating over rectangular submerged non-porous breakwaters was performed by using the eigenfunction expansion method. In this study, random waves were generated by superposition of several monochromatioc waves. Reflection coefficients were calculated by summing each numerical results of regular waves. Predicted results from the eigenfunction expansion method were in a good agreement with the results of laboratory measurements. Reflection coefficients of random waves were also resonated at the Bragg reflection condition.

• Journal of Korea Water Resources Association
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• v.40 no.11
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• pp.899-908
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• 2007

In this study, wave reflection due to depression of seabed is calculated by using eigenfunction expansion method. The proper numbers of steps and evanescent modes needed for analysis are suggested by applying the eigenfunction expansion method to bottom topography of which slope or curvature varies. While satisfying shallow or intermediate water depth condition, the optimal figure of depression of seabed is obtained by calculating reflection coefficient for various depressions of seabed. The reflection coefficient with distance between the depression of seabeds is then calculated after arraying the optimal geometry in two and three rows.

• 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.

• International Journal of Naval Architecture and Ocean Engineering
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• v.2 no.3
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• pp.146-154
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• 2010

In the present study, the wave excitation forces acting on an array of porous circular cylinders are examined based on diffraction problems. To calculate the wave forces, the fluid domain is divided into three regions i.e. a single exterior region, N interior regions and N beneath regions, and the diffraction in each fluid region is expressed by an eigenfunction expansion method with using 3-dimension liner potential theory (Williams and Li, 2000). Especially, the present method is extended to the case of an array of truncated porous circular cylinders to calculate the heave forces as well as surge and sway forces. To verify this method, the numerical results obtained by eigenfunction are compared with these results obtained by higher order boundary element method (Choi et al., 2000). The numerical results obtained by this study are in good agreement with those results. By changing the numbers of porous circular cylinders, the angle of incident wave and the porosity rate of circular cylinders, the wave excitation forces such as surge, sway and heave on an array of truncated porous circular cylinders are investigated.