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Journal ArticleDOI

Diffraction of Water Waves by Porous Breakwaters

01 Nov 1995-Journal of Waterway Port Coastal and Ocean Engineering-asce (American Society of Civil Engineers)-Vol. 121, Iss: 6, pp 275-282
TL;DR: In this article, the authors derived a relation for the fluid motion through thin porous structures in addition to the conventional governing equation and boundary conditions for small-amplitude waves in ideal fluids.
Abstract: Diffraction of water waves by porous breakwaters is studied based on the linear potential wave theory. The formulation of the problem includes a newly derived relation for the fluid motion through thin porous structures in addition to the conventional governing equation and boundary conditions for small-amplitude waves in ideal fluids. The porous boundary condition, indirectly verified by collected experimental data, is obtained by assuming that the flow within the porous medium is governed by a convection-neglected and porous-effect-modeled Euler equation. A vertically two-dimensional problem with long-crested waves propagating in the normal direction of an infinite porous wall is first solved and the solution is compared with available experimental data. The wave diffraction by a semiinfinite porous wall is then studied by the boundary-layer method, in which the outer approximation is formulated by virtue of the reduced two-dimensional solution. It is demonstrated that neglect of the inertial effect of the porous medium leads to an overestimate of the functional performance of a porous breakwater.
Citations
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Journal ArticleDOI
TL;DR: In this article, the authors reviewed recent progress in the study of perforated/slotted breakwaters, with an emphasis on two main groups of such breakwaters: (1) perforators with impermeable back walls, and (2) breakwaters without a back-wall.

189 citations

Journal ArticleDOI
TL;DR: In this article, the authors presented a numerical model of wave interactions with a thin vertical slotted barrier extending from the water surface to some distance above the seabed, and described laboratory tests undertaken to assess the numerical model.
Abstract: The present paper outlines the numerical calculation of wave interactions with a thin vertical slotted barrier extending from the water surface to some distance above the seabed, and describes laboratory tests undertaken to assess the numerical model. The numerical model is based on an eigenfunction expansion method and utilizes a boundary condition at the barrier surface that accounts for energy dissipation within the barrier. Numerical results compare well with previous predictions for the limiting cases of an impermeable barrier and a permeable barrier extending down to the seabed. Comparisons with experimental measurements of the transmission, reflection, and energy dissipation coefficients for a partially submerged slotted barrier show good agreement provided certain empirical coefficients of the model are suitably chosen, and indicate that the numerical method is able to account adequately for the energy dissipation by the barrier. The effects of porosity, relative wave length, wave steepness, and irregular waves are discussed and the choice of suitable parameters needed to model the permeability of the breakwater is described.

163 citations

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a simple, inexpensive, and effective type of floating breakwater for deep-sea aquaculture, which can effectively protect fish and fish cages.

114 citations

Journal ArticleDOI
TL;DR: In this article, the reflection and transmission coefficients of a thin vertical porous wall with different porous shapes with different shapes have been analyzed, and the porous effect parameter G has been obtained.
Abstract: The present paper aims at getting the porous effect parameter G of a thin permeable wall. The reflection and transmission coefficients of a thin vertical porous wall with different porous shapes an...

112 citations


Cites background or methods or result from "Diffraction of Water Waves by Porou..."

  • ...The method consists of the present experimental formula and the formula of Yu [1995] for calculating G with f and s....

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  • ...In addition, some researchers [Losada et al., 1993; Yu, 1995; Isaacson et al., 1998, 1999; Zhu and Chwang, 2001b] have offered some values off and s in their comparisons between numerical results and experimental data....

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  • ...In practices, there are two main forms of vertical permeable structures: (1) single or several ver"'" tical permeable plates [Yu, 1995; Isaacson et al., 1998, 1999; Mciver, 1999; Twu and Liu, 2004], (2) a solid back wall with single or several vertical permeable plates in front [Jarlan, 1961; Kondo, 1979; Tanimoto and Yoshimoto, 1982; Zhu and Chwang, 2001a]....

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  • ...In addition, some researchers [Losada et al., 1993; Yu, 1995; Isaacson et al., 1998, 1999; Zhu and Chwang, 2001b] have offered some values of f and s in their comparisons between numerical results and experimental data....

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  • ...But f tends to be a constant value 2.0 as the rubble structure [Yu, 1995] when b/d ≥ 0.1, where it may not be much appropriate employing the thin plate hypothesis....

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Journal ArticleDOI
TL;DR: In this article, the authors presented the numerical calculation of wave interactions with a pair of thin vertical slotted barriers extending from the water surface to some distance above the seabed, and described laboratory tests undertaken to assess the numerical model.

101 citations

References
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Book
01 Jan 1978
TL;DR: A self-contained presentation of the methods of asymptotics and perturbation theory, methods useful for obtaining approximate analytical solutions to differential and difference equations is given in this paper.
Abstract: This book gives a self-contained presentation of the methods of asymptotics and perturbation theory, methods useful for obtaining approximate analytical solutions to differential and difference equations. Parts and chapter titles are as follows: fundamentals - ordinary differential equations, difference equations; local analysis - approximate solution of linear differential equations, approximate solution of nonlinear differential equations, approximate solution of difference equations, asymptotic expansion of integrals; perturbation methods - perturbation series, summation series; and global analysis - boundary layer theory, WKB theory, multiple-scale analysis. An appendix of useful formulas is included. 147 figures, 43 tables. (RWR)

4,776 citations


"Diffraction of Water Waves by Porou..." refers background in this paper

  • ...Since the outer solution (38) is essentially independent on y, the inner solution, if obtained, is then also the uniform solution (Bender and Orszag 1978) and can, therefore, be used to represent the wave field around the semi-infinite porous wall....

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Journal ArticleDOI
TL;DR: In this article, a porous wavemaker theory is developed to analyse small-amplitude surface waves on water of finite depth, produced by horizontal oscillations of a porous vertical plate, and analytical solutions in closed forms are obtained for the surface-wave profile, the hydrodynamic-pressure distribution and the total force on the wavemaker.
Abstract: A porous-wavemaker theory is developed to analyse small-amplitude surface waves on water of finite depth, produced by horizontal oscillations of a porous vertical plate. Analytical solutions in closed forms are obtained for the surface-wave profile, the hydrodynamic-pressure distribution and the total force on the wavemaker. The influence of the wave-effect parameter C and the porous-effect parameter G, both being dimensionless, on the surface waves and on the hydrodynamic pressures is discussed in detail.

277 citations

Journal ArticleDOI
TL;DR: The linear theory for water waves impinging obliquely on a vertically sided porous structure is examined in this article, where the reflection and transmission coefficients are significantly altered and they are calculated using a plane-wave assumption.
Abstract: The linear theory for water waves impinging obliquely on a vertically sided porous structure is examined. For normal wave incidence, the reflection and transmission from a porous breakwater has been studied many times using eigenfunction expansions in the water region in front of the structure, within the porous medium, and behind the structure in the down-wave water region. For oblique wave incidence, the reflection and transmission coefficients are significantly altered and they are calculated here. Using a plane-wave assumption, which involves neglecting the evanescent eigenmodes that exist near the structure boundaries (to satisfy matching conditions), the problem can be reduced from a matrix problem to one which is analytic. The plane-wave approximation provides an adequate solution for the case where the damping within the structure is not too great. An important parameter in this problem is Γ 2 = ω 2 h ( s - i f )/ g , where ω is the wave angular frequency, h the constant water depth, g the acceleration due to gravity, and s and f are parameters describing the porous medium. As the friction in the porous medium, f , becomes non-zero, the eigenfunctions differ from those in the fluid regions, largely owing to the change in the modal wavenumbers, which depend on Γ 2 . For an infinite number of values of ΓF 2 , there are no eigenfunction expansions in the porous medium, owing to the coalescence of two of the wavenumbers. These cases are shown to result in a non-separable mathematical problem and the appropriate wave modes are determined. As the two wavenumbers approach the critical value of Γ 2 , it is shown that the wave modes can swap their identity.

260 citations

Journal ArticleDOI
TL;DR: In this paper, a theory termed the "arbitrary-shape harbour" theory is developed, where the solution of the Helmholtz equation is formulated as an integral equation which is then approximated by a matrix equation.
Abstract: Wave-induced oscillations in harbours of constant depth but arbitrary shape in the horizontal plane connected to the open-sea are investigated both theoretically and experimentally. A theory termed the ‘arbitrary-shape harbour’ theory is developed. The solution of the Helmholtz equation is formulated as an integral equation which is then approximated by a matrix equation. The final solution is obtained by equating, at the harbour entrance, the wave amplitudes and their normal derivatives obtained from the solutions for the regions outside and inside the harbour. Special solutions using the method of separation of variables for the region inside circular and rectangular harbours are also obtained. Experiments were conducted to verify the theories. Four specific harbours were investigated: two circular harbours with 10° and 60° openings respectively, a rectangular harbour, and a model of the East and West Basins of Long Beach Harbour, California. In each case, the theoretical results agreed well with the experimental data.

221 citations

Journal ArticleDOI
TL;DR: In this paper, the authors examined the diffraction of plane water waves by a stationary obstacle with vertical sides, in particular the variation of amplitude along the sides and the average steady pressure due to the wave motion.
Abstract: The diffraction of plane water waves by a stationary obstacle with vertical sides is examined, in particular the variation of amplitude along the sides and the average steady pressure due to the wave motion. Results similar to those in other diffraction problems are obtained for an infinite plane and for cylinders of circular or parabolic section, and approximations are made for sections of ship form. The examination was made in view of possible applications in the problem of a ship advancing through a train of waves, and the results are discussed in relation to the average additional resistance in such circumstances. It appears that the mean pressure obtained on diffraction theory from the second order terms can only account, in general, for a small proportion of the observed effect; the motions of the ship, and in particular its oscillations, are essential factors in the problem.

170 citations