Journal ArticleDOI

# Wave interactions with double slotted barriers

01 Apr 1999-Applied Ocean Research (Elsevier)-Vol. 21, Iss: 2, pp 81-91
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.
Abstract: The present article outlines 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 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 surface of each barrier which accounts for energy dissipation within the barrier. Comparisons with experimental measurements of the transmission, reflection, and energy dissipation coefficients for partially submerged slotted barriers show excellent agreement and indicate that the numerical method is able to adequately account for the energy dissipation by the barriers.
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TL;DR: In this paper, a hydrodynamic model of perforated or slotted structures is proposed, in which the openings are infinitely small and numerous, and the wall thickness is assumed to be nil.
Abstract: A hydrodynamic model of perforated or slotted structures is proposed. It is asymptotic in the sense that the openings are supposed to be infinitely small and numerous, and the wall thickness to be nil. At variance with other work, a quadratic, not linear, law, relating the pressure differential to the traversing velocity, is assumed. As a result the hydrodynamic coefficients (added mass and damping) become amplitude dependent. The model is applied to bodies of various shapes including cylinders, plates and disks, in forced motion or submitted to incoming waves. Good agreement with experimental data is generally observed.

125 citations

Journal ArticleDOI
, Yong Liu1, Bin Teng1
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 "Wave interactions with double slott..."

• ...There are several porous shapes in general as follows: slit [Isaacson et al., 1998, 1999; Tanimoto and Yoshimoto, 1982; Zhu and Chwang, 2001a], screen [Twu and Lin, 1991; Bennett et al., 1992], circular holes [Kondo, 1979] and rectangular holes [Li et al., 2002, 2003a, 2003b]....

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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....

[...]

• ...However, many researchers [e.g. Sollit and Cross, 1972; Losada et al., 1993; Yu, 1995; Isaacson et al., 1998, 1999; Zhu and Chwang, 2001b; Hossain et al., 2001] have used the value of Cm = 0 i.e. s = 1 for comparing the numerical predictions of reflection and transmission coefficients of permeable…...

[...]

• ...In practices, there are two main forms of vertical permeable structures: (1) single or several vertical 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,…...

[...]

• ...…medium hypothesis, Yu [1995] derived a porous boundary condition, through which the whole wave domain around the porous plate can be solved with analytical method [Isaacson et al., 1998, 1999; Li et al., 2003a; Teng et al., 2004] or boundary element method [Cheng et al., 2004; Zhao and Teng, 2004]....

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Journal ArticleDOI
TL;DR: In this paper, the authors investigated the hydrodynamic performance of a pile-supported OWC structure as a breakwater, for which the air-flow through a small opening in the top cover contributes to energy extraction from waves and reduction in transmission coefficients.
Abstract: Oscillating water column (OWC) is one of the mechanisms for extracting wave energy from ocean waves. In this study, we experimentally investigated the hydrodynamic performance of a pile-supported OWC structure as a breakwater, for which the air-flow through a small opening in the top cover contributes to energy extraction from waves and reduction in transmission coefficients. The effects of relative breadth, draught and opening conditions on wave reflection, wave transmission, energy dissipation and the pressure fluctuation inside the OWC chamber were examined. Compared with other types of pile-supported breakwaters, the hydrodynamic performance of the pile-supported OWC structure is remarkable and the pile-supported OWC structure has the potential for wave energy utilization.

107 citations

Journal ArticleDOI
TL;DR: In this article, the reflection characteristics of a slotted seawall depend mainly on the porosity of the slotted plate and the incident wave height, and it is found that the reflection coefficient reaches its minimum value as the chamber width is about a quarter of the incident wavelength.
Abstract: Based on the linear wave theory and the eigenfunction expansion method, the interaction between waves and a slotted seawall is studied analytically as well as experimentally. The analytical investigations show that the reflection characteristics of a slotted seawall depend mainly on the porosity of the slotted plate and the incident wave height. It is found that the reflection coefficient reaches its minimum value as the chamber width is about a quarter of the incident wavelength. The reflection behaviour becomes optimal when the porosity is moderate (about 0.2 in the present study). The immersed depth has some effect on the reflection coefficient of the seawall structure, but the improvement is small when the immersed depth is larger than the half of the water depth. A series of physical model experiments are carried out to examine the analytical results. Comparisons between the analytical and experimental results of reflection coefficients are made for some comparable cases and show good agreement provided certain parameters of this model are suitably chosen. This demonstrates that the analytical model is able to account adequately for energy dissipation by the slotted plate and can provide instruction for the design of such seawalls.

76 citations

Journal ArticleDOI
TL;DR: In this article, the effect of different wave and structural parameters on the hydrodynamic performance of a vertical wall with permeable lower part (horizontal slots) was experimentally and theoretically studied under normal regular waves.
Abstract: The hydrodynamic performance of a vertical wall with permeable lower part (horizontal slots) was experimentally and theoretically studied under normal regular waves. The effect of different wave and structural parameters was investigated e.g. the wave length, the upper part draft, and the lower part porosity. Also, the theoretical model based on an Eigen Function Expansion Method and a Least Square Technique was developed. In order to examine the validity of the theoretical model, the theoretical results were compared with the present experimental results and with the results obtained from different previous studies. Comparison between experiments and predictions showed that the theoretical model provides a good estimate of the wave transmission, reflection, and energy dissipation coefficients when the friction factor f = 5.5. In general, the tested model gives transmission coefficients less than 0.5 and reflection coefficients larger than 0.5 when the relative wave length h / L is larger than 0.3, the relative upper part draft D / h larger than 0.36, and lower part porosity e less than 0.5. Also, the tested model dissipates about 50% of the incident wave energy when the relative wave length h / L is in the range of 0.25 to 0.35.

65 citations

##### References
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Book
01 Jan 1981

1,210 citations

Journal ArticleDOI
29 Jan 1972
TL;DR: In this article, an approximate solution to conventional rubble mound breakwater designs is formulated in terms of an equivalent rectangular breakwater with an additional consideration for wave breaking, and experimental and theoretical results are compared and evaluated.
Abstract: A theory is derived to predict ocean wave reflection and transmission at a permeable breakwater of rectangular cross section. The theory solves for a damped wave component within the breakwater and matches boundary conditions at the windward and leeward breakwater faces to predict the reflected and transmitted wave components. An approximate solution to conventional rubble mound breakwater designs is formulated in terms of an equivalent rectangular breakwater with an additional consideration for wave breaking. Experimental and theoretical results are compared and evaluated.

477 citations

Journal ArticleDOI
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.

280 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 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