Complementary approximations to wave scattering by vertical barriers
TL;DR: In this paper, a Galerkin approximation method was proposed to solve the wave scattering problem in finite-depth water with respect to vertical barriers in a rectangular tank and a vertical barrier in a vertical pool.
Abstract: Scattering of waves by vertical barriers in infinite-depth water has received much attention due to the ability to solve many of these problems exactly. However, the same problems in finite depth require the use of approximation methods. In this paper we present an accurate method of solving these problems based on a Galerkin approximation. We will show how highly accurate complementary bounds can be computed with relative ease for many scattering problems involving vertical barriers in finite depth and also for a sloshing problem involving a vertical barrier in a rectangular tank.
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TL;DR: In this article, a wave energy device consisting of a thin vertical surface-piercing barrier next to a vertical wall in finite depth water is considered, and power is extracted due to a normally incident wave forcing the free surface of the fluid between the barrier and the wall to oscillate.
Abstract: We consider a wave energy device consisting of a thin vertical surface-piercing barrier next to a vertical wall in finite depth water. Power is extracted due to a normally incident wave forcing the free surface of the fluid between the barrier and the wall to oscillate, in turn pumping the volume of air above the free surface through a uni-directional turbine housed at the opening of the device. Under the assumptions of linear water wave theory, the important hydrodynamic properties are expressible in terms of integral quantities of functions proportional to the fluid velocity under the barrier. These functions each satisfy integral equations, the solutions of which are approximated very accurately and efficiently using a Galerkin method as described in Porter and Evans [Porter, R. & Evans, D. V., Complementary approximations to wave scattering by vertical barriers. J. Fluid Mech., 294 (1995) 155–80].
267 citations
TL;DR: In this paper, an oscillating water column (OWC) is studied experimentally to examine energy efficiencies for power take-off in a wave environment with plane progressive waves of steepness ranging from kA = 0.01 to 0.22 and water depth ratios varying from kh=0.30 to 3.72.
Abstract: An oscillating water column device enables the conversion of wave energy into electrical energy via wave interaction with a semi-submerged chamber coupled with a turbine for power take off. This present work concentrates on the wave interaction with the semi-submerged chamber, whereby a shore based oscillating water column (OWC) is studied experimentally to examine energy efficiencies for power take-off. The wave environment considered comprises plane progressive waves of steepnesses ranging from kA=0.01 to 0.22 and water depth ratios varying from kh=0.30 to 3.72, where k, A, and h denote the wave number, wave amplitude, and water depth, respectively. The key feature of this experimental campaign is a focus on the influence of front wall geometry on the OWC’s performance. More specifically, this focus includes: front wall draught, thickness, and aperture shape of the submerged front wall. We make use of a two-dimensional inviscid theory for an OWC for comparative purposes and to explain trends noted in the experimental measurements. The work undertaken here has revealed a broad banded efficiency centered about the natural frequency of the OWC. The magnitude and shape of the efficiency curves are influenced by the geometry of the front wall. Typical peak magnitude resonant efficiencies are in the order of 70%.
176 citations
TL;DR: In this paper, the authors combined theoretical and experimental studies of the two-dimensional piston-like steady-state motions of a fluid in a moonpool formed by two rectangular hulls (e.g. a dual pontoon or catamaran).
Abstract: This paper presents combined theoretical and experimental studies of the two-dimensional piston-like steady-state motions of a fluid in a moonpool formed by two rectangular hulls (e.g. a dual pontoon or catamaran). Vertical harmonic excitation of the partly submerged structure in calm water is assumed. A high-precision analytically oriented linear-potential-flow method, which captures the singular behaviour of the velocity potential at the corner points of the rectangular structure, is developed. The linear steady-state results are compared with new experimental data and show generally satisfactory agreement. The influence of vortex shedding has been evaluated by using the local discrete-vortex method of Graham (1980). It was shown to be small. Thus, the discrepancy between the theory and experiment may be related to the free-surface nonlinearity.
142 citations
Cites background or methods or result from "Complementary approximations to wav..."
...A similar technique for other surfacewave problems was presented by Porter & Evans (1995) and Gavrilyuk et al. (2006)....
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...…online version of the paper. truncated series by Bessel functions as the most CPU-expensive operation (a similar situation appeared in the papers of Porter & Evans (1995), Kuznetsov et al. (2001), Gavrilyuk et al. (2006), where the functional basis captured the singularities at the sharp edges…...
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...The integral equations are in part similar to the results of Porter & Evans (1995) and Kuznetsov et al. (2001)....
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...The series-based integral kernels G(k)i , i = I, . . . , IV , are common in the literature on the domain-decomposition method (see Drobyshevski 2004; Kuznetsov et al. 2001; Mavrakos 2004; Porter & Evans 1995; Williams & Abul-Azm 1997)....
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...In contrast, accounting for the singular character of the traces should improve the convergence (Porter & Evans 1995; Kuznetsov et al. 2001; Gavrilyuk et al. 2006)....
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107 citations
TL;DR: In this paper, the two-dimensional problems of scattering and radiation of small-amplitude water waves by thin vertical porous plates in finite water depth are considered using the linear water wave theory.
Abstract: The two-dimensional problems of scattering and radiation of small-amplitude water waves by thin vertical porous plates in finite water depth are considered using the linear water wave theory. Applying the method of eigenfunction expansion, these boundary value problems are converted to certain dual series relations. Solutions to these relations are then obtained by a suitable application of the least squares method. For the scattering problem, four different basic configurations of the barriers are investigated, namely, (I) a surface-piercing barrier, (II) a bottom-standing barrier, (III) a totally submerged barrier, and (IV) a barrier with a gap. The performance of these types of barriers as a breakwater are examined by studying the variation of their reflection and transmission coefficients, hydrodynamic forces and moments for different values of the porous effect parameter defined by Chwang [J. Fluid Mech. 132, 395–406 (1983)], or the Chwang parameter. For the radiation problem, three types of wavemakers, which resemble types (I), (II), and (III) of the above-mentioned configuration, are analyzed. The dependence of the amplitude to stroke ratio on other parameters is also investigated to study the features of these wavemakers.
90 citations
References
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01 Jul 1947
TL;DR: In this paper, it was shown that when the normal velocity is prescribed at each point of an infinite vertical plane extending from the surface, the motion on each side of the plane is completely determined.
Abstract: In this paper the two-dimensional reflection of surface waves from a vertical barrier in deep water is studied theoretically.It can be shown that when the normal velocity is prescribed at each point of an infinite vertical plane extending from the surface, the motion on each side of the plane is completely determined, apart from a motion consisting of simple standing waves. In the cases considered here the normal velocity is prescribed on a part of the vertical plane and is taken to be unknown elsewhere. From the condition of continuity of the motion above and below the barrier an integral equation for the normal velocity can be derived, which is of a simple type, in the case of deep water. We begin by considering in detail the reflection from a fixed vertical barrier extending from depth a to some point above the mean surface.
299 citations
01 Nov 1945
TL;DR: In this paper, the reflexion of waves on the surface of water by a thin plane vertical barrier is considered and the coefficient of reflexion (the ratio of the amplitudes, at a great distance from the barrier, of the reflected and incident waves) is calculated.
Abstract: 1. The reflexion of waves on the surface of water by a thin plane vertical barrier is considered and the coefficient of reflexion (the ratio of the amplitudes, at a great distance from the barrier, of the reflected and incident waves) is calculated. If the top edge is at a depth a below the surface, it is found that the coefficient of reflexion is about ¼ when where T is the period of the incident waves, so that the condition that the coefficient may exceed ¼ is a .
118 citations
TL;DR: In this article, a thin vertical plate makes small, simple harmonic rolling oscillations beneath the surface of an incompressible, irrotational liquid, and a train of plane waves of frequency equal to the frequency of oscillation of the plate, is normally incident on the plate.
Abstract: A thin vertical plate makes small, simple harmonic rolling oscillations beneath the surface of an incompressible, irrotational liquid. The plate is assumed to be so wide that the resulting equations may be regarded as two-dimensional. In addition, a train of plane waves of frequency equal to the frequency of oscillation of the plate, is normally incident on the plate. The resulting linearized boundary-value problem is solved in closed form for the velocity potential everywhere in the fluid and on the plate. Expressions are derived for the first- and second-order forces and moments on the plate, and for the wave amplitudes at a large distance either side of the plate. Numerical results are obtained for the case of the plate held fixed in an incident wave-train. It is shown how these results, in the special case when the plate intersects the free surface, agree, with one exception, with results obtained by Ursell (1947) and Haskind (1959) for this problem.
118 citations
TL;DR: In this article, the effects of a vertical baffle on the resonant frequencies of fluid within a rectangular container were investigated using the linearized theory of water waves, and the accuracy of simple approximate solutions was assessed by comparison with an accurate solution based on eigenfunction expansions.
Abstract: The effects of a vertical baffle on the resonant frequencies of fluid within a rectangular container are investigated using the linearized theory of water waves. The accuracy of simple approximate solutions is assessed by comparison with an accurate solution based on eigenfunction expansions. It is found that a surface-piercing barrier can change the resonant frequencies significantly while the effect of a bottom-mounted barrier is usually negligible.
94 citations
TL;DR: In this article, the scattering of regular surface water waves by a single, flat, submerged plate is extended to consider the scattering by submerged, curved plates and also by surface-piercing, flat plates.
Abstract: Previous work on the scattering of regular surface water waves by a single, flat, submerged plate is extended to consider the scattering by submerged, curved plates and also by surface-piercing, flat plates. Problems are again formulated as hypersingular integral equations for the discontinuity in potential across the plate, which are then solved numerically using Chebyshev expansions and collocation. New results are given for submerged plates in the shape of a circular arc, and for surface-piercing plates at small angles of inclination to the horizontal. The latter configuration supports a hitherto unsuspected quasi-resonant behaviour, with a very spiky frequency response.
78 citations