Wave interaction with a semi-porous cylindrical breakwater mounted on a storage tank
Introduction
Recently, the interaction of linear surface waves with a semi-porous cylindrical breakwater protecting an impermeable circular cylinder was investigated theoretically by Darwiche et al. (1994). The breakwater consisted of a bottom-mounted, surface-piercing structure which was porous in the vicinity of the free-surface while at some distance below this surface it became impermeable. Under the assumptions of linearized potential flow, analytical expressions were obtained for the wave motion in both the interior and exterior flow regions. Numerical results were presented to illustrate the effects of the various wave and structural parameters on the hydrodynamic loads and interior and exterior wave fields.
Several other investigators have studied wave interaction with thin porous structures. The use of porous plate structures as wavemakers has been studied by Chwang (1983) and Chwang and Li (1983). The problem of the reflection and transmission of small-amplitude waves by a vertical porous plate has been treated by Chwang and Dong (1984). The use of rigid and flexible porous structures as breakwaters has been investigated theoretically by Twu and Lin (1991) and Wang and Ren (1993a), respectively. Wang and Ren (1993b) have also studied the wave-trapping effect due to a flexible porous breakwater located in front of a vertical impermeable wall. Yu and Chwang (1994) investigated the interaction of surface waves with a submerged horizontal porous plate. All of these studies were two-dimensional.
In the present paper, the analysis of Darwiche et al. (1994) is extended to deal with the case where the interior cylinder is mounted on a storage tank. Again, under the assumptions of linearized potential flow, analytical expressions are obtained for the wave motion in both the interior and exterior flow regions based on an eigenfunction expansion approach. The solutions in the two fluid domains are then matched using the appropriate boundary conditions at the interface between them. Numerical results are presented to illustrate the effects of the various wave and structural parameters on the hydrodynamic loads and interior and exterior wave fields. It is found that for certain parameter combinations the semi-porous, cylindrical breakwater may result in a significant reduction in the wave field and hydrodynamic forces experienced by the interior cylinder.
Section snippets
Theoretical formulation
The geometry of the problem is shown in Fig. 1. A bottom-mounted, surface-piercing, impermeable, circular cylinder of radius a is mounted on a cylindrical storage tank of radius b. A thin, semi-porous cylindrical breakwater of radius b rests on the storage tank as shown. The three structures, interior cylinder, storage tank and breakwater, are concentric and situated in water of uniform depth d. The cylindrical breakwater is porous to a depth h1 beneath the still-water level, below this depth,
Analytical solutions
The velocity potential amplitudes in the interior and exterior regions are now expressed in the following forms:Suitable forms for the functions which satisfy the appropriate free-surface, sea-bed and radiation boundary conditions in region 1 and the free-surface and sea-bed conditions in region 2 are
Numerical results
The effects of various wave and structural parameters on the interior and exterior wave field and on the hydrodynamic forces experienced by both the breakwater and the interior cylinder will now be investigated. The numerical results for these quantities will be presented in terms of the water depth to wavelength ratio. This parameter is related to the so-called Chwang's parameter (Chwang, 1983), Cw=g/ω2d=(k0d tanh k0d)−1.
The dimensionless hydrodynamic force amplitudes on the interior and
Conclusions
This paper has presented a theoretical study on the interaction of linear water waves with a cylindrical breakwater surrounding a rigid circular cylinder mounted on a storage tank. The breakwater consisted of a surface-piercing structure, porous in the vicinity of the free-surface while at some distance below the water surface it becomes impermeable. Assuming linearized potential flow, analytical expressions have been obtained for the wave motion in both the interior and exterior flow regions.
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