Linear Water Wave Damping by a Bottom-Mounted Porous Structure and by Vertical Dual Porous Plates
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2014
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Abstract
Breakwaters and wave absorbers are structures constructed in the coastal areas to protect harbours, inlets and beaches by attenuating incoming wave energy. Different types of breakwaters can be constructed such as caisson type breakwaters where the vertical side is backed up with vessels, rubble-mound breakwaters that consist of different layers of materials, preferably sand and gravels on the outermost layer, to absorb most of the energy and inner concrete layer in order to block water to transmit. Breakwaters may also consist of metallic foams formed from different types of metals and alloys. This thesis mainly studies oblique water wave scattering by a vertical porous structure placed on (i) an elevated horizontal bottom and (ii) a multi-step impermeable bottom in the presence of a rigid vertical wall. Linear water wave theory is considered along with time harmonic motion. In both cases, governing equation, boundary conditions and dispersion relation for flow inside the porous structure are derived. For the horizontal bottom case, a linearized friction factor is calculated to damp the motion whereas the friction factor is taken as fixed for the multi-step bottom. In the later part of the thesis, oblique water wave scattering by two thin vertical (i) surface piercing and (ii) fully submerged porous plates of different heights and having different porous effect parameters in an infinite channel of finite depth is also considered. Boundary value problems consisting of the governing equation, boundary conditions and matching conditions in terms of the porous effect parameters are derived. First, a rectangular shaped porous structure, attached to a rigid vertical wall, is placed on an elevated horizontal impermeable bottom. Oblique waves are incident on the porous structure. Some part of the waves gets reflected by the sea-ward face of the porous structure and the rest of them passes through the porous structure before getting reflected by the rigid vertical wall. Inside the porous structure, the reflected and transmitted waves are reflected back and forth. Boundary value problems are set up with the help of the governing equation along with the boundary conditions in both porous and water regions. In order to find the reflection coefficient, matching conditions along the vertical boundaries are used to deduce a system of equations which are solved by a matrix method. It is observed that the propagating mode controls the reflection phenomenon up to a certain wave number beyond which the evanescent modes start affecting reflection. The value of the reflection coefficient decreases with an increase in the height of bottom elevation as well as in the values of porosity. Moreover, minimum reflection is observed for a fixed range of angles of incidence. Further, the problem is extended by placing the porous structure at some distance from the rigid vertical wall. In this case, the transmitted waves coming out from the porous structure pass through the water region between the porous structure and the rigid vertical wall, and get reflected by the wall.
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Supervisor: Swaroop Nanadan Bora
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MATHEMATICS