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Studies on Wave Transformation over Rigid Porous Medium on Sand Seabed of Finite Thickness
mild slope equation
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|摘要:||The porous characteristics of the permeable submerged breakwater can reduced the energy of the incident waves. The porous construction also promotes the Ecology cicada chrysalis. Hence the submerged breakwater may prevent the coastal erosion and disaster. For the purpose to investigate the wave attenuation on the water surface elevation and the porous pressure in the sand bed when the waves pass through the submerged breakwater, we derive the analytic solution of wave interaction with a rigid porous medium above a poro-elastic sandy bottom of finite thickness. Then we extend the result to a new mild slope equation and establish a numerical model to analysis the wave transformation and the soil porous pressure when the waves pass through the submerged breakwater on the inclined sand bed. In the theorem, we apply the potential theorem and consider the inertial and friction effect of the flow in the rigid porous medium, while the soil response is based on the consolidation theorem. As results of the interaction among the waves, rigid porous medium and the elastic porous sand bed of finite thickness, the study obtains a new dispersion relationship in the complex type. The new dispersion relation includes the water depth, period, wave number and the parameters of the rigid and elastic porous medium. The analyzed result shows that different incident wave conditons and water depth will influence the wave attenuation. The wave attenuation will significantly occur when the porosity of the rigid porous medium or the poro-elastic medium increases. Moreover, increasing the relative thickness of the rigid porous medium and poro-elastic medium will also reduce the wave height and energy in the propagation.
In this thesis, we also derived a new time-dependent mild slope equation to explore the transformation of wave height and the soil pore pressure as the waves passing over the permeable submerged breakwater, which includes the parameters of the rigid and elastic porous medium. The study discusses the influence of the wave transformation with the conditions of the sand bed, the submerged depth and height, width and friction of the submerged breakwater. We also discuss the distribution of the pore pressure under the submerged breakwater. Based on the numerical simulations, the larger wave decay is found over the breakwater. The height and width of the submerged breakwater increase, the wave decade more. The larger the friction coefficient and porosity are, the wave decay larger. For the coarse sand and fine sand conditions, the wave decay larger than in the impermeable bed condition. On the distribution of the soil pressure under the submerged breakwater, the maximum pore pressure forms on the front toe, then decay with the distance. The minimum pore pressure forms on the middle of the submerged breakwater. The subordination pore pressure forms on the rear toe. And the pore water pressure reduces beneath the breakwater as the height or width of submerged breakwater is larger, which are also found for the larger porosity or friction in the porous breakwater. The pore pressure in the fine sand bed is larger than in the coarse sand.|
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