Wave Propagation On 3-D Local Permeable Seabed

Most islands and reefs are corals in the South China Sea. Compared with impermeable seabed, coral reefs are with high porosity. It is necessary to consider the permeation of coral reefs. Thus, it is crucial to study the characters of hydrodynamic environment around the coral reefs in the South China Sea. This paper is intended to analyze the characters of wave propagation on 3-D local permeable seabed.The control equation of permeable seabed is derived from the Darcy law. The boundary condition of potentials on the permeable seabed’s surface is developed by the continuous conditions of normal velocity and pressure on the interface between permeable seabed and water. By taking 3D Laplace equation as the governing equation, a numerical solution based on a frequency-domain higher-order boundary element method is presented for wave propagation on local permeable seabed. The integration equation of potentials is derived from Green’s second theorem based on the linear potential flow theory. By the adoption of wave Green function with surface based on the theory of wave diffraction, the integration is confined on the boundary of permeable seabed. Then, when wave pass through the permeable seabed, the diffraction potentials of free surface and the variation of wave amplitude can be calculated after solving the boundary integral equations by higher-order boundary element method. The validity and effectiveness of the present frequency domain method is verified by the results comparison with time domain method, in that case the wave diffractions on cylindrical hump seabed are considered.The characteristic of wave propagation on large rectangular permeable seabed is investigated by the present numerical method, and the effects of parameters such as wave length and the porosity parameter are discussed further. The computation results show that the wave amplitudes decrease after propagating into the local permeable seabed, and then the wave amplitudes increase out of the local permeable seabed. Because of the three-dimensional effect, the closer to the midline, the more wave amplitudes attenuation and the larger scale of attenuation on the direction perpendicular to wave propagation. The distribution of wave amplitudes is in strength three-dimensional character. Moreover, the wave amplitudes attenuation is more obvious with the increasing wave length and the porosity parameter. The reflection of wave appears significantly on the boundary of local permeable seabed where the permeability changes suddenly. The reflection is more apparent with the increasing wave length and the porosity parameter.Then, the characteristic of wave propagation on large half ellipsoid permeable seabed is investigated by the present numerical method, and the effects of parameters such as wave length, the porosity parameter and the height of permeable seabed are discussed further. Compared with impermeable reefs, the wave amplitudes decrease after propagating into the local permeable reefs. When the wave length is constant, with the increasing porosity parameter, the wave amplitudes attenuation is obvious over the midline of the reef and unobvious away from the midline. When the porosity parameter is constant, the wave amplitudes decrease over the reef with the increasing wave length, the scale of wave amplitudes attenuation increases perpendicular to wave propagation. When the porosity parameter is zero and the wave length is constant, with the increasing permeable seabed height, the increase of the wave amplitudes over the midline of seabed and the decrease of the wave amplitudes over both sides of seabed is more apparent.