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中文摘要：
为在数学模型中考虑渗透性介质对波浪传播的影响，在多孔介质流体运动方程中引入拖曳阻力和惯性力，引出Laplace方程和边界条件．对控制方程无因次化，并以自由表面处速度势和交界面上的速度势进行幂级展开，推导了以静止水平面上速度、交界面上速度和波面升高3个变量表达的Boussinesq方程．给出积分平均速度或任一水深处速度与以上2个速度之间的关系式，进而推导出另外2个Boussinesq方程，并通过引入高阶色散项对方程进行加强以拓展其适用水深．对方程进行了理论分析，将相速度及衰减率与解析解进行了比较，发现四阶色散性方程具有最佳精度．不考虑渗透影响时，在2％误差下，四阶方程可适用最大无因次水深达到5．82．该高阶Boussinesq方程不仅可用于研究渗透海床上波浪的传播变形，也适用非渗透海床上的深水波浪传播变形．
英文摘要：
To consider the effect of porous media on wave propagation in mathematical model, the drag resistance force and inertial force of the porous media were included in the fluid motion, and the corresponding Laplace equa-tion and boundary conditions were given. First cancelling out the dimensions of control equations, and then starting from the velocity potentials in still water depth and in the interface to conduct exponential expansion, thus a Bouss- inesq model was derived with the expressions of three variables, including two velocities in still water depth and in the interface, and wave surface lifted height. The other two sets of Boussinesq equations were also derived, which were formulated using integrated mean velocities, or relational expression of the velocity in arbitrary water depth and the above-mentioned two velocities. The high-order dispersion term embodied in the newly derived equations for the purpose of expanding it to deeper water depth was theoretically analyzed, and phase speed and damping rate were compared against the analytical solutions. The fourth-order dispersive model was found to be the most accurate one. Neglecting the effect of porous seabed, the fourth-order Boussinesq model had a promising dispersive property and can be applicable to maximum water depth = 5.82 within 2% error. The high-order Boussinesq model is thus expec-ted to be applicable to wave propagation not only over permeable seabed but also over deep water evolution over im-permeable seabed.
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