多孔介质中波浪传播的高阶Boussinesq方程*

准确模拟波浪在多孔介质中传播变形对于研究抛石防波堤等结构的消能作用是十分必要的。对Laplace方程、自由表面处的运动学方程和动力学方程以及海底运动学方程进行无因次化，且以自由表面处速度势为切点，进行幂级展开，最终给出4个不同的高阶Boussinesq水波方程。在常水深下对这些方程的一维问题进行了理论研究，并将无因次相速度和无因次虚波数与解析解结果进行对比，方程的相速度与解析解吻合程度较好，虚波数与解析解基本吻合，表明高阶Boussinesq方程可用于模拟波浪在多孔介质中的传播变形。

High-order Boussinesq equations for water-wave propagation in porous media

Wave is an important environmental load on porous structures in coastal engineering.A reasonable mathematical model is very important when the problem mentioned above is numerically solved.To be applicable in such problem,with both of the drag resistance and inertia resistance considered,Laplace equations with boundary controlling conditions are given.First these equations are nondimensionalized,and started from the free surface velocity potential in still water depth,a power series of potential are supposed,and four sets of different Boussinesq models are derived.In a constant water depth,the dispersive relationship expressions of the four models in one dimension are given.And theoretical solutions of the Boussinesq models are compared against the analytical solution.Overall,both of the phase speed and imaginary wave number are in good agreement.And the high order Boussinesq models can be expected to be applicable for waves propagation in porous media.