非平整、多孔介质海底上波浪传播的复合方程

为了反映近岸区域实际存在的多孔介质海底效应，并且考虑到波浪在刚性海底上传播模型的 最新研究进展，运用Green第二恒等式建立了波浪在非平整、多孔介质海底上传播的复合方 程. 假设水深和多孔介质海底层厚度均由两种分量组成：慢变分量，其水平变化的长度尺度大于 表面波的波长；快变分量，其水平变化的长度尺度与表面波的波长等阶，但其振幅小于表面 波的振幅. 另外，多孔介质层下部边界的快变分量比水深的快变分量小1个量级. 针对水体层和多孔介质层，选择Green第二恒等式方法给出了波浪传播和渗透的复合方程， 它在交接面上满足压力和垂直渗透速度的连续性条件,可充分考虑波数变化的一般连续性， 并包含了某些著名的扩展型缓坡方程.

Composite equations of water waves over uneven and porous seabed

The composite equations for water waves propagating over a porous uneven bottoms are derived from Green's second identity, which incorporates the effects of porous medium in the nearshore region and considers the advances in models of water waves propagation over rigid bottoms. Assuming that both water depth and thickness of the porous layer consist of two kind of components: The slowly varying component whose horizontal length scale is longer than the surface wave length, and the fast varying component with the horizontal length scale as the surface wave length. The amplitude of the fast varying component is, however, smaller than the surface wave length. In addition, the fast varying component of the lower boundary surface of the porous layer is one order of magnitude smaller than that of the water depth. By Green's second identity and satisfying the continuous conditions at the interface for the pressure and the vertical discharge velocity the composite equations are given for both water layer and porous layer, which can fully consider the general continuity of the variation of wave number and include some well-known extended mild-slope equations.