Composite equations of water waves over uneven and porous seabed
非平整、多孔介质海底上波浪传播的复合方程

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.