Mathematical study of wave interaction with a mound type of composite poroelastic submerged breakwater

• The composite poroelastic submerged breakwater is constructed as a mound type.
• Governing equations are considered in the turbulent drag of high permeability.
• An analytical solution is reached in terms of orthogonal eigenfunctions.
• Influence parameters of the poroelastic breakwater on wave variations are discussed.

In order to investigate the impact of applying pseudo-natural and ecological engineering protection means for coastal protection, the problem of wave propagation over a mound-type submerged poroelastic breakwater was solved theoretically. In this study, a breakwater was designed to be a double-layer structure to mimic a pseudo-natural structure with an inner rigid part and an outer soft layer. Different parameters, e.g. the relative dimensions of the inner and outer layers, the porosity and permeability were used to describe the characteristics of the breakwater. An analytical solution for describing the dynamic response of wave interaction with poroelastic media is presented. Linear wave theory was used to analyze wave motion based on an extension of Biot's theory including the turbulent frictional effect. An equation set was developed and solved to achieve a general solution for this type of problem. The solution was first validated by the theoretical solution and experiments of this problem. This solution was further applied to investigate the additional effect arising owing to flexibility of composite submerged permeable breakwaters on wave scattering and energy dissipation. The solution provides a theoretical and general way to pre-investigate problems of wave transformation over this type of submerged breakwaters.