Water wave interaction with porous structures of irregular cross-sections

A general unsteady porous flow model is developed based on the assumption that the porous media can be treated as a continuum. The model clearly defines the role of solid and fluid motions and henceforth their interactions. All the important resistant forces are clearly and rigorously defined. The model is applied to the gravity wave field over a porous bed of finite depth. By applying linear wave theory, an analytical solution is obtained, which is applicable to the full range of permeability. The solution yields significantly different results from those of contemporary theory. The solution requires three empirical coefficients, respectively representing linear, nonlinear and inertial resistance. Laboratory experiments using a standing wave system over a porous seabed were conducted to determine these coefficients and to compare with analytical results. The coefficients related to linear and nonlinear resistances were found to be close to those obtained by previous investigators. The virtual mass coefficient was determined to be around 0.46, close to the theoretical value of 0.5 for a sphere. The analytical solution compared well with the experiments.; Based on this porous flow model and linear wave theory, two numerical models using boundary integral element method with linear elements are developed for permeable submerged breakwaters and berm breakwaters, respectively. Due to the establishment of a boundary integral expression for wave energy dissipation in a porous domain and the application of the radiation boundary condition on the lateral boundary(ies), the numerical models are highly efficient while maintaining sufficient accuracy. The numerical results show that the wave energy dissipation within a porous domain has a well defined maximum value at certain permeability for a specified wave and geometry condition. The nonlinear effects in the porous flow model are clearly manifested, as all the flow field properties are no longer linearly proportional to the incident wave heights. The numerical results agreed reasonably well with the experimental data on the seaward side. On the leeward of the breakwater, despite the appearance of higher order harmonics, the numerical model produces acceptable results of energy transmission based on energy balance.