Nonlinear Wave Interaction with Submerged and Surface-piercing Porous Structures

A coupled Boussinesq-boundary integral method is developed to simulate nonlinear water wave interaction with structures consisting of multiple layers with different physical and hydraulic characteristics. The flow field in the water region is modeled with a modified set of Boussinesq-type equations, with additional terms to account for the flow of water into/out of the porous region. The equations of motion for the porous regions include an empirical Forchheimer-type term for laminar and turbulent frictional losses, and an inertial term for acceleration effects. A boundary integral formulation based on Green’s third identity is used to close the problem for the porous region. The coupled equations for the evolution of the free surface and boundary values of the tangential velocities are integrated in time using an iterative Crank-Nicolson scheme. At each time step, the Boussinesq problem is solved for the water region to determine the pressure at porous interface. The boundary integral problem for the porous region is then solved to determine the normal velocities along porous interface. The model is used to investigate wave interaction with a vertical surface-piercing porous structure and wave transmission over submerged breakwaters. Comparisons between the numerical model predictions and laboratory data show generally good agreement for both the wave field inside the structure and the reflection/transmission coefficients.