Scattering of water waves by multiple porous plates with variable porosity over an undulated bottom

Abstract

The water wave interaction with multiple floating thin porous plates with varying porosity placed over an undulating seabed is investigated using linear potential flow theory. The porous plate is modeled based on [Wave transmission through permeable breakwaters Sollitt and Cross Coastal Eng. 1827-1846 (1972)] theory. The undulated bottom is approximated through stepwise discretization, representing it as a sequence of steps and shelves. The model includes several plate configurations governed by a set P of indices, each corresponding to a region containing a porous plate. Further, the porosity variation is incorporated through a piecewise-constant approximation. The problem is formulated assuming the fluid is incompressible and inviscid. By using the method of step approximation and the eigenfunction expansion method, the problem coins to a system of equations, which is solved numerically to compute the values of reflection, transmission coefficients, energy dissipation, and free surface elevation. The model is validated against existing results and through the energy balance relation. The effects of plate arrangements with or without a gap, wave incidence angle, seabed undulation parameters, and different variable porosity patterns (increasing, sinusoidal, constant, and decreasing) are examined. The influence of varying porosity patterns on wave characteristics indicates that a decreasing porosity pattern provides 5% more energy dissipation as compared to a constant porosity pattern. Further comparison among the three types of decreasing porosity configurations highlights their effectiveness, revealing that the quadratic decreasing pattern results in greater dissipation and reduced reflection. Additionally, the study investigates porous plates with intervening gaps, demonstrating that placing the plates with gaps can result in higher dissipation, but only up to a certain gap size. Also, the effect of the optimal number of plates and the placement of plates is also analyzed.