An analytical method to evaluate the efficiency of porous screens as wave dampers

Abstract The linear theory for water waves impinging obliquely on dissipative multilayered media is used to evaluate the reflection and transmission coefficients. The case of periodic medium consisting of alternating layers of upright porous walls and water of equal or different thicknesses is examined. Wave propagation in these media exhibits Bragg reflection. Using a plane wave assumption, which involves neglecting the evanescent eigenmodes that exist near the structure boundaries (to satisfy matching conditions), the problem can be reduced to a matrix equation which relates the complex amplitudes of the incident and reflected plane waves to the complex amplitude of the transmitted wave. The problem of wave propagation is analysed for an infinite channel, and for a wave flume in which a paddle generates the waves and a backwall limits waves propagation. The variation of the magnitude of the reflection coefficient, | R |, with k 1 Λ is discussed, where k 1 is the wavenumber in the water and Λ is the width of a unit cell consisting of two layers, one porous and another water. Increasing the porous layer width or decreasing the wave period broadens the range of k 1 Λ values for which resonance occurs. Furthermore, with increase in the angle of wave incidence, θ, the value of | R | decreases and the dependence of | R | on k 1 Λ is damped; for large angle of incidence the reflection is almost constant and negligible. On increasing the number of absorber units, an overall decrease in the reflection coefficient is achieved, but an increase in the number of oscillations between resonant peaks and in the peak amplitude also occurs.