Wave interaction with a rigid porous structure under the combined effect of refraction–diffraction

Abstract

Water wave scattering, trapping, and generation by a thin porous structure placed on an uneven bottom are studied approximately. The classical eigenfunction expansion method is employed for the uniform bottom, whereas the Galerkin-Eigenfunction expansion method is employed for the uneven bottom. The solution is derived in the form of a system of algebraic equations through matching procedure. Wave reflection, transmission, and wave-induced forces on the porous structure and backwall are investigated under the combined refraction–diffraction effect. In the scattering problem with periodic bottom, Bragg resonance is minimized at the Bragg frequency, whereas the porous structure at other frequencies maximizes wave reflection. Consequently, wave transmission is very low for all wave frequencies in this situation. In the wave trapping problem, forces on the porous structure and the backwall are reduced substantially when the water depth ratio decreases. Feasible locations of the porous structure are shown at which wave reflection and forces on it and backwall are optimized. In the wave generation problem, the comparison of results for flat and uneven bottoms reveals that waves have a smaller amplitude at infinity as uniform bottom levels become farther for relatively small values of the reciprocal of the wave-effect parameter (C).