Effect of a porous sea-bed on water wave scattering by two thin vertical submerged porous plates

Abstract

A hydrodynamic model, with incorporation of porosity, is considered to investigate oblique water wave scattering by two fully submerged parallel porous plates with the wave propagating over a porous bed in a homogeneous fluid flow with the upper surface exposed to atmosphere. The porous plates are assumed to follow the theory of thin plates and the wave propagation through the porous structure follows porous wave-maker theory. The behavior and properties of the roots of the dispersion relation are analyzed by adopting counting argument and contour plot. Time-harmonic propagating waves propagate with exactly one wavenumber along the free surface for any given frequency. Methods of eigenfunction expansion and least square are employed to acquire the complete analytical solution for interaction of water waves with submerged porous plates. Subsequently the reflection and transmission coefficients as well as the energy loss are computed. Then those are examined corresponding to various values of parameters such as porous-effect parameter, the submergence depth of plates from free surface, angle of incidence, porosity of the sea-bed. Present investigation clearly demonstrates that the wave reflection is of oscillatory nature. It further shows that the occurrence of minima in wave reflection is due to an increase in the inertial effect of the porous plates which dissipate a significant portion of the wave energy. The effect of the porous bed under consideration on surface gravity waves is carried out by introducing various numerical values to the hydrodynamic wave characteristics and it is noticed that a reasonable change in porosity of the sea-bed has a significant impact when the propagating wave encounters the submerged structure. The present approach is expected to be of great significance in designing and construction of different types of effective wave absorbers utilized in sea for studying reflection as well as dissipation of wave energy in coastal regions and hence for the purpose of coastal as well as offshore engineering. The present model is validated by comparing it with some established result.