Reflection of oblique ocean water waves by a vertical porous structure placed on a multi-step impermeable bottom

Abstract

Based on linear water wave theory, wave reflection by a vertical porous structure placed on an elevated impermeable seabed, assumed to consist of a number of horizontal steps, is considered. The reflection phenomenon is investigated for two forms of the bottom topography: first a 2-step one and then a p-step one. An oblique incident wave propagates through the porous structure and gets reflected by the steps and a vertical solid wall which supports the structure at one end. Boundary value problems are set up in the two different media, the first medium being water and the second medium being the porous structure consisting of p vertical regions – one above each step. By using the matching conditions along the vertical boundaries, a system of linear equations is deduced. Reflection coefficient is obtained by solving this system of equations. The behavior of the reflection coefficient due to different relevant parameters is studied: the effect of various parameters, such as depth, porosity, number of evanescent modes, structure width and angle of incidence is studied graphically for both cases. It is observed that when the porous structure is considered above a 2-step bottom, the number of evanescent modes, porosity and the angle of incidence do not affect the reflection coefficient for relatively long waves. Lower values of friction factor results in oscillation in the reflection coefficient which vanishes with an increase in the values of friction factor. Up to a certain range of the angles of incidence, reflection coefficient is independent of the values of porosity. When a p-step bottom is considered, certain observations remain the same except that the behavior of reflection coefficient against the angle of incidence is different. In the end, both cases are compared by considering the same set of parameters. Justification of our model is presented by matching it with an available one.