Reflection of oblique ocean water waves by a vertical rectangular porous structure placed on an elevated horizontal bottom

Abstract

Based on linear water wave theory, water wave reflection by a vertical rectangular porous structure placed on an elevated impermeable horizontal bottom is considered. A wave propagates through water and the porous structure and gets reflected by a vertical solid wall which supports the structure at one end. The reflection phenomenon is investigated by evaluating the reflection coefficient with the help of a system of linear equations obtained from the matching conditions along the vertical boundaries in the two different media. The roots of the dispersion relation are used in setting up the system of equations. The behavior of the reflection coefficient due to different relevant parameters such as depth, porosity, number of evanescent modes, height of the elevation, and structure width is studied graphically. It is observed that up to a certain small wave number (long waves), reflection can be described by the propagating mode alone. For short waves, the effect of number of evanescent modes is evident, that is, higher number of modes gives rise to higher reflection. But for intermediate values of the wave number, the evanescent modes and the incident wave neutralize each other and higher number of modes results in lower reflection. It is noticeable that the values of the reflection coefficient decreases as the porosity increases. Some more observations are made with respect to depth, height of elevated bottom and width of the porous structure. We also study reflection due to oblique incidence by considering different angles of incidence and observe the effect due to change in angles. The same investigation is carried out with the porous structure placed directly on the horizontal ocean bottom (without any elevation). The results of this particular case are compared with the elevated bottom case in order to examine the effect of presence of the elevated bottom. Comparison of our results with available ones, whenever possible, shows excellent agreement.