Wave transformation due to multiple bottom-standing porous barriers

The scattering of oblique surface gravity waves due to the presence of multiple bottom-standing flexible porous barriers in finite water depth is analyzed based on the linearized theory of water waves. Using the eigenfunction expansion method the velocity potentials for the boundary value problem (BVP) are obtained and the unknown coefficients associated with the BVP are determined by the method of least square approximation on suitable application of edge conditions. The analysis for the wave interaction with multiple bottom-standing barriers is carried out using both the direct method and the wide-spacing approximation method. The vertical bottom-standing barriers having (i) free edge at. upper end and clamped at lower end and (ii) moored edge at upper end and clamped at lower end are analyzed to study the effect of wave energy dissipation. The detail comparison of both the edge conditions is carried out to understand the propagation of surface gravity wave in the presence of the multiple barriers. The numerical results for the reflection coefficient, surface elevation, force and overturning moments are analyzed for multiple submerged barriers. The comparison of the numerical result for single submerged bottom-standing barrier is carried out for the validity of derived analytical solution. The reduction of wave height in the transmitted region due to the presence of the multiple bottom-standing barriers is presented and discussed. The force and overturning moment of the bottom-standing barriers are studied to understand the effect of the dissipation of wave energy due to the presence of multiple porous barriers. In addition, the resonating patterns in the reflection coefficient due to multiple bottom-standing barriers are also discussed in detail. The present study on multiple bottom-standing barriers will be useful for the coastal engineers and designers for proper design and to analyze the feasibility of the submerged barriers as an effective breakwater. (c) 2014 Elsevier Ltd. All rights reserved.