A mathematical study of a two-layer fluid flow system in the presence of a floating breakwater in front of VLFS

Abstract

The present study deals with the usefulness of a surface-piercing porous structure of definite width in a two-layer fluid placed at a finite distance from a floating elastic plate to mitigate the hydrodynamic response of the elastic plate. We use linear water wave theory with the eigenfunction expansion approach to develop analytical solutions to the model problem in finite water depth. Here, we identify and explore the complete parameter space associated with the problem by examining the hydrodynamic coefficients for waves in surface and internal modes, plate elevation, shear force, bending moment, wave loads on the elastic plate, flow amplitude in the plate-covered region and wave attenuation. We investigate the effectiveness of structures of various configurations and geometries on wave scattering. This study demonstrates an oscillatory pattern of wave reflection in the confined region between the plate and the breakwater. Moreover, optima in the oscillatory pattern can be observed due to the resonating interaction of waves and the breakwater-plate system. Furthermore, the research shows that an ideal width and distance between the breakwater and floating plate can be calculated while assuming an appropriate configuration of the porous structure to create a breakwater-plate system with a reasonable efficiency that possesses both reflection and dissipation properties. The design of various types of coastal structures employed in the marine environment for the reflection and dissipation of wave energy at continental shelves dominated by stratified fluid, described here as a two-layer fluid, will significantly benefit from the findings of the current study.