Linear water wave interaction with a composite porous structure in a two-layer fluid flowing over a step-like sea-bed

ABSTRACT The present work is concerned with the interaction of oblique surface gravity waves by a simple and composite porous block of finite width placed on a multi-step bottom in a two-layer fluid. The ocean depth is taken to be finite and its bed impermeable. The problem is studied by employing linearised water wave theory and eigenfunction expansion. The dispersion relations and their roots are analysed which give a clear understanding of the phenomenon. The cases of simple and composite interface-piercing structures are taken up separately to investigate the impact of porosity in wave attenuation for surface and interface modes. Waves propagate through the porous structure with distinct eigenvalues. The appropriateness of structures of various configurations on the scattering of surface waves is investigated by examining the reflection coefficients for waves in surface and interface modes as well as their effects on the free surface and interface elevations, the wave-loads on the structure and the rigid wall supporting the structure at one end. Further, as a special case, the sea-bed preceding the step bottom is considered to be porous and its effect on reflection is examined. The investigation establishes that for a suitable configuration of the porous structure, an optimum width can be ascertained to design a breakwater of reasonable efficiency possessing characteristics of both reflection and dissipation processes. The problems are solved analytically and the results are presented in graphical form. This kind of study is likely to have immense significance for designing of different types of coastal structures with respect to reflection and dissipation of wave energy at continental shelves which is influenced by a stratified fluid, which is modelled in this work as a two-layer fluid for convenience. Comparison of present results with available results show good agreement and this points towards the effectiveness of the model described in this work.