Scattering and trapping of water waves by a composite breakwater placed on an elevated bottom in a two-layer fluid flowing over a porous sea-bed

Abstract

The present work is concerned with the scattering and trapping of oblique surface waves due to a vertical composite type porous breakwater placed on an elevated rigid block in a two-layer fluid. The ocean depth is taken to be finite and the sea-bed to be porous. The problem is studied by employing linearized water wave theory and eigenfunction expansion. The objective is to investigate the impact of various porous parameters in wave attenuation for surface and interface modes. Water waves propagate through the porous structure with distinct eigenvalues. Further, a perforated front wall on the structure is also considered to study its effect in wave trapping. In the scattering model, reflection and transmission coefficients are investigated for two propagating modes along with the waveloads on the breakwater in order to ascertain the appropriateness of the structures of various configurations. Similarly, appraisals of the reflection coefficients, their effects on the free surface and interface elevations and the waveload on the structure as well as on the wall are analyzed to review the impact of various structure characteristics in the trapping model. In choosing the present model, it is ensured that the model conforms to realistic physical scenario so that it is useful for applications. Also, in carrying out numerical experiments, the selection of values of parameters is done in such a way that they are physically meaningful. Before proceeding with the investigation, validation of the present model is carried out by comparing a present result with one available in the literature. It points to a very good agreement which establishes the efficiency of the present model and the associated study which paves the way for completing the present study. The investigation establishes that, for a suitable configuration of the porous structure, an optimum width can be worked out to design a breakwater of reasonable efficiency possessing the characteristics of both reflection and dissipation. 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 modeled in this work as a two-layer fluid for convenience.