Gravity wave interaction with porous structures in two-layer fluid

Abstract

Oblique wave interaction with rectangular porous structures of various configurations in two-layer fluid are analyzed in finite water depth. Wave characteristics within the porous structure are analyzed based on plane wave approximation. Oblique wave scattering by a porous structure of finite width and wave trapping by a porous structure near a wall are studied under small amplitude wave theory. The effectiveness of three types of porous structures—a semi-infinite porous structure, a finite porous structure backed by a rigid wall, and a porous structure with perforated front and rigid back walls—in reflecting and dissipating wave energy are analyzed. The reflection and transmission coefficients for waves in surface and internal modes and the hydrodynamic forces on porous structures of the aforementioned configurations are computed for various physical parameters in two-layer fluid. The eigenfunction expansion method is used to deal with waves past the porous structure in two-layer fluid assuming the associated eigenvalues are distinct. An alternate procedure based on the Green’s function technique is highlighted to deal with cases where the roots of the dispersion relation in the porous medium coalesce. Long wave equations are derived and the dispersion relation is compared with that derived based on small amplitude wave theory. The present study will be of significant importance in the design of various types of coastal structures used in the marine environment for the reflection and dissipation of wave energy.