Waves Past Porous Structures in a Two-layer Fluid

Abstract

Havelock's type of expansion theorems, for an integrable function having a single discontinuity point in the domain where it is defined, are utilized to derive analytical solutions for the radiation or scattering of oblique water waves by a fully extended porous barrier in both the cases of finite and infinite depths of water in two-layer fluid with constant densities. Also, complete analytical solutions are obtained for the boundary-value problems dealing with the generation or scattering of axi-symmetric water waves by a system of permeable and impermeable co-axial cylinders. Various results concerning the generation and reflection of the axisymmetric surface or interfacial waves are derived in terms of Bessel functions. The resonance conditions within the trapped region are obtained in various cases. Further, expansions for multipole-line-source oblique-wave potentials are derived for both the cases of finite and infinite depth depending on the existence of the source point in a two-layered fluid.

Wave scattering by flexible porous vertical membrane barrier in a two-layer fluid

“…Furthermore, the wave reflection in SM is found to be significantly smaller than the wave reflection in IM, which suggests that a membrane barrier is more effective in IM wave motion than in SM wave motion. Similar observations are reported by Manam and Sahoo (2005).…”

“…Sherief et al (2003) analysed the effect of gravity waves generated by a porous wave maker in a two-layer fluid with the upper fluid having a free surface. Recently, Manam and Sahoo (2005) tackled analytically the same problem of waves past rigid porous structures in two-layer fluid by making use of the generalized orthogonal relation. Also they obtained complete analytical solutions for the boundary value problems corresponding to the generation or scattering of axisymmetric waves by two impermeable and permeable coaxial cylinders.…”

Oblique wave trapping by porous and flexible structures in a two-layer fluid

“…Sherief et al 21 analyzed the effect of gravity waves generated by a porous wavemaker in two-layer fluid with the upper fluid having a free surface. Manam and Sahoo 22 studied the problem of wave past porous structures in a two-layer fluid. Kumar et al 23 analyzed the wave scattering by porous membrane extended from the free surface till the bottom in a two-layer fluid in two dimensions.…”

On capillary gravity-wave motion in two-layer fluids

“…On the other hand, in the case of gravity-wave propagation in a two layer fluid having a free surface and an interface, two progressive waves exist which are generated at the free surface and the interface. For example; (i) Barthelemy et al [15] analyzed the scattering of surface waves by a step bottom in a two-layer WKBJ technique and (ii) Manam et al [16] developed the expansion formulae for a two-layer fluid and analyzed the wave scattering by a porous barrier for both surface and interfacial modes in a two-layer fluid. Unlike the case of surface waves which exist in open water surface, internal waves occur when there is a sharp density change between two layers of different fluids.…”