Scattering and radiation of water waves by permeable barriers

Abstract

The two-dimensional problems of scattering and radiation of small-amplitude water waves by thin vertical porous plates in finite water depth are considered using the linear water wave theory. Applying the method of eigenfunction expansion, these boundary value problems are converted to certain dual series relations. Solutions to these relations are then obtained by a suitable application of the least squares method. For the scattering problem, four different basic configurations of the barriers are investigated, namely, ͑I͒ a surface-piercing barrier, ͑II͒ a bottom-standing barrier, ͑III͒ a totally submerged barrier, and ͑IV͒ a barrier with a gap. The performance of these types of barriers as a breakwater are examined by studying the variation of their reflection and transmission coefficients, hydrodynamic forces and moments for different values of the porous effect parameter defined by Chwang ͓J. Fluid Mech. 132, 395-406 ͑1983͔͒, or the Chwang parameter. For the radiation problem, three types of wavemakers, which resemble types ͑I͒, ͑II͒, and ͑III͒ of the above-mentioned configuration, are analyzed. The dependence of the amplitude to stroke ratio on other parameters is also investigated to study the features of these wavemakers.

Waves Past Porous Structures in a Two-layer Fluid

“…The scattering and generation of waves by permeable barriers are well studied in the recent literature [12][13][14] under the assumptions of the linearised theory of water waves in a singlelayer fluid of finite depth. However, negligible progress has been made in the literature on the study of wave past porous structures in a two-layer fluid having a free surface and interface.…”

Reflection and transmission of regular waves at a surface-pitching slotted barrier

“…Isaacson et al [8] later extended their theory to the wave scattering by double slotted barriers. Lee and Chwang [9] and Sahoo et al [10] , using a method similar to Isaacson et al [1] , studied the reflection and transmission of regular waves by partially submerged permeable barriers.…”

Diffraction of surface water waves by an undulating bed topography in the presence of vertical barrier

“…Kanoria et al (1999) discussed the problem involving scattering of water waves by different kinds of thick vertical barriers. Sahoo et al (2000) and Lee and Chwang (2000) discussed the problem of water wave scattering by vertical permeable barriers with the help of eigenfunction expansion method. Yip et al (2002) discussed the trapping of surface waves by vertical porous and flexible barrier and observed that the deflection at the free end is smaller for the bottom touching barrier than for the surface-piercing barrier.…”