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, ~I! a surface-piercing barrier, ~II! a bottom-standing barrier, ~III! a totally submerged barrier, and ~IV! 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 ~1983!#, or the Chwang parameter. For the radiation problem, three types of wavemakers, which resemble types ~I!, ~II!, and ~III! 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. © 2000 American Institute of Physics.