Scattering of oblique water waves by two thin unequal barriers with non-uniform permeability

Bragg Resonance of Water Waves by Multiple Permeable Thin Barriers over Periodic Breakwaters

“…To make the solution uniquely solvable, the following far-field conditions must be satisfied: η = a e i k1.0 x + K R e iθ R e −i k1.0 x e ik y y as x → −∞ (11) and η = aK T e iθ T e i kM.0 x e ik y y as x → ∞,…”

“…Following Gupta and Gayen [11], the proposed EMM was utilized to estimate the scattering of water waves by dual permeable barriers over a uniform bottom where h 1 = h 2 = h 3 = 1.0 m. First, for the case of dual surface-piercing barriers, the permeable parameter was equal to 0.5 and the barrier lengths were set to a 1 /h 1 = 0.4 and a 2 /h 1 = 0.5 located at v 1 /h 1 = 0 and v 2 /h 1 = 0.4, respectively. For the case of dual bottom-standing barriers, the permeability parameter was set to 1.0, and the barrier lengths were b 1 /h 1 = 0.7 and b 2 /h 1 = 0.6 located at w 1 /h 1 = 0 and w 2 /h 1 = 0.4, respectively.…”

“…Following Gupta and Gayen [11], the proposed EMM was utilized to estimate the scattering of water waves by dual permeable barriers over a uniform bottom where Sequentially, the effect of the evanescent mode number N was additionally examined. Figure 7a Sequentially, the effect of the evanescent mode number N was additionally examined.…”

“…Das et al [7] studied the impact of multiple impermeable thin barriers on the scattering of water waves. To further dissipate wave energy, the issues of permeable structures that are thin barriers have been studied [8][9][10][11]. By solving integral equations, Macaskill [12] considered waves scattered by a single permeable barrier at a finite water depth.…”

Water Wave Scattering by a Thin Vertical Submerged Permeable Plate

“…The objective of the present article is to develop an alternative method to encounter the problem of scattering of water waves by a permeable plate submerged in deep water by reducing it to a hypersingular integral equation using Havelock's theorems and to introduce a new approximate method of evaluating the integral equation numerically. Several researchers [8,9,10,13,23,28] used Havlock's expansion and inversion theorems as an essential tool to solve the boundary value problems associated with the scattering problems involv-ing thin barriers by reducing them into integral equations. The structure of this paper is given as follows.…”