Scattering of water waves by a submerged nearly vertical plate

TLDR: In this paper, the scattering of surface water waves by a nearly vertical plate, completely submerged in deep water, has been deduced employing two mathematical methods: integral equation formulation of the problem obtained by a suitable use of Green's integral theorem in the fluid region, while the second method concerns a simple and straightforward perturbational analysis along with the application of Green’s integral theorem.

Abstract: Some new results concerning the scattering of surface water waves by a nearly vertical plate, completely submerged in deep water, have been deduced employing two mathematical methods. The first method concerns an integral equation formulation of the problem obtained by a suitable use of Green’s integral theorem in the fluid region, while the second method concerns a simple and straightforward perturbational analysis along with the application of Green’s integral theorem. The two methods produce the same result for the first order corrections to the reflection and transmission coefficients. Considering some particular shapes of the curved plate, numerical calculations are also performed.