Propagation of Water Waves in the Presence of Thin Vertical Barrier on the Bottom Undulation

The problem involving diffraction of water waves by submerged thin vertical barrier over irregular bottom is examined using linearized theory of water waves. While formulating the problem mathematically, a mixed boundary value problem (BVP) occurs. The problem is solved using perturbation theory along with least-squares method and Green’s integral theorem. The first order reflection and transmission coefficients are obtained in terms of integrals involving the shape function \(c(x)\) representing the bottom undulation and the solution of the scattering problem by the submerged barrier. A special case of bottom undulation is considered to evaluate the first order reflection and transmission coefficients in detail. The numerical results of these coefficients are shown graphically.