Effect of Inertial Surface on Surface Gravity Wave Propagation by Thick Rectangular Barrier

Abstract

In presence of an inertial surface, this paper develops new analytical solutions of two-dimensional water wave scattering problem of thick vertical barrier of rectangular cross section of uniform depth, considering the linear theory. Four types of barrier, surface-piercing or bottom standing or fully submerged in water or in the form of a thick vertical rectangular wall with submerged gap in water are examined. The problem is formulated in terms of integral equation by assuming symmetric and anti-symmetric parts of velocity potential. The analytical solutions make use of the multi-term Galerkin method which involves ultra-spherical Gegenbauer polynomials as its basis function. The reflection coefficients are obtained for different parametric values, which are depicted graphically against the wave number using very accurate numerical estimation. It is remarkable that the reflection coefficients depend significantly on the width of the barrier.