On the scattering of water waves by a submerged slender barrier

P. K. Kundu
Department of Applied Mathematics, Vidyasagar University Midnapore-721102, INDIA
and
N. K. Saha
Department of Mathematics, Bhatter College, P.O.: Dantan, Distt. Midnapore (W.B.), INDIA

Abstract:

An approximate analysis, based on the standard perturbation technique, is described in this paper to find the corrections, up to first order to the reflection and transmission coefficients for the scattering of water waves by a submerged slender barrier, of finite length, in deep water. Analytical expressions for these corrections for a submerged nearly vertical plate as well as for a submerged vertically symmetric slender barrier of finite length are also deduced, as special cases, and identified with the known results. It is verified, analytically, that there is no first order correction to the transmitted wave at any frequency for a submerged nearly vertical plate. Computations for the reflection and transmission coefficients up to O $(\varepsilon)$, where $\varepsilon$ is a small dimensionless quantity, are also performed and presented in the form of both graphs and tables.