DIFFRACTION OF WATER-WAVES BY SLENDER BARRIERS

Linear water-wave theory is used to tackle the problem of diffraction of surface waves by a fixed slender barrier in deep water for two basi c situations: (i) when the barrier is partially immersed, and (ii) whe n the barrier is completely submerged. Analytical expressions for the first-order corrections to the reflection and transmission coefficient s are derived in terms of integrals involving the shape functions desc ribing the two sides of the slender barrier. A relatively straightforw ard perturbation technique is used along with the application of Green 's theorem in the fluid region. Corresponding analytical expressions r epresenting the reflection and transmission coefficients are also dedu ced, (i) for a nearly vertical barrier and (ii) for a vertically symme tric slender barrier, as special cases for both the problems. For a ne arly vertical barrier it is observed, analytically, that there is no f irst-order correction to the transmitted wave at any frequency. Comput ations for the reflection and transmission coefficients up to O(epsilo n), where epsilon is a Small nondimensional number, are also performed and presented here.