Oblique wave diffraction by a bottom-standing thick barrier and a pair of partially immersed barriers

On the basis of linearised theory of water waves, the present study has demonstrated a semi-analytical method to assess the hydrodynamic performance of a pair of partially immersed barriers just above a thick bottom-standing barrier. By means of eigenfunction expansion method, a system of first kind Fredholm-type integral equation involving horizontal component of velocity as unknown functions is developed for interaction of water waves with both types of barriers. The multi-term Galerkin approximation is adopted to determine these unknown functions having square root singularities at the submerged edge of the thin barriers and one-third singularities at the corners of the thick barrier. In order to overcome such types of singularities, Chebychev polynomials for half-singularities and ultra-spherical Gegenbauer polynomials for one-third singularities with suitable weight functions have been taken into consideration. The numerical examples of both reflection and transmission coefficients are presented to examine the hydrodynamic performance of breakwater. Some fascinating results like resonant frequencies are obtained for practical engineering. At the same time, reflection coefficients for the present breakwater agree reasonable for the limiting cases with previous available result.