Water Wave Propagation in the Presence of a U-Shaped Barrier

Abstract

In this paper, wave scattering by a U-shaped barrier and an inverse U-shaped barrier, both fixed in position and fully submerged in deep water, is illustrated. The Fredholm-type integral equations of the first kind are derived using the Havelock expansion of wave potentials and employing a matching technique. The wave reflection and transmission coefficients are derived in closed-form expressions. The integral equations are solved approximately using the Galerkin method with simple polynomials multiplied by exponential decay functions and appropriate weight functions as the basis functions. The computational results are validated against known results for a simple barrier configuration. The ways of affecting the barrier width and the submerged depth from the free surface on wave reflection, wave transmission, wave forces, and overturning moments are analyzed. The findings reveal that both barriers are highly wave-reflective over a wide range of incident wavelengths. The findings show reductions in the wave forces and the overturning moments with increases in the width and submerged depth of the barriers. These results are expected to be useful to engineers in the design of breakwaters in deeper depths.