Wave propagation over sloping bottom and submerged breakwaters

An approximate method is presented for the prediction of wave propagation over impermeable submerged breakwaters as well as over sloping sea bottom. A monochromatic small amplitude 2-D gravity wave of frequency omega propagating on the surface of an irrotational and inviscid fluid is considered. Submerged breakwaters or sloping sea bottom is approximately represented by a stepwise geometry so that the fluid region over those areas are divided into rectangular subregions extending from the corresponding bottom to the surface of the fluid. In each region the potential solutions are expanded into series of eigen functions satisfying the Laplace equation and boundary conditions associated with the corresponding sea bottom and the free surface. These solutions are then matched on the common vertical boundaries of the neighbouring subregions such that the continuity of mass flux and pressure are secured throughout the fluid. In order to reach the limiting solution the above analysis is successively repeated by 'interval halving'. This procedure is terminated when the resultant numerical error is made smaller than a permissible value. Based on the present analysis some examples of sloping underwater geometry and submerged breakwaters are examined with regard to their wave transmission and reflection characteristics. (A)