Oblique scattering of gravity waves by moored floating membrane with changes in bottom topography

The interaction of oblique incident wave with a moored floating membrane as a breakwater is analyzed for both the cases of finite water depth and shallow water approximation based on the linearized water wave theory, including the effect of changes in bottom topography. In the case of finite water depth the eigenfunction expansion method and orthogonal mode-coupling relation is used whereas the continuity of pressure and mass flux is used in the case of shallow water approximation. The energy relation for the oblique gravity wave in the presence of floating membrane due to abrupt change in bottom topography for various cases are derived using the law of conservation of energy flux and alternately by the direct application of Green's second identity. The wide-spacing approximation is also used using the result of single step, to analyze the wave transformation due to change in bottom topography. Numerical results for the reflection coefficient and the vertical deflection are obtained to understand the effect of spring mooring stiffness and change in bottom topography on the wave interaction with floating membrane. (C) 2012 Elsevier Ltd. All rights reserved.