Flexible-Membrane Wave Barrier. I: Analytic and Numerical Solutions

Abstract

The interaction of water waves with a tensioned, unstretchable, vertical flexible membrane extended to the seabed is solved in the context of two-dimensional linear wave theory. First, analytic solutions are obtained based on the eigenfunction expansion of the velocity potential in two fluid domains and a continuous tensioned-string dynamic model. In contrast to the rigid-body hydrodynamics, the velocity potentials and membrane equation of motions are obtained simultaneously, since the membrane boundary condition is not known in advance. Second, a boundary element program based on a discrete membrane dynamic model and simple source distribution method is developed. Two different numerical methods, the iteration and whole matrix methods, are developed and both agree well with analytic solutions. Using those computer programs, the performance of a flexible-membrane wave barrier with varying initial tension, length, and mass density is investigated. It is found that almost complete reflection of incident waves by a flexible-membrane wave barrier is possible despite appreciable fluctuating motions of the membrane in a vertically sinusoidal manner. It is also found that the efficiency is not sensitive to the density of the membrane but can be significantly affected by the magnitude of tension and boundary conditions.