Wave Trapping by Porous and Flexible Partial Barriers in a Two-Layer Fluid

摘要

The wave trapping in surface and internal modes by porous and flexiblernsurface-piercing and bottom-standing barriers near the end of a semiinfinitelyrnlong channel is analyzed in a two-layer fluid of finite depthrnhaving a free surface and an interface. The problem is analyzed in tworndimensions in the linearized theory of water waves with the assumptionrnof small amplitude barrier response. The surface-piercing barrier isrnclamped above the free surface and is free at the other end, which isrnsubmerged in the fluid. On the other hand, the bottom-standing barrierrnis fixed at the seabed and the other end is having a free edge. Thernassociated mixed boundary value problem is reduced to a linear systemrnof equations by utilizing a more general orthogonal relation along withrnthe use of least squares approximation method. The reflectionrncoefficients are obtained and discussed in surface and internal modesrnfor different values of the non-dimensional fluid density ratio, thernporous-effect parameter, the normalized distance between the barrierrnand the channel end-wall, the length of submergence and the flexuralrnrigidity of the barriers for both surface-piercing and bottom-standingrncases.