An alternative analytical solution for water-wave motion over a submerged horizontal porous plate

Abstract

This study gives an alternative analytical solution for water-wave motion over an offshore submerged horizontal porous-plate breakwater in the context of linear potential theory. The matched-eigenfunction-expansions method is used to obtain the solution. The solution consists of a symmetric part and an antisymmetric part. The symmetric part is also the solution of wave reflection by a vertical solid wall with a submerged horizontal porous plate attached to it. In comparison with previous analytical solutions with respect to finite submerged horizontal porous plates, no complex water-wave dispersion relations are included in the present solution. Thus, the present solution is easier for numerical implementation. Numerical examples show that the convergence of the present solution is satisfactory. The results of the present solution also agree well with previous results by different analytical approaches, as well as previous numerical results by different boundary-element methods. The present solution can be easily extended to the case of multi-layer submerged horizontal porous plates, which may be more significant in practice for meeting different tide levels.

Water-wave scattering and energy dissipation by a floating porous elastic plate in three dimensions

“…They solved the semi-infinite problem analytically by the Wiener-Hopf and residue calculus techniques, using the Cauchy integral method to avoid requiring knowledge of eigenfunctions in the plate region, and the finite-length problem using a quickly convergent numerical method. Liu and Li (2011) and Liu et al (2012) solved the two-dimensional problem using an eigenfunction-matching method, but with non-standard eigenfunctions in the plate region, thereby avoiding complicated dispersion relations at the cost of increasing the number of unknowns in the numerical solution process considerably. and reported on comparisons with experiments conducted in a wave flume with one and two submerged porous plates, respectively.…”

Propagation of Gravity Waves Past Multiple Bottom-Standing Barriers

“…Lo [21,22] ana lyzed the performance of a vertical flexible membrane wave bar rier of a finite extent using the eigenfunction expansion method. Liu and Li [24] examined the hydrodynamic performance o f a wave absorbing double curtain-wall partial breakwater that consists of a seaward perforated wall and a shoreward impermeable wall. They performed both theoretical and experimental studies for the multi ple barriers and it is observed that increasing the tension o f the membrane, the wave transmission decreases.…”

Interaction between obliquely incident waves and an infinite array of multi-chamber perforated caissons

“…8 denotes that the horizontal mass fluxes must be continuous at the perforated wall, and the second equal sign denotes that the normal fluid velocity passing the perforated wall is linearly proportional to the pressure difference between the two sides of the wall [32]. It should be mentioned that the linear porous boundary conditions have also been used for curve porous wall, horizontal porous plate, flexible porous plate and so on [34,[36][37][38]. Moreover, a different quadratic relationship between the pressure difference and the normal fluid velocity across the porous plate has been used by Molin [39].…”