A second-order solution of waves passing porous structures

Abstract

Only linear theoretical analyses of wave interaction with porous structures exist, mainly due to both the complexities of flows inside the porous medium, and the mathematical inhomogeneous boundary-value problem. Since the hydrodynamic flow mechanism is non-linear, a non-linear analysis can better describe the characteristic nature of the problem. In this paper, a generalized potential theory is used to describe both the internal and external water flows. An implicit non-linear model is used to describe flow mechanism inside the porous medium. The perturbation method is used to solve the problem analytically up to the second order. The second-order solution is decomposed into time-dependent and time-independent parts. And, correspondingly, the inhomogeneous boundary-value problems are solved analytically. In the analysis, the second-order characteristics of the problem, including the dispersion equation, wave numbers and friction coefficient, as well as wave reflection and transmission, are investigated in detail. It is shown that the mode swapping of the second-order wave numbers only occurs among the evanescent modes. The second-order friction effects become important in shallow-water cases. The comparison of the results of present theory with experimental results shows that the second-order solution is good correction to the linear theory.