Nonlinear analysis of wave interaction with permeable structures

Abstract

The nonlinear effect of wave interaction with permeable structures is studied analytically. Based on the theory by Sollitt and Cross (1972), by assuming incompressible fluid and irrotational flow and reserving the convection term of the equation of motion, the Bernoulli equation applicable to permeable structures and pure water is derived. Using the perturbation method, the nonlinear boundary value problem (BVP) of wave interaction with permeable structures is solved up to the second order. The eigenvalues of the second-order BVP are calculated which have two kinds. The dispersion relation of the time-dependent BVP have the same form as the first-order problem, whereas the one of the time-independent BVP is not function of time and the eigenvalues have no effect on the characteristics of progressing waves. Two types of linear friction factor are calculated considering flow velocities by physical meaning and by perturbation viewpoint. The second-order solutions calculated from present theory are compared with the linear theory and experimental results. It shows that the nonlinear theory can describe better the phenomenon of wave interaction with permeable structures.