Water Wave Control by Submerged Pitching Porous Plate

Abstract

The feasibility of using a pitching porous plate to actively control water waves is investigated on the basis of the linearized wave theory. The two-dimensional (2D) problem is formulated to deal with a fully submerged porous plate, pitching about its middle point and scattering an incident monochromatic wave. The plate thickness is negligible in comparison with the water depth and the wavelength of the incident wave. The pitching amplitude is assumed to be small, while the frequency of pitching is kept the same as that of the incident wave. The porous flow through the plate is governed by Darcy's law. The method of matched eigenfunction expansions is used to analyze the reflected and transmitted waves as well as the wave force and moment on the porous plate. It is found that the heights of reflected and transmitted waves vary rapidly for small values of porous-effect parameter, which is a direct measure of the porosity effect to the incident wave. A small value of porous-effect parameter is found to be optimal to dissipate incident wave energy. Because porosity counters the efforts of pitching, the wave transformation due to pitching reduces rapidly as the porous-effect parameter increases. The performance of the plate has less sensitivity on its dimension and submerged depth when the porous-effect parameter is large.