Eigenfunction analysis of water wave propagation down a wave flume

Abstract

An eigenfunction expansion method is used to analyze the generation and propagation of linear water waves down a wave flume consisting of a wavemaker, an abrupt expansion, (possibly) a finite width vertical porous breakwater spanning the channel, and a fully absorbing ending wall.

Progressive wave modes, as well as vertical evanescent modes (which exist near the wave-maker, the expansion section, and the upstream and downwave faces of the porous wall), are considered. Moreover, in order to satisfy the lateral boundary conditions along the flume walls, a transversal variation of the velocity potential is included allowing the propagation of an obliquely incident wave train, scattered modes at the same frequency, and additional evanescent modes in the transversal direction. Thus, the wave solutions are expanded in eigenseries in two orthogonal directions, one over the depth, and the other across the channel cross-section.

Laboratory experiments were conducted to verify the reflection and transmission process at the channel junction and at a porous structure.

The oscillating behavior of reflection and transmission coefficients with kb2 indicates occurrence of resonance, which is subsequently analyzed.