EIGENFUNCTION ANALYSIS OF WATER-WAVE PROPAGATION DOWN A WAVE FLUME

An eigenfunction expansion method is used to analyze the generation an d propagation of linear water waves down a wave flume consisting of a wavemaker, an abrupt expansion, (possibly) a finite width vertical por ous 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 orde r to satisfy the lateral boundary conditions along the flume walls, a transversal variation of the velocity potential is included allowing t he propagation of an obliquely incident wave train, scattered modes at the same frequency, and additional evanescent modes in the transversa l direction. Thus, the wave solutions are expanded in eigenseries in t wo orthogonal directions, one over the depth, and the other across the channel cross-section. Laboratory experiments were conducted to verif y the reflection and transmission process at the channel junction and at a porous structure. The oscillating behavior of reflection and tran smission coefficients with kb2 indicates occurrence of resonance, whic h is subsequently analyzed.