EFFECTS OF CHANNEL CROSS-SECTIONAL GEOMETRY ON LONG-WAVE GENERATION AND PROPAGATION

Joint theoretical and experimental studies are carried out to investig ate the effects of channel cross-sectional geometry on long wave gener ation and propagation in uniform shallow water channels. The existing channel Boussinesq and channel KdV equations are extended in the prese nt study to include the effects of channel sidewall slope at the water line in the first-order section-mean equations. Our theoretical result s show that both the channel cross-sectional geometry below the unpert urbed water surface (characterized by a shape factor kappa) and the ch annel sidewall all slope at the waterline (represented by a slope fact or gamma) affect the wavelength (lambda) and time period (T-s) of wave s generated under resonant external forcing. A quantitative relationsh ip between lambda, T-s, kappa, and gamma is given by our theory which predicts that, under the condition of equal mean water depth and equal mean wave amplitude, lambda and T-s increase with increasing kappa an d gamma. To verify the theoretical results, experiments are conducted in two channels of different geometries, namely a rectangular channel with kappa equivalent to 1, gamma = 0 and a trapezoidal channel with k appa = 1.27, gamma = 0.16, to measure the wavelength of free traveling solitary waves and the time period of wave generation by a towed vert ical hydrofoil moving with critical speed. The experimental results ar e found to be in broad agreement with the theoretical predictions. (C) 1997 American Institute of Physics.