Laboratory generation and propagation of ripples

The generation of gravity-capillary waves (ripples) by a flap-type wavemaker is examined theoretically and experimentally. Qualitative agreement is found in the trapped wave region; measured amplitudes exceed those predicted by the linear theory and the data extend further from the wavemaker. The air-water-aluminum contact line on the paddle face appears to cause a phase shift away from the paddle in the measured results. Excellent agreement is found with the linear dispersion relation for the progressive waves when the water is scrupulously cleaned of ions and organics, and filtered of minute particles. The presence of minute particles (only) necessitates introduction of the notion of ''dynamic'' surface tension which is about 30% lower than the measured static value. When particles are removed the dynamic and static values of surface tension are equivalent. The amplitudes of the progressive waves agree well with theory when the product of the wavenumber and water depth does not exceed seven, and the inviscid theory is modified to account for decay by viscosity. Agreement requires the assumption of a ''fully contaminated'' surface even when the water is particle filtered. Otherwise, the viscous decay is about twice that predicted by the fully contaminated surface model. Longitudinal instabilities of the progessive waves are observed when the product of wavenumber and water depth exceeds about seven. These instabilities appear to be modeled well by the nonlinear Schrödinger equation. Transverse instabilities are also observed in the data over the full range of wave frequencies investigated.