Waves in narrow channels: faster capillary waves

Abstract

DURING experiments on the propagation of water waves in channels with parallel sides made of Perspex, it was found that the phase velocities of small-amplitude waves with wavelengths in the range 40–100 mm were consistently higher than predicted by the standard hydrodynamic theory1,2. The original observations of this anomaly were made in a channel 100 mm wide filled to a depth of 50 mm. For these none too small dimensions, the standard theory might be expected to provide a close approximation to the wave velocity, but velocities ∼0.5% too high were observed. Highly surface-clean water and clean apparatus was used in all the experiments, and with these precautions the measurements proved to be wholly reproducible, prompting a closer examination, which is described here, of the wave motion to detect the cause of the anomaly. It was seen that the lines of contact between the water surface and the sides of the channel did not in fact rise and fall in step with the movement of the surface at the centre of the channel, instead remaining fixed in their original locations with the water at rest.