An experimental and numerical study of parasitic capillary waves

We report laboratory measurements of nonlinear parasitic capillary waves generated by longer waves in a channel. The experiments are conducted for three frequencies of longer waves (4, 5, and 6 Hz), corresponding to wavelengths of approximately 11, 7, and 5 cm. For these wavelengths we apply a model developed recently by Fedorov and Melville [J. Fluid Mech. 354, 1 (1998)] to predict the wave profile. Based on a viscous boundary layer approximation near the surface, the model enables us to efficiently calculate gravity-capillary waves. We present direct comparisons that show good agreement between the measurements and numerical predictions over a range of parameters. Finally, we give some simple estimates for a sharp cutoff in the wave number spectra observed in both the numerical solutions and the laboratory measurements of short gravity-capillary waves.