AN EXPERIMENTAL AND NUMERICAL STUDY OF PARASITIC CAPILLARY WAVES

We report laboratory measurements of nonlinear parasitic capillary wav es generated by longer waves in a channel. The experiments are conduct ed for three frequencies of longer waves (4, 5, and 6 Hz), correspondi ng to wavelengths of approximately 11, 7, and 5 cm. For these waveleng ths we apply a model developed recently by Fedorov and Melville [J. Fl uid Mech. 354, 1 (1998)] to predict the wave profile. Based on a visco us boundary layer approximation near the surface, the model enables us to efficiently calculate gravity-capillary waves. We present direct c omparisons that show good agreement between the measurements and numer ical predictions over a range of parameters. Finally, we give some sim ple estimates for a sharp cutoff in the wave number spectra observed i n both the numerical solutions and the laboratory measurements of shea gravity-capillary waves. (C) 1998 American Institute of Physics.