Bispectral analysis of gravity capillary waves

Abstract

We perform a laboratory study of the nonlinear phase relation between short gravity waves with wavelengths of the order of 10 cm and their higher harmonics including “spurious” capillary ripple. The presence of higher harmonics of the basic low-frequency component in the spectrum of gravity capillary waves (GCWs) is confirmed on the basis of the methods of bispectral analysis. To determine the quantitative relations between the contributions of free and forced components in the GCW spectrum, we use the normalized bicoherence function. We show that it is correctly defined for both broadband random processes and polyharmonic random signals. The quantitative relation between the contributions from free and forced waves in the GCW spectrum at the frequency of the second harmonic is obtained.