Modulation of short wind waves by long waves

A laboratory experiment is reported in which paddle-generated waves a few meters long and with initial slopes interact with centimetric wind-generated waves. The short waves are modified by the orbital velocity gradients of the long waves and by the modulation of the airflow over the long waves. Both of these effects produce a modulation of the short-wave energy density on the phase of the long waves. The Wavelet Directional Method is used to track the varying energy density of the short waves with long-wave phase. Two sets of trials are run at six wind speeds for five different long waves for a total of 60 trials. The sensitivity of the mean short-wave energy density to wind speed, long-wave slope, and long-wave period is explored in terms of a balance between wind input and dissipation source terms in the evolution of a spectrum of water waves. The magnitude and phase of the modulation of the short-wave energy reveals the relative effects of straining by orbital velocities and modulation of wind input. We show that these effects are very similar to those measured on the ocean.