Experimental evidence of the rapid distortion of turbulence in the air flow over water waves

Detailed observations of the air flow velocity, pressure and Reynolds stresses above water waves in a wave flume are presented. The static pressure fluctuations induced by the waves are observed following a new procedure that eliminates acoustical contamination by the wave maker. The measurements are analysed by comparing them with numerical simulations of the air flow over waves. In these numerical simulations the sensitivity to the choice of turbulence closure is studied. We considered both first-order turbulence closure schemes based on the eddy viscosity concept, and a second-order Reynolds stress model. The comparison shows that turbulence closure schemes based on the eddy viscosity concept overestimate the modulation of the Reynolds stress in a significant part of the vertical domain. When an eddy viscosity closure is used, the overestimated modulation of the Reynolds stress gives a significant contribution to the wave growth rate. Our results confirm the conclusions Belcher & Hunt reached on the basis of the rapid distortion theory. The ratio of the wind speed to the phase speed of the paddle wave in the experiment varies between 3 and 6. The observed amplitudes of the velocity and pressure perturbation are in excellent agreement with the simulations. Comparison of the observed phases of the pressure and velocity perturbations shows that the numerical model underpredicts the downwind phase shift of the undulating flow. The sheltering coefficients for the flow over hills and the growth rates of waves that are slow compared to the wind calculated with the Reynolds stress model are in excellent agreement with the analytical model of Belcher & Hunt. Extending the calculations to fast waves, we find that the energy flux to waves travelling almost as fast as the wind is increased on going from the mixing length turbulence closure to the Reynolds stress model.