An investigation of the turbulent flow structure over a progressive water wave, as well as the structure of the wave-induced flow field in a transformed wave-following frame, is reported. Experimental results are given for a free-stream velocity of 2·4 m s−1 over a 1 Hz mechanically generated deep-water wave. The velocity components were measured with a cross hot-film probe oscillating in a transformed wave-following frame. The amplitude and phase of the wave-induced velocity components are deduced by correlation to the generated water wave. The mean flow tends to follow the wave form so that the water wave should not be regarded as surface roughness. The mean velocity profile is basically log-linear and is similar to that over a smooth plate, because ripples riding on the waves do not produce sufficient roughness to interfere with the wind field. The wave-induced motion in the free stream is irrotational; but, in the boundary layer, it has strong shear behaviour related to the wave-associated Reynolds stress. The shear stress production as well as the energy production from the mean flow is concentrated near the interface. A phase jump of 180° in the wave-induced turbulent Reynolds stresses in the middle of the boundary layer was observed. The relationships between the induced turbulent Reynolds stresses and the induced velocities are of an eddy-viscosity type.

This experimental study extends our earlier work (Hsu, Hsu & Street 1981) on U∞/c = 1.54 to U∞/c = 0.88, 1.10, 1.36 and 1.87, where U∞ is the mean-free-stream wind velocity and c is the celerity of the water wave. This was accomplished by changing the speed of the turbulent wind, while the water wave was maintained at a frequency of 1.0 Hz and wave slope of 0.1. The consistency between the results of the present and earlier experiments is established. The experimental results indicate that the mean velocity of the typical log-linear profile basically follows the waveform. However, the surface condition for the wind is regarded as supersmooth because the mean turbulent shear stress supported by the current is relatively lower than that supported by a smooth flat plate. The structure of the wave-induced velocity fields is found to be very sensitive to the height of the critical layer. When the critical height is high enough that most of the wave-induced flow in the turbulent boundary layer is below the critical layer, the structure of the wave-induced velocity field is strongly affected by the Stokes layer, which under the influence of the turbulence can have thickness comparable to the boundary-layer thickness. When the critical height is low enough that most of the wave-induced flow in the boundary layer is above the critical layer, the structure of the wave-induced velocity fields is then strongly affected by the critical layer. The structure of the critical layer is found to be nonlinear and turbulently diffusive. This implies that the inclusion of both the nonlinear and the turbulent terms in the wave-perturbed momentum equations is essential to success in the numerical modelling. The response of the turbulent Reynolds stresses to the wave is found to depend on the flow regimes near the interface or in the boundary layer. Near the interface, the wave-induced turbulent Reynolds stresses are found to be produced mainly from the stretching and changing in the direction of the turbulent velocity fluctuations due to the surface displacements. In the boundary layer, the eddy-viscosity-type relation between the wave-induced turbulent Reynolds stresses and the wave-induced velocities as found in Hsu et al. (1981) for U∞/c = 1.54 is also found to hold for the other U∞/c values of this study.

Measurements of the aerodynamic pressure distribution at the interface between air and simple progressive water waves are obtained with the use of a pressure sensor that follows the water surface. The theory of Miles (1957, 1959) and Benjamin (1959) on shear flows past a wavy boundary predicts a phase shift between the pressure distribution along the boundary and the boundary itself. An experimental verification of this theory is sought especially. A wind–wave facility 115 ft. long, 6 ft. high and 3 ft. wide was used. The facility is equipped with an oscil-lating-plate wave-generator which is capable of generating sinusoidal or arbitrary wave-forms, and a suction fan which can produce wind velocities up to 80 ft./sec when the water is at a nominal depth of 3 ft. The pressure sensor used for the measurements of pressure, was mounted on an oscillating device such that the sensor could be maintained at a fixed small distance (within 1/4 in.) above a propagating wavy surface at all times. The perturbation pressure over progressive waves is extracted from recorded data sensed by the moving sensor. The results compare favourably with the theoretical predictions of Miles (1959).

The primary objective of this work was to study the response of gravity water waves to wind excitation and, in particular, the applicability of the Miles inviscid shear-flow theory of gravity wave growth, by conducting experiments in a laboratory wind-wave channel under conditions approximating the assumptions of the mathematical model. Mechanically generated wave profiles subjected to wind action were measured with capacitance wire sensors and wave energy was calculated at seven stations spaced at 10ft. intervals along the channel test section. Waves varied in length from about 2·5 to 6·5 ft. and maximum wind speeds ranged from 12 to 44 ft./sec. Vertical mean air velocity profiles were taken at six stations in the channel, fitted near the air-water interface with semi-logarithmic profiles, and used in a stepwise computation of theoretical wave growth. The results show that the measured wave energy growth is exponential but considerably larger than the growth predictions of Miles's theory. Derived experimental values of the phase-shifted pressure component β are greater than theoretical values by a factor varying from 1 to 10, with a mean of about 3. Wind mean velocity profiles appear to be closely logarithmic near the air-water interface. Wind-generated ripples superposed on mechanically generated waves created a rough water surface with standard deviation larger, in all cases, than the respective critical-layer thickness.

The structure of the pressure and velocity fields in the air above mechanically generated water waves was investigated in order to evaluate their contribution to the transfer of momentum and energy from wind to water waves. The measurements were taken in a transformed Eulerian wave-following frame of reference, in a wind-wave research facility at Stanford University.The organized component of the fluctuating static pressure at the channel roof was found to contain contributions from both the sound field and the reflected water wave. The acoustic contributions were accounted for by appropriately correcting the pressure amplitude and phase (relative to the wave) and its contribution to the momentum and energy exchange. The wave-induced pressure coefficient at the fundamental mode shows in general an exponential decay behaviour with height, but the rate of decay is different from that predicted by potential-flow theory. The wave-induced pressure phase relative to the wave remains fairly constant throughout the boundary layer, except when the ratio of the wave speed to the freestream velocity, c/Uδ0 = 0.78 and 0.68. This phase difference was found to be about 130° during active wave generation, with the pressure lagging the wave. The momentum and energy transfer rates supported by the waves were found to be dominated by the wave-induced pressure, but the transfer of the corresponding total quantities to both waves and currents may or may not be so dominated, depending on the ratio c/Uδ0. The direct contribution of the wave-induced Reynolds stresses to the transfer processes is negligible.