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.
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