Laboratory modeling of aerodynamic roughness of water surface under severe wind conditions

Wind-wave interaction at extreme wind speed is of special interest now in connection with the problem of explanation of the sea surface drag saturation at the wind speed exceeding 30 m/s. The saturation (and even reduction) of the coefficient of aerodynamic resistance of the sea surface at hurricane wind speed predicted theoretically by K.Emanuel was confirmed in both field and laboratory experiments. Now it is established that at hurricane wind speed the sea surface drag coefficient is significantly reduced in comparison with the parameterization obtained at moderate to strong wind conditions. Several possible theoretical mechanisms for explanation of the effect of the sea surface drag reduction were suggested, including explanations based on peculiarities of the air flow over breaking waves or exploiting the effect of sea drops and sprays on the wind-wave momentum exchange. However lack of experimental data prevents from specifying a definite mechanism. We supposed that the peculiarities of surface drag coefficient can be explained by dependence of the form drag of surface waves at strong wind conditions. To verify the supposition we measured simultaneously aerodynamic resistance of the water surface and frequency-wave number spectra of wind waves in wide range of wind speeds in the laboratory tank of the Institute of Applied Physics. The parameters of the facility are as follows: airflow 0 - 25 m/s (equivalent 10-m neutral wind speed U10 up to 60 m/s), dimensions 10m x 0.4m x 0.7 m. Aerodynamic resistance of the water surface was measured by the profile method at a distance of 7 m from the inlet. Wind velocity profiles were measured by the L-shaped Pitot tube with differential pressure transducer Baratron MKS 226A with accuracy of 0.5% of full scale range i.e. 3 cm/s. A method for data processing taking into account the self-similarity of the air-flow velocity profile in the aerodynamic tube was applied for retrieving wind friction velocity and surface drag coefficients. Similar to data by Donelan etal, 2004 surface drag coefficient showed tendency to saturation for wind speed exceeding 25 m/s. Simultaneously with the airflow velocity measurements, the wind wave field parameters in the flume was investigated by three wire gauges positioned in corners of an equal-side triangle with 2.5 cm side, data sampling rate was 100 Hz. Three dimensional frequency-wave-number spectra with the wavenumbers up to 1 cm-1 were retrieved from this data by the algorithm similar to the wavelet directional method based on window fast Fourier processing. One-dimensional short wave spectra (2-10cm-1 ) were measured by the optical method based on analyzing of the shape of air-water interface illuminated by the laser sheet and taken by the high-speed CCD-camera with the resolution 1280 on 1000 pixels (10 cm on 7.8 cm) and frame rate 500 frames per second. Analysis of the wind wave spectra showed tendency to saturation for mean square slope for wind speed exceeding Ucr =25 m/s simultaneously with the surface drag coefficient and linear dependence between surface drag coefficient and mean square slope. Video filming indicates onset of wave breaking with white-capping and spray generation at wind speeds approximately equal to Ucr. We compared the obtained experimental dependencies with the predictions of the quasi-linear model of the turbulent boundary layer over the waved water surface. Comparing shows that theoretical predictions give low estimates for the measured drag coefficient and wave fields. We took into account small scale (high frequency) part of the surface roughness (k <1 см-1). First, we add the model short wave spectra suggested by Elfouhaily et al, 1997 to measured long wave part. New theoretical results are in better agreement with experiment. The agreement was improved significantly, when we added high-wave-number part of the wind wave spectra measured by the laser system. Basing on the experimental data we can conclude that the drag saturation at severe wind conditions in the laboratory tank can be explained by saturation of the form drag of surface waves under these conditions. Tearing of the wave crests at severe wind conditions leads to the effective smoothing (decreasing wave slopes) of the water surface, which in turn reduces the aerodynamic roughness of the water surface. Quantitative agreement of the experimental data and theoretical estimations of the surface drag occurs if momentum flux associated with short wave part of the wind wave spectra is taken into account.