D xuax ln H10S

Wind velocity profiles were measured for 12 values of the centerline velocity from 6 m/ s to 24 m/s with the resolution 0.3-0.5 cm. Each point at the velocity profile was determined by averaging over 30 sec. CD and U10 were calculated by equations (15) and (11) respectively. The obtained dependency of the surface drag coefficient on 10-m wind speed is presented in fig. 4a together with the data taken from the paper by Donelan et al, 2004. The data obtained at two different facilities are rather close to each other both at the low and high wind speeds; the difference in CD is less than 10%. The tendency to saturation of the surface drag coefficient is clearly visible for both data sets, although the thresholds of wind speeds for the saturation are slightly different (33 m/s for the data by Donelan et al, 2004 and 24.5 m/s for our data set). Possibly it is due to differences in the details of data processing. The values of CD obtained in laboratory by (Donelan et al., 2004) slightly exceed the data obtained in field conditions (see fig.4b). Besides, decreasing of CD for 10-m wind speed exceeding 35 m/s reported in (Powel et al., 2003) was not observed by (Donelan et al., 2004). Our laboratory data set is in better agreement with the field data, although, extremely large wind speeds, when CD is decreasing, were not achieved in our facility. Possibly, the differences between field and lab data are due to two main reasons. First, although similarity between lab and sea conditions1 can be expected at strong winds, because in both cases the wave phase velocities is much less than the wind speed and then the peculiarities of the air flow over the waves are similar, the fetches in the laboratory facilities are much lower than in the field conditions. Then the waves in the lab are shorter and steeper than in the sea and enhanced aerodynamic resistance of the water surface can be expected. Second

1 The question about similarity between labortory modeling of air-sea interaction and field conditions is not obvious. We will briefly discuss it in section 5.5.

reason was suggested by (Donelan et al., 2004). In laboratory facility we investigate wind-wave interaction in stationary conditions of spatially developing turbulent boundary layer. In the field conditions, the wind in hurricane eye walls is strongly unsteady and inhomogeneous flow.

0.003

20 30

0.003

Fig. 4. Surface drag coefficient. (a) - laboratory data, black open symbols (squares, circles, diamonds, asterics) are taken from Donelan et al, 2004, closed circles - measurements at TSWiWaT, (b) - compilation of the field and laboratory data.

4.3 Wave field at strong winds in laboratory conditions

Aerodynamic roughness of the sea surface is conditioned to waves at the water surface including strong wind conditions. According to (Powel, 2007) surface drag depends significantly on the part of the tropical cyclone, where it is measured. The sea surface drag is strongly enhanced in the left front part of the tropical cyclone in comparison with right and rare parts. The data are not sufficient for final conclusions, but it seems, that the aerodynamic drag depends on the wave field, which is significantly different in different sectors of the tropical cyclone.

The wind wave field parameters in the flume was investigated by three wire gauges positioned in corners of an equal-side triangle with 2 cm side, data sampling rate was 100 Hz Three dimensional frequency-wave-number spectra were retrieved from this data by the wavelet directional method (M.Donelan et al., 1996). The wave fields at different wind speeds are characterized by narrow wave-number spectra (fig. 5a) with the peak wave-number decreasing with the wind speed. It is clearly visible from fig.5a that the shapes of the spectra tend to saturation from the 10-m wind speed Uw exceeding 24.5 m/s. The similar tendency occurs in the dependence of the integral parameters of the wave field on the wind speed. For example, fig.5b clearly shows, that the average slope of the peak wave S=Hs kp/4 (where Hs is the significant wave height, kp is peak wave number) saturates when Uio>25m/s (see fig.5b). It means that at the wind speed about 24.5 m/s changing of the regime of the wave field occurs. Comparing the dependencies of the dominant wave slope on the wind speed with the drag coefficient dependency also shown in fig. 5b shows that the wave field regime changing correlate with saturation of the surface drag dependence of the wind speed.

The photos of top views of the water surface elucidate a possible origin of the changing of the regime of the waves wave field at 10-m wind speeds exceeding 24.5 m/ s. Starting from this threshold wave breaking is intensified, because the crests of the waves are blown away by the strong tangential wind stress. It is accompanied with sprays, drops and bubbles near the wave crests, visible at the photos. Blowing away the crests of waves which steepness exceeds a definite threshold lead to the effective smoothening of the waves and the slope of the dominant wave then does not depend on wind speed as it shows fig. 6c. Basing on the theoretical model of wind turbulent boundary layer over wavy water surface, we investigated, whether this wind smoothening of the surface is sufficient for explanation the surface drag reduction.

5. Theoretical model of aerodynamic resistance of the wavy water surface at extreme wind conditions

The first step in the theoretical interpretation of the effect of the sea surface drag reduction at strong winds is calculation of the surface form grad. This part of the total aerodynamic resistance describes influence of the roughness of the surface. We can expect, that smoothening of the water surface by very strong wind significantly reduces the form drag and possibly can explain the experimental results. Then the effect of sprays and drops will be estimated.

15.4

Slope

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