## 4 Results and Discussion
### General Characteristics of Velocity Profiles  
Figure 10 compares the \(U\) velocity profile of the smooth wall case with the riblet wall case obtained by hot-wire anemometry. The plotted data correspond to the temperature-corrected \(U\) velocity for an average duration of 15 s (\(N\) = 300,000 points) at each height point. The \(U\) velocity and the height were scaled to the nondimensional values \(u^{+}\) and \(z^{+}\), respectively, to emphasize the difference of the profile in the logarithmic region, where \(z^{+}\) appears to be in the order of 100. Nondimensional \(U\) velocity (\(u^{+}\)) and height (\(z^{+}\)) are expressed by Equation (34) and Equation (35), respectively. The friction velocity (\(u_{\tau}\)) expressed by Equation (5) was calculated using Equation (18) for the smooth wall case and Equation (23) for the riblet wall case, respectively. The reference height position for the smooth wall was \(z\) = 0 mm and that for the riblet wall was \(z\) = 50 \(\mu\)m as aforementioned. \(u^{+}\) was normalized by the maximum value for each wall surface to put an emphasis on comparing the \(U\) velocity in the logarithmic region:  
\[u^{+}=\frac{U}{u_{\tau}}, \tag{34}\]  
\[z^{+}=\frac{z\cdot u_{\tau}}{v}. \tag{35}\]  
In Figure 10, the error bar range is the uncertainty \(q_{123}\) described previously. Above \(z^{+}\) = 500 (which corresponds to \(z\) = 4.5 mm), the difference between those two cases is negligibly small. On the other hand, in the region near the wall below \(z^{+}\) = 500, the riblet case shows a higher velocity than that of the smooth wall case. This observation is consistent with those obtained by previous studies [8,19]. Figure 11 presents histograms for the fluctuating component of the \(U\) velocity (\(u^{\prime}\)) obtained by Reynolds decomposition (Equation (8)) at \(z\) = 2 mm (\(z/\delta_{smooth}\) = 0.196: Representing the boundary layer flowfield above the riblet peak) and at \(z\) = 20 mm (\(z/\delta_{smooth}\) = 19.6: Representing the freestream region) for the smooth wall. Because the boundary layer height was approximately 10 mm in this study and the effect of riblets on reducing skin friction drag should notably appear around the height of 20% to 30% of the boundary layer thickness from the wall [8], the study focused on the height of \(z\) = 2 mm. It should be noted here that the flow conditions were not identical to those of the former study [8]. The histogram for \(z\) = 20 mm shows a sharp distribution around its mean value and the variance is small. However, for \(z\) = 2 mm, the histogram shows a Gaussian distribution, indicating that the velocity variance can be treated as random data, which indicates isotropically homogeneous turbulence according to turbulence theory. Table 3 summarizes the statistical properties for the smooth wall and riblet cases with regard to the \(U\) velocity. The Kurtosis for \(z\) = 2 mm is approximately 3, which means that the distribution is Gaussian; the skewness for \(z\) = 2 mm also shows that the distribution is closer to being Gaussian. The turbulence intensity at \(z\) = 2 mm for the riblet surface shows an 8.3% reduction compared to the smooth surface. This observation is consistent with those found in previous studies [2,8,19].