## 4 Results and Discussion
### General Characteristics of Velocity Profiles
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Uncertainty Source** & **Symbol** & **Value, \%** & **Note** \\ \hline Temperature correction & \(q_{1}\) & 0.26 & \begin{tabular}{c} Obtained from the difference between the temperature corrected hot-wire data and the pitot \\ probe data for \(z\) = 1.0–4.0 mm \\ \end{tabular} \\ \hline Hot-wire anemometry & \(q_{2}\) & 0.035 + 0.05 & \begin{tabular}{c} Variance from five measurement points in the \\ freestream region (\(z\) = 12–20 mm) \\ \end{tabular} \\ \hline Systematic error & \(q_{3}\) & 0.56 & \
\begin{tabular}{c} Equations. (28) through (30) accounting for the \\ directional sensitivity of the velocity measurement \\ \end{tabular} \\ \hline Derivation of integral & \(q_{4}\) & 1.72 &
\begin{tabular}{c} \(q_{4}\) = 0.1\(\Delta t/(t_{0.}\) freestream in smooth wall) = \\ 0.005 ms/0.291 ms \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of possible uncertainty sources. In addition to those statistics, other boundary layer characteristics are summarized in Table 4. The boundary layer thickness for the smooth wall and riblet wall cases are \(\delta_{smooth}\) = 10.2 mm and \(\delta_{riblet}\) = 10.2 mm, respectively. As seen in Table 4, the local boundary layer thicknesses (\(\delta^{*}\) and \(\theta\)) and the local Reynolds number (\(Re_{\theta}\)) for the riblet case were reduced. If the reduction of total skin friction where the local skin friction coefficient (\(c_{f}\)) in Equation (13) is replaced with the total skin friction coefficient (\(C_{F}\)) expressed by Equation (22) is considered, the reduction of the total skin friction value becomes 3.1%. Therefore, the reduction of those boundary layer statistics is related to the reduction of skin friction drag. Note that [PERSON] et al. [2] concluded that the reduction of the turbulence intensity is indicative of the fact that the transition to turbulence in the viscous sub-layer was delayed [2]. The observation obtained in this study may be related to their results, but further study is needed to clarify it. Figure 11: Histograms of the fluctuating component of the \(U\)-velocity for a smooth wall. Figure 10: Comparison of \(U\)-velocity profiles for smooth wall and riblet cases. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Smooth Wall**} & \multicolumn{2}{c}{**Riblet**} \\ \cline{2-5}
**Statistical** & \multicolumn{2}{c}{\(z\) = 2 mm} & \multicolumn{2}{c}{\(z\) = 20 mm} & \multicolumn{2}{c}{\(z\) = 2 mm} & \multicolumn{2}{c}{\(z\) = 20 mm} \\
**Properties** & \multicolumn{2}{c}{(z/\(\delta_{smooth}\) = 0.196: \(\text{Inside}\) the & \(\text{Freesream}\) & \(\text{Inside}\) the & \(\text{Freesream}\) \\  & **Boundary Layer)**} & \multicolumn{2}{c}{**Region)**} & **Boundary Layer)**} & **Region)** \\ \hline Mean (\(\overline{U}\)), m/s & 30.10 & 41.85 & 30.41 & 41.83 \\ Standard deviation & 2.88 & 0.89 & 2.68 & 0.85 \\ (\(\sigma_{u}\)), m/s & 2.76 & 8.36 & 2.76 & 9.13 \\ Skewness, m/s & 0.13 & 0.28 & 0.15 & 0.26 \\ Turbulence & 0.096 & 0.021 & 0.088 & 0.020 \\ intensity (\(\sigma_{u}/\overline{U}\)) & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical properties for smooth wall and riblet surfaces.