## 3 Measurement Technique and Data Reduction Methodologies
### Evaluation of Skin Friction Drag Reduction  
The effect of reducing skin friction drag was evaluated by Equation (13), which accounts for a ratio between the difference of the local skin friction coefficient (\(\Delta c_{f}\)) between the riblet and smooth wall cases and the reference value for the smooth wall:  
\[\frac{\Delta c_{f}}{c_{f,\ smooth}}=\frac{c_{f,\ riblet-c_{f,\ smooth}}}{c_{f, \ smooth}}. \tag{13}\]  
In general, the local skin friction coefficient in the turbulent boundary layer for a smooth flat plate surface with zero incidence can be calculated by Equation (7). However, the local skin friction coefficient for the riblet surface (\(c_{f,riblet}\)) cannot be calculated properly by Equation (7) since the constant coefficient value may be different. To evaluate the local skin friction coefficient in case for the riblet surface, a unique approach was proposed here by emphasizing the turbulent Reynolds number and the turbulent scale. The detailed procedure for the evaluation is given in this section. The procedure for calculating \(\Delta c_{f}\) is described here in more detail. The local skin friction was basically calculated based on the turbulent boundary layer theory and the 1/7 power law applied to a flat smooth plate based on the Blasius formula [29] as presented by Equation (14). Note that this equation is equivalent to Equation (7) in case for a flat smooth plate:  
\[c_{f}=\frac{\tau_{0}}{\frac{1}{2}\rho\overline{U}^{2}}=C\left(\frac{\overline {U}\cdot\delta}{v}\right)^{-\frac{1}{4}}, \tag{14}\]  
where \(C\) is a constant coefficient, which is usually 0.045 for a smooth flat plate. This value may be different for different surface conditions as aforementioned; since the actual value for the riblet surface is unknown, a simple estimate of this parameter will be given; details will be given later in this section. The value of the parenthesized quantities on the right side of Equation (14) was equivalent to the turbulent Reynolds number (\(Re_{turb}\)), given by Equation (15). Here, it was assumed that the integral length scale (\(L_{0}\)) generally increases to the boundary layer thickness (\(\delta\)), and the boundary layer thickness increases as the flow proceeds downstream. Therefore, the integral length scale was considered to grow with movement downstream. Additionally, the characteristic velocity scale was considered to be the root-mean-square velocity (\(\sigma_{u}\)) to focus on the turbulent characteristics of the boundary layer flow. Thus, the turbulent Reynolds number was calculated based on the integral length scale and the root-mean-square velocity. This relationship emphasizes the relation between the turbulent structure and the skin friction coefficient. Furthermore, another objective of introducing the turbulent Reynolds number in this procedure was to compute the unknown constant coefficient in Equation (14) for the riblet wall surface. The integral length scale and the velocity fluctuations were  
Figure 7: Illustration of the computation of the integral time scale. calculated based on measured data at \(z=1.0\) mm where the measured point was closest to the wall surface:  
\[Re_{turb}=\frac{\sigma_{u}\cdot L_{0}}{v}=\frac{\sigma_{u}\cdot\overline{U}\cdot t _{0}}{v}. \tag{15}\]  
In Equation (15), \(t_{0}\) is the integral time scale calculated by Equation (10). The kinematic viscosity was determined from the total temperature of the wind tunnel freestream under the assumption of incompressible flow since the flow condition in this study was incompressible as aforementioned. By inserting Equations (14) and (15) into Equation (13), Equation (13) is reduced to Equation (16) to express the degree of reduction of skin friction drag.