# Mean Reattachment Length of Roof Separation Bubbles Using Proper Orthogonal Decomposition
## 4 Results
### Validation of the POD-Based Mean Reattachment Length (\(X_{r}\))
ated with the intermediate turbulence intensity (\(I_{u}=12.7\%\)), occurs at a distance of about 340 mm from the leading edge of the roof surface. On the other hand, in the case of the low turbulence intensity (\(I_{u}=0.6\%\)), the reduced pressure coefficient (\(C^{*}{}_{p}\)) of 0.38 occurs at a distance of about 657 mm from the leading edge of the roof surface due to the influence of low turbulence effects. Table 4 compares the mean reattachment lengths (\(X_{r}\)) along the roof centerline as determined via the current POD-based method with those proposed by [PERSON] [17]. The results in Table 4 indicate that the mean reattachment lengths (\(X_{r}\)) derived from the proposed first eigenmode of the POD closely match those from [PERSON]'s [17] methodology, with a relative error of less than 5%. Discrepancies in this comparison may arise from the differences in flow characteristics between the datasets, variations in model configurations, the interpolation methods employed for generating the first POD eigenmode contour lines, and other influencing factors. As the analysis of our results is concluded, it is crucial to recognize the inherent limitations of this study. Our focus was on the centerline of the roof with a wind angle (\(\alpha\)) of \(0^{\circ}\), a choice that provided significant insights but also came with specific constraints. This particular location and angle were selected primarily due to the availability of comparative data, enabling a robust validation of the proposed methodology. However, our validation process was limited when considering other locations on the roof and additional wind angles (\(\alpha\)) (beyond \(0^{\circ}\)), such as a wind angle (\(\alpha\)) of \(5^{\circ}\). This limitation predominantly stemmed from the lack of detailed empirical data for these other locations and wind angles in the existing literature, thereby constraining the scope of the validation. These limitations highlight the need for further research that encompasses various locations on the roof and a broader range of wind angles. Future efforts in this area, especially those involving the acquisition of more comprehensive datasets, will help in validating and enhancing the applicability of the proposed methodology to diverse locations and wind angles. Such advancements will not only strengthen the robustness of our findings but also \begin{table}
\begin{tabular}{l c c} \hline \hline
**Turbulence Intensity (\(I_{u}\), \%)** & **12.7** & **0.6** \\ \hline Mean reattachment length according to the current POD-based method (\(X_{r}\), mm) & 324 & 689 \\ Mean reattachment length according to [PERSON]’s method [17] (\(X_{r}\), mm) & 340 & 657 \\ Relative error (\%) in the mean reattachment length (\(X_{r}\)) between the current & 4.9 & 4.6 \\ POD-based method and [PERSON]’s method [17] & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the mean attachment lengths (\(X_{r}\)). contribute to a more comprehensive understanding of flow separation and reattachment dynamics in low-rise building roofs.