# Mean Reattachment Length of Roof Separation Bubbles Using Proper Orthogonal Decomposition
## 5 Conclusions  
This research utilized proper orthogonal decomposition (POD) to evaluate the mean reattachment length (\(X_{r}\)) of roof separation bubbles on a three-dimensional rectangular bluff body model, offering key insights:  
* Primary POD eigenmode: This mode effectively characterizes the major global mechanisms influencing the roof pressure field. The regions of high magnitude in the eigenmodes are closely associated with intense pressure fluctuations, reflecting the complex and variable fluid flow within the separation bubble. Conversely, areas of low magnitudes in the eigenmode are indicative of low-pressure fluctuations, characteristic of the more stable flow found in the reattachment area. Notably, these regions are distinguished by reversed signs in the eigenmode. This comprehensive characterization captures the dynamics associated with flow separation and reattachment, demonstrating the detailed nature of the pressure field's variability in these regions. * Secondary POD eigenmode: This mode reveals the presence of vortex structures within the separation bubbles. This finding offers a deeper understanding of the complex flow behaviors and the underlying mechanics within the roof separation bubble. * Third POD eigenmode: This mode exhibits pronounced effects at the windward front corners of the roof caused by the wind flow. The distribution of this eigenmode strongly correlates with the pressure fluctuations at these corners, indicating the impact of roof corners on flow dynamics. * Estimation of the mean reattachment length (\(X_{r}\)) using the first POD eigenmode: By evaluating the dominant POD eigenmodes and eigenvalues, it was deduced that the mean reattachment length (\(X_{r}\)) can be represented as the distance from the leading edge to the first zero-valued contour line after the first POD eigenmode reaches its maximum value. This offers a clear, quantifiable measure of the mean reattachment length (\(X_{r}\)) on the roof. * Validation of the POD-based mean reattachment length (\(X_{r}\)): The mean reattachment length (\(X_{r}\)) determined via the proposed POD-based method closely aligns with those obtained from an established aerodynamic database, with observed discrepancies being less than 5%. This underscores the robustness and precision of the POD approach in estimating the mean reattachment length (\(X_{r}\)) using the first POD eigenmode. * Methodological advantages: The technique's capacity to precisely pinpoint the flow reattachment location across the entire separation region, using solely pressure data, is a significant advancement. This negates the need for specialized aerodynamic databases, making the approach adaptable to a model regardless of its shapes and flow conditions. Based on the results of this study, it is deemed necessary to conduct additional research into the evaluation of pressure characteristics and mean reattachment lengths (\(X_{r}\)) for various bluff body geometries. Future studies should focus on evaluating the applicability of the proposed POD-based methodology to a diverse range of bluff body shapes and sizes. This is crucial for understanding how different geometric configurations influence flow separation and reattachment phenomena. Additionally, building upon the research conducted in this study, further extending the investigation to include the effects of varying turbulence intensities and wind directions is considered important for enhancing the generalization of the proposed method. In conclusion, the use of the first POD eigenmode to identify the flow reattachment location offers numerous advantages. It provides a streamlined, accurate, and intuitive approach for experimental researchers and holds significant implications for the realms of wind engineering and fluid dynamics. **Author Contributions:** Conceptualization, H.J.H. and S.L. ; methodology, H.J.H. and S.L. ; experiments, H.J.H. and S.L. ; validation, H.J.H. and S.L. ; investigation, H.J.H., S.L. and H.-J.K.; data curation, H.J.H. and S.H.C. ; writing--original draft, H.J.H.