## 4 Results
### Cylinder
#### 4.1.2 Flow Transition Localization  
Figure 6 shows the intensity profile (blue) and the intensity gradient profile (orange) of the center row (white dashed line) of each flow visualization image from Figure 5. The approximation result for each profile is shown with a dashed line in the corresponding  
Figure 5: Thermographic flow visualization of the cylinder object in cross-flow with a Reynolds number of \(5.2\times 10^{5}\). Temporal mean value and temporal standard deviation as well as principal components (PC) no. 1–3 from the PCA of the image series. Systematic inhomogeneities in the flow regimes are reduced while a contrast between the laminar and turbulent flow regime is maximized in PC 2 with CNR = 3.70.  
color. The flow transition position derived from the approximations is marked with a vertical dotted line. The intensity profile of the temporal mean value shows the impact of the systematic temperature gradient within the laminar flow regime between \(60^{\circ}<\theta<110^{\circ}\) and in the turbulent flow regime between \(117^{\circ}<\theta<145^{\circ}\). Due to the course of the intensity profile, the approximation does not fit to the profile outside the turbulent flow regime. Because of this, the approximation curve does not center itself between the laminar and turbulent flow regimes and results in an estimated flow transition position within the turbulent flow regime. In addition, there is no sharp jump in intensity between the flow regimes, but a continuous steady increase that causes a flat slope of the approximation curve. The approximation of the intensity gradient profile fits to the gradient peak at \(\theta\approx 118^{\circ}\) instead of centering between the laminar and turbulent flow regimes. This is due to the different systematic gradients in the flow visualization and the absence of a single prominent gradient peak between the flow regimes. The intensity profile of the temporal standard deviation does not have two distinct plateaus representing the laminar and turbulent flow regime. The approximation therefore fails to fit to the profile correctly and has a high systematic error in the localization of the flow transition. The intensity gradient, however, has a prominent peak between the laminar and turbulent flow regime, allowing for a more accurate localization of the flow transition. The intensity evaluation of the PC 2 illustrates the advantageous of the enhanced image processing by means of the PCA. Two distinct intensity plateaus are present due to the high CNR, while a sharper gradient between the laminar and turbulent flow regime persists. As a result, the approximations of the intensity profile as well as of the corresponding gradient profile successfully locate the flow transition between the laminar and turbulent flow regimes with a minimal error to the center position between them. Figure 6: The intensity profile (blue line), intensity gradient profile (orange line) along the white dotted line in the temporal mean value, temporal standard deviation and PC 2 flow visualization in Figure 5. The approximation of the intensity profile (blue dashed) and intensity gradient profile (orange dashed), respectively. The flow transition localization results of both methods are depicted with a vertical dotted line in the respective color. Different expressions of the intensity plateaus are visible in each profile with varying gradient amplitudes between the plateaus. The most distinct expression of two plateaus including a steep step between them exists in the PC 2.