## 4 Identification of Noise Sources around Rearview Mirror
### Relationship between Noise Sources and Flow Field  
The dipole noise sources at locations 1, 2, 3 and 4 were selected by understanding the distribution of dipole noise sources. We built flow lines passing through these four locations and extract data on a section of the flow line, including vorticity, velocity, and other relevant flow field physical quantities. The relationship between the dipole noise sources and the flow field physical quantities was analyzed to reveal the mechanism of aerodynamic noise generated by the mirrors. In order to facilitate the comparative analysis of the different data, a linear normalization process was performed on the physical quantities in the streamlines. The extracted physical quantities were mapped to the range [0, 1], and the specific normalization formula is as described in Equation (12):  
\[X_{nom}=\frac{X-X_{min}}{Xmin_{max}} \tag{16}\]  
where \(X\) is the original data; \(X_{max}\) and \(X_{min}\) are the maximum and minimum values of the data, respectively. As shown in Figure 7, streamlines were created on the upper surface of the rearview mirror, and one of the streamlines was selected to extract the relevant physical quantities of the flow field above it: the flow velocity \(\mathbf{u}\), the vorticity \(\mathbf{\omega}\), the intensity of the noise source \(\mathbf{\omega}\times\mathbf{u}\), and the sinusoid of the angle \(\theta\) between the flow velocity and the vorticity. The extracted physical quantities were linearly normalized to obtain the results shown in Figure 8. According to the trend of the physical quantities in the figure, it can be seen that:  
1. Comparison of the trends of the physical quantities shows that the change of the vorticity before and after the junction of the mirror shell and the mirror ring is the most drastic, which is the main reason for the generation of the dipole noise source. As shown in Figure 9, the same method as above was used to create streamlines in the rearview mirror near the side window mirror stalk; we selected one of the streamlines to extract the relevant flow field physical quantities and then applied linear normalization to obtain the results shown in Figure 10. According to the trend of each physical quantity in the figure, it can be seen that:  
1. The vorticity \(\omega\) and noise source intensity \(\omega\times\mathbf{u}\) reach the maximum value near point 18, and the angle \(\theta\) between the flow velocity and the vorticity has a sinusoidal value of 1, which is located at the rounded corner of the mirror stalk, which is the main location of the airflow separation. 2. Compared with the vorticity and noise source intensity, the flow velocity \(\mathbf{u}\) reaches the peak value earlier, and the peak position is located at point 14. Figure 8: Variation of each physical quantity on the upper surface of the rearview mirror with streamlines. Figure 9: Partial flow diagram at the mirror stalk of the rearview mirror. Comparison of the trends of each physical quantity shows that the vorticity \(\mathbf{\omega}\), flow velocity \(\mathbf{u}\), the angle sine value sin\(\theta\), and the intensity of the sound source \(\mathbf{\omega}\times\mathbf{u}\) all reach the maximum near point 18, and the flow velocity and the vortex angle sine value sin\(\theta\) basically remain unchanged, while the rest of the physical quantities undergo great change before and after point 18, among which the intensity of the noise source \(\mathbf{\omega}\times\mathbf{u}\) changes most drastically, and the trends of the change of the vorticity and the intensity of the noise source are basically the same. The main reason for the noise source at this point is that the vortex \(\mathbf{\omega}\) and the flow velocity \(\mathbf{u}\) change drastically when the gas flows through here, while the angle \(\theta\) between the velocity and the vortex is close to 90 degrees.