## 5 Results and Discussion
### Drag Force Sensitivity to Sampling Frequency and Period  
In this section, we aim to determine the minimum sampling frequency (\(f_{s}\)) and sampling period (\(T_{w}\)) required to acquire sufficient data for modal decomposition and ensure the convergence of key aerodynamic parameters, such as the drag coefficient, \(C_{D}\). Initially, we analyzed the power spectral density (PSD) of the global drag on the Ahmed body, as well as the pressure and friction drag on the body, nose, and rear fascia. This FFT spectral analysis was performed with a sampling frequency of \(f_{s}\) = 10 kHz and a time window of 4 s. Figure 5 shows the PSD of the drag force without any smoothing. The raw spectrum indicates that the most energetic components are within below a non-dimensional frequency or Strouhal number (\(St\)) of 0.36 (i.e., below 50 Hz). Beyond this, energy decreases consistently up to 1 kHz (\(St\) = 7.2), with an exception around 350 Hz (\(St\) = 2.52). In Section 4, we identify significant oscillatory components at 245, 294, and 400 Hz (\(St\) = 1.76, 2.11, and 2.88). Although the pressure signal is sampled at 10 kHz, giving a Nyquist frequency of 5 kHz, Figure 5 (marked in the red square) shows that the maximum resolvable structure by this IDDES simulation is about 1 kHz (\(St\) = 7.2), beyond which, the signal flattens and carries little useful information. This is primarily because the mesh resolution used in this study is incapable of spatially resolving smaller-scale flow structures of about 1 kHz. Next, we study the frequency spectrum and cumulative sum of friction and pressure drag individually for the nose, body, and rear fascia, which are plotted in Figure 6a-f, where we can clearly see that the PSD values of the pressure drag for all three body-regions exhibit similar trends. Note that in these figures, to plot pressure and friction drag components--which have different orders of magnitude--on the same graph, these quantities are normalized. Each drag component, whether pressure or friction, is scaled so that its cumulative sum equals one over the range of non-dimensional frequency considered. Similarly, the spectra of the pressure and friction drags are normalized by their respective total energy to bring them to the same order of magnitude. In these figures, we can observe a few very low-frequency structures (1-10 Hz, corresponding to \(St=0.007\)-0.07), which are not well-explained in the literature. Additionally, significant high-frequency components appear near 349 Hz (\(St=2.54\)) and 600 Hz (\(St=4.32\)). As frequency increases, the amplitude decreases drastically, with minimal notable peaks. Figure 5: Power spectral density of the pressure drag signal at the rear fascia of the Ahmed body, sampled at \(f_{s}=10\) kHz (\(St=72\)) with a time window of \(T_{w}=4\) s; the encircled area illustrates that IDDES method’s inability to resolve contributions from structures above 1 kH. Figure 6: Power spectral density normalized by total energy and cumulative drag normalized by the respective total drag component (pressure or friction) for different body regions: (**a,b**) pressure drag at the nose, body, and rear fascia; (**c,d**) friction drag at the nose and body; (**e,f**) comparison between friction and pressure drag for the entire body. As discussed earlier, the turbulence model and grid resolution used in this study were not capable of resolving turbulent structures beyond 1 kHz, which is corroborated by the cumulative sum of frequency spectrum components. Figure 6b,d,f show that the system's energy does not change significantly beyond 400 Hz (\(St=2.88\)). In Figure 6b, the pressure drag (\(C_{D,p}\) at the rear fascia reaches 90% of its energy within the range of \(St=0.18\) (approximately 26 Hz). There is a spike at 349 Hz \(St=2.51\)), which is likely caused by the interaction of coherent vortex shedding structures from the side, lower, and upper edges of the [PERSON] body, representing an averaged effect.