**4.2 PSD of the modal coefficients**

The power spectral density of the first two POD modes coefficients for the 0° and 90° AOA cases are compared in **Figure 8**. Generally, the twisted flow had a larger effect on the low-frequency region than the high-frequency region for the first mode, while this observation was exactly the opposite for the second mode.

In the case of 0°AOA, as marked by a rectangle in **Figure 8**(a1), the low-frequency shift mode dominated the first pressure pattern for case CWP while it became less pronounced for case TWP30. The second POD mode of case CWP was distinctively controlled by the vortex shedding phenomenon with the peak appearing at *f11* ≈ 0.1.

**Figure 7.** *Energy contributions of (a) dominant modes; (b) normalized cumulative number of modes.*

*Mode Interpretation of Aerodynamic Characteristics of Tall Buildings Subject to Twisted… DOI: http://dx.doi.org/10.5772/intechopen.103757*

However, the twisted wind reduces this peak energy, indicating that the Karman vortex motion is weakened in the presence of TWP.

In the case of 90°, as shown in **Figure 8**(b1), although the multi-peak region can be observed in the PSD of the first-order mode for the two wind profiles, it should be noted that the shift mode only appeared in the case of CWP. The second mode under CWP is controlled by two types of vortices shedding behavior with *f21* = 0.04 and *f22* = 0.102, and as a result, these two different flow motions around a large aspect ratio building (3:1) can be speculated to be leading-edge vortex shedding (LEVS) and trailing-edge vortex shedding (TEVS) respectively [25]. The existence of twisted flow significantly changes the energy magnitude, the main frequency and the number of peaks. For example, in the case of TWP30, there was only one pronounced peak, whose energy was slightly reduced but the frequency increased to f31 = 0.048. Thus, it is reasonable to surmise that the second mode of TWP 30 is highly related to alternateedge vortex shedding (AEVS) [25, 26].

#### **4.3 POD pressure pattern**

The first two POD modes of the pressure field on the building surface for case CWP and TWP30 with 0°AOA are shown in **Figure 9**. When exposed to CWP, the first mode pattern had a similar distribution with the mean pressure filed on the

**Figure 8.**

*Power spectral density of the first two POD mode coefficients for two AOA cases of (a) 0°; (b) 90°.*

building surface as depicted in **Figure 8**, which implies that the first POD mode possibly corresponds to the low-frequency shift mode. Moreover, it is reasonable to deduce that the second asymmetrical mode shape well captured the fluctuating properties induced by the periodic vortex shedding.

In the presence of twisted wind, the POD mode pattern on the building surfaces became asymmetric and non-uniform. It was evident that the vertical varying wind direction had a noticeable influence on the mode shape on the leeward surface. Specifically, the first mode shape was significantly deflected towards the right side near the downstream region (see black dash circle). However, the second mode shape indicated that twisted flow can amplify the positive region near the left-side surface but shrink the negative area near the right-side surface, as indicated by the dashed rectangle in **Figure 9** (a2) and (b2). The possible reason could be that the conical vortex near the left side was enhanced but suppressed near the right side on the appearance of TWP.

The first two POD modes of the pressure field on the building surface for case CWP and TWP30 with 90°AOA was shown in **Figure 10**. Under CWP, a shift mode can also be observed for the first POD mode. Notably, the pressure pattern on the left and right sides are symmetrically distributed, but experiences an initially upward and then downward process from the windward edge to the leeward edge. Such finding indicates that flow separation and reattachment simultaneously occur at the side

*The first two POD modes of surface pressure field at 0°AOA for (a) CWP; (b) TWP30.*

*Mode Interpretation of Aerodynamic Characteristics of Tall Buildings Subject to Twisted… DOI: http://dx.doi.org/10.5772/intechopen.103757*

**Figure 10.**

surface of the building with side ratio of 3:1. Similar to the 0°AOA case, the asymmetrical second mode of CWP is strongly related to the vortex shedding phenomenon. Affected by TWP, the continuous varying wind directions along the building height cause the reattachment location on the right-side surface to move upstream (see the red dash circle), however, that on the left-side surface becomes weaker (see blue dash circle). This observation indicates that the conical vortex near the left side is significantly weakened and merges into the wake flow. Overall, TWP has a distinctively different impact on the mode shape of buildings with different aspect ratios.
