## 4 Wind Field Characteristics
### Turbulence Intensity and Turbulence Integration Scale  
The turbulence intensity reflects the degree of pulsation of wind. The first panel of Figure 11 shows the variation of slow-varying turbulence intensity \(I_{\delta}(\delta=u,v)\) (Equation (8)) with the time during the occurrence of thunderstorm wind at the height of 64 m. It is to be noted that the large turbulence intensity, caused by very small wind speeds, has been ignored (\(\overline{u}<5\) m/s, \(I>0.2\)) [5]. The results showed that the slow-varying turbulence intensity changed with respect to time, and it increased significantly during the occurrence of thunderstorm winds. The second panel of Figure 11 presents a series of vertical profiles of the longitudinal and lateral slowly-varying turbulence intensities (a) and (b) at a series of significant instants. As previously noted, the large value has been ignored, so some information in the figure is not presented. In this case, during the pass of the gust front, the longitudinal and lateral turbulence intensities gradually increase and show a zigzagged pattern with the change in height. It is difficult to give an obvious pattern at present, but the turbulence intensity at the bottom is significantly greater than that at the top. Different from the synoptic wind, whose turbulence intensity gradually decreases with the increase in height, the slowly-varying turbulence intensity of the thunderstorm wind decreases, increases and then decreases with height near the time when the peak wind speed occurs (Moment (5) and (6)), and the nasal tip appears at the height of about 64 m. In addition, the lateral value is slightly larger than the longitudinal value, which may be related to the special characteristics of the scattered ring wind field of thunderstorms. The third panel of Figure 11 shows the profiles of the longitudinal and lateral mean turbulence intensity \(\overline{I}_{u}\) (a) and \(\overline{I}_{v}\) (b) (the 10-min time interval centered with the analysis moment). For the mean turbulence intensity, the longitudinal component (a) generally shows a decreasing trend with the increase in height, which is similar to the results obtained based on the thunderstorm outflows in the Northern Tyrrhenian [21]. While the lateral component (b) appears differently, when approaching the peak of the thunderstorm wind speed, the lateral component decreases first and then increases along the height for low heights. This was not found in [PERSON] et al. [21], which only presented 20 min mean turbulence intensity. With the height exceeding 80 m, it continues to show a decreasing trend. Obviously, this result is significantly different from that of the synoptic wind. The turbulence integral length scale is a measure which can be used to evaluate the average size of turbulent vortices of fluctuating wind. It has considerable significance in  
Figure 11: Spatial–temporal variation of longitudinal (red) and lateral (blue) turbulence intensity at some significant instants. the analysis of structural wind load, and the size of it determines the influence range of fluctuating wind on the structure. Herein, the turbulence integral length scale is calculated based on [PERSON]'s hypothesis and the auto-correlation function method with a threshold of 0.05 [32]. Figure 12 shows the profiles of the longitudinal and lateral turbulence integral length scales, \(L_{u}\) (a) and \(L_{v}\) (b), at the same significant instants as Figure 9. In general, the longitudinal turbulence integral length scales are larger than the lateral. In the case of this thunderstorm, with the increase in wind speed during the pass of the gust front, longitudinal and lateral turbulence integral length scales gradually become larger, i.e., the size of the generated vortices becomes larger. An obvious nose shape profile can be observed with the nasal tip appearing at the height of 64 m. This height corresponds to the tip position of the wind speed profile, and it is also a common height of tall buildings and tall structures.