# Dynamic Response of Slender Vertical Structures Subjected to Thunderstorm Outflows
## 3 Numerical Application
### Thunderstorm Wind Velocity and Loading Modeling
It is worth pointing out that the profiles also follow the model in Equation (A2) for lower values of \(z\), whilst the guidelines suggest assuming a constant profile below a certain height, fixed according to the exposure category [40]. This recommendation is disregarded for the purpose of showing the differences between the thunderstorm and synoptic events from a theoretical point of view. Concerning the turbulence intensity, its dependence on the height above the ground and roughness length is still a matter of discussion. Studies in the literature based on a large amount of full-scale data have shown that the dependence of the turbulence intensity on the ratio \(z/z_{0}\) is weak [5, 29], and the values observed are on average lower than the ones associated with synoptic winds. However, these studies were based on data collected by anemometers located in coastal areas, and thus have similar roughness lengths with which it is difficult to detect a significant dependence on the roughness. Other studies carried out on different sites have shown increasing trends for the vertical profile of the turbulence intensity, as well as greater values comparable to those observed during synoptic events [45, 46, 47]. Moreover, it was shown that the vertical profile of the turbulence intensity on the height changes during the thunderstorm, showing a decreasing trend during the ramp-up phase of the wind speed [32]. In order to carry out a meaningful comparison with  
Figure 5: Vertical mean speed profile of the thunderstorm outflow (blue lines) and synoptic wind (red lines): (a) lighting pole; (b) telecommunications tower. the synoptic case, two different models covering the possible scenarios of the turbulence intensity of the thunderstorm are investigated:  
* \(\theta_{T}(z)=1\), \(I_{v}(h)=1/\ln\left(\frac{h}{z_{0}}\right)\) as the synoptic case [40];
* \(\theta_{T}(z)\) provided by Equation (A3) (Appendix A), \(I_{v}(h)=1/\ln\left(\frac{h}{z_{0}}\right)\). Figure 6 plots the vertical profiles of the turbulence intensity of the thunderstorm (Equation (A3)) and synoptic wind (Equation (A4)) events for the two structures. The definition of the mean wind loading is pursued through the derivation of the drag coefficients and the calculation of the parameter \(a_{1}\) (Equation (17)). The drag coefficients of the two structures are evaluated according to the Italian CNR guidelines [40]. Due to its cross-section with sharp corners, the drag coefficient of the lighting pole does not depend on the Reynolds number and hence on the wind velocity. Moreover, the contributions of the drag due to the metallic bell at the base of the pole and the lighting devices at the top are neglected in these analyses. Instead, the telecommunications tower presents a circular cross-section, and thus the drag coefficient depends on the Reynolds number and on the vertical profile of the wind velocity. The drag coefficients for the two structures are plotted in Figure 7.  
Figure 6: Vertical profile of the turbulence intensity of the thunderstorm (blue lines, Equation (A3)) and synoptic wind (red lines, Equation (A4)) events: (**a**) lighting pole; (**b**) telecommunications tower. Figure 7: Drag coefficients: (**a**) lighting pole; (**b**) telecommunications tower. It is worth pointing out that the drag coefficient adopted corresponds to a stationary wind field. Suitable aerodynamic coefficients able to account for the transient nature of thunderstorm outflows are a matter of current research; however, recent studies have shown that these effects are negligible [48; 49].