## 5 Analysis of Fluctuating Parameters
### Relations Between Fluctuating Parameters and Gust Duration  
There are limited field measurements studying the relations between the fluctuating parameters and gust duration. [PERSON] revealed the statistical relations between turbulence intensity and gust factor under different gust durations and the corresponding mean hourly wind speeds for open and flat terrains [27]. [PERSON] and [PERSON] determined the variation in longitudinal turbulence intensity with time interval based on measured results [28]. [PERSON] and [PERSON] obtained the Gust factor and turbulence for a subsurface tropical cyclone and evaluated the variations with terrain roughness and gust duration [29]. On the basis of wind field records on the roof of Shanghai World Financial Centre, [PERSON] et al. presented and assessed the variations in the gust factor and turbulence with gust duration [12]. Different gust durations (short-time interval \(t\)) exert a remarkable effect on the values of fluctuating parameters, such as turbulence intensity, gust factor, and peak factor, with the long-time interval (\(T\)). The expression for the longitudinal gust factor and turbulence intensity for a specific short-time interval is  
Figure 13: (**a,b**) Turbulence intensity against gust factor: (**a**) and (**b**) are scatter plots and fitting results respective for the longitudinal and lateral direction. \[G_{u}(T,t)=u_{\max}(T,t)/U(T) \tag{11}\] \[SD_{u}(T,t)=\frac{\sqrt{\sum\limits_{i=1}^{N}u_{i}^{\prime 2}(t)/(N-1)} }{U(T)} \tag{12}\]  
In Equation (11), \(u_{\max}(T,t)\) indicates the longitudinal fluctuating wind within basic time interval T, and maximum mean wind speed \(U(T)\) is the mean wind speed with time interval \(t\) within the basic time interval. In Equation (12), \(u_{i}^{\prime}\) indicates the longitudinal fluctuating wind speed. In this study, with \(T\) = 3600 s, time interval variable \(T\) is set to from 1 s to 1 h, and \(N=T/t\). When gust duration \(t\) = 3 s, \(SD_{u}(T,t)\) approximates turbulence \(I_{u}\), as previously described. In addition, in \(G_{u}(T,t)\) and \(SD_{u}(T,t)\), by replacing \(u^{\prime}\) with \(v^{\prime}\), the gust factor in the across-wind direction \(G_{v}(T,t)\) and turbulence \(SD_{v}(T,t)\) can be evaluated by Equations (11) & (12), respectively. The strong wind record for 18 h is split into 1 h time intervals, and the variations in turbulence intensity and gust factor with mean gust duration (\(SD_{u}\) and \(G_{u}\)) are shown in Figures 14 and 15. As shown in Figure 14, the longitudinal turbulence intensity for the three buildings gradually decreases and the difference between the two fitting curves also decrease with increasing time interval. Within the same time interval, the turbulence intensity in the along-wind direction and the Gust factor of building B with low wind speed are the highest, and building C are the lowest. In addition, those of building A with high wind speed are the highest, and building C are the lowest. However, the variations in turbulence intensity in the across-wind direction and those in the Gust factor of building A and C are basically to the same as the turbulence intensity in the along-wind direction. The turbulence intensity and Gust factor of building B slightly fluctuated due to the interference among the high-rises. The results of fluctuating parameters substantially decreased with the increase in the value of \(t\). The differences among the three buildings are relatively large at every wind speed when \(t\) < 100 s. However, approximately no difference is observed among them when \(t\) > 100 s. This condition indicates that turbulence intensity and Gust factor are mainly affected by short-term wind fluctuations. Figure 14: Comparison of the three high-rises with turbulence and gust factor varying with gust duration and wind speed. (**a**) Estimated values of \(SD_{u}(T,t)\); (**b**) Estimated values of \(SD_{p}(T,t)\). Figure 16: Wind speed spectra of the three high-rises in the along-wind direction. **(a)** Building A; **(b)** Building B; **(c)** Building C.