# Full-Scale Measurements of Wind Characteristics on a High- Rise Building during Typhoon Sarika
## 3 Wind Characteristics of Typhoon Sarika
### Turbulence Intensity and Integral Scale
#### 3.3.2 Turbulence Integral Scale  
The Turbulence integral scale (\(L_{i}^{x}\)) is a measure of the average size of eddies in the turbulent flow. The values \(L_{u}^{x}\) and \(L_{v}^{x}\) can be expressed as longitudinal and lateral turbulence integral scales. According to [PERSON]'s hypothesis, the turbulence integral scale can be calculated directly according to the following formula:  
\[L_{i}^{x}=\frac{\overline{U}}{\sigma_{i}^{2}}\int_{0}^{R_{i}=0.05}R_{i}(\tau) d\tau\ \ \ i=u,v \tag{8}\]  
where \(\overline{U}\) is mean wind speed; \(\sigma_{i}\) and \(R_{i}(\tau)\) are the standard deviation and auto-correlation function of the longitudinal and lateral fluctuating velocity components \(u\) and \(v\), respectively. To get a more consistent estimate of the integral scale, the auto-correlation function is integrated until the correlation drops to 0.05 and [PERSON]'s hypothesis is used to convert the integral time scale to the integral length scale. Equation (8) shows that the turbulence integral scale is closely related to mean wind speed and the standard deviation of S.D of fluctuating wind. Therefore, the rules of turbulence integral scale concerning the mean wind speed and S.D of fluctuating wind are significant. Figure 8a,b shows the variations of the measured longitudinal and lateral turbulence integral scales with respect to the mean wind speeds and S.D of fluctuating wind with a 10-min interval. The results show that the measured turbulence integral scale is basically in the range of 0-200 m when  
Figure 7: The measured longitudinal and lateral turbulence intensities. (**a**) \(I_{u}\) and \(I_{v}\) with respect to 10-min \(\overline{U}\); (**b**) \(I_{u}\) and \(I_{v}\) with respect to wind direction; (**c**) \(I_{u}\):\(I_{v}\) with respect to 10-min \(\overline{U}\); (**d**) \(I_{u}\):\(I_{v}\) with respect to wind direction.  
the 10 min mean wind speed is less than 8 m/s, while the measured turbulence integral scale is basically in the range of 200-500 m when the 10 min mean wind speed is within 8-21 m/s, Figure 8a,b shows that the measured longitudinal and lateral turbulence integral scales increase with the increasing mean wind speed and S.D of fluctuating wind, which shows that the turbulence integral scales are positively correlated with the intensity of inflow wind.  
Figure 8c,d shows the ratios of the turbulence scale between the turbulence components (\(L_{u}^{x}\):\(L_{v}^{x}\)) with respect to the mean wind speed and wind direction, \(L_{u}^{x}\):\(L_{v}^{x}\) are basically within 2-4 under the excitation of static wind, and \(L_{u}^{x}\):\(L_{v}^{x}\) are within of 4-7 if the 10 min wind speeds are higher than 10 m/s, which explains that \(L_{u}^{x}\):\(L_{v}^{x}\) increases with the increasing mean wind speed, and further discloses that the increasing mean wind speed has greater influence on longitudinal turbulence integral scales than that on lateral turbulence integral scales.  
Moreover, the ratios of the turbulence scale between the turbulence components (\(L_{u}^{x}\):\(L_{v}^{x}\)) near 160\({}^{\circ}\) (close to terrain roughness category A) of the wind direction is generally larger than that along other wind direction. The results demonstrate that the ratio of the turbulence scale between the turbulence components are closely related to the terrain categories, and \(L_{u}^{x}\):\(L_{v}^{x}\) will reach larger values when the terrain roughness is category A.