Wind Characteristics Investigation on The Roofs of Three Adjacent High-Rise Buildings in a Coastal Area during Typhoon Meranti
Wind Characteristics Investigation on The Roofs of Three Adjacent High-Rise Buildings in a...
Wang, Chequan;Li, Zhengnong;Luo, Qizhi;Hu, Lan;Zhao, Zhefei;Hu, Jiaxing;Zhang, Xuewen
2019-01-22 00:00:00
applied sciences Article Wind Characteristics Investigation on The Roofs of Three Adjacent High-Rise Buildings in a Coastal Area during Typhoon Meranti 1 1 , 1 2 3 1 Chequan Wang , Zhengnong Li *, Qizhi Luo , Lan Hu , Zhefei Zhao , Jiaxing Hu and Xuewen Zhang Key Laboratory of Building Safety and Efficiency of the Ministry of Education, Hunan University, Changsha 410082, China; wangchequan@hnu.edu.cn (C.W.); Qizhi@fosu.edu.cn (Q.L.); hjxcivil@163.com (J.H.); hover_aoxiang@hotmail.com (X.Z.) Civil Engineering College, Hunan University of Technology, Zhuzhou 412007, China; hulan19761010@163.com School of Vocational Engineering, Health and Sciences, RMIT University, GPO Box 2476, Melbourne VIC 3001, Australia; zhefeizhao@gmail.com * Correspondence: zhn88@263.net Received: 7 December 2018; Accepted: 16 January 2019; Published: 22 January 2019 Abstract: This paper presents the study of the pulsating characteristics of three adjacent high-rise buildings A, B, and C under typhoon ‘Moranti’ (2016) based on the measurement of the actual top wind speed. The studied pulsating characteristics included mean wind speed and direction, turbulence intensity, gust factor, turbulence integral scale, wind speed spectrum and correlation. The relationships between each pulsating parameter and the relationship between the pulsating parameter and gust duration have been investigated. Results show that the mean wind speed and wind direction of three buildings are close. When U 10 m/s in three different sites at the same time, the turbulence intensity variation of three buildings is consistent and decreases when mean wind speed increases. Once only two locations are acquired simultaneously and the wind angle between 35 and 45 , the mean values of the along-wind and cross-wind turbulence of building A and building C are close. The along-wind turbulence of the three buildings is greater than the predicted Chinese codes for various terrains. The turbulence intensity and gust factors obtained through the analysis of the samples with the mean wind speed U 10 m/s are reasonable. The turbulence integral scales of buildings A and C are equal to the predicted values of ASCE-7 and AIJ-2004, whereas the turbulent integral scale of building B is evidently small. The gust factors of three buildings increase when the turbulence intensity increases; these two characteristics have a linear relationship. At the same time interval, building B has the maximum along-wind turbulence intensity and gust factors during the low wind speed period and building C achieves the minimum values. Building A acquires the maximum and building C obtains the minimum values in the high wind speed period. The turbulence intensity and gust factors of building B show a certain pulsation. Results show that turbulence intensity and gust factors are mainly affected by the short-term fluctuation of wind. The longitudinal wind speed spectrum of three buildings conforms well to the von Karman model. The correlation of along-wind speed depends on the wind speed, whereas the correlation of cross-wind direction is independent of wind speeds. The measured data and statistical parameters provide useful information for the wind resistance design of high-rise buildings in typhoon-prone areas. Keywords: high-rise building; field measurement; typhoon; wind characteristics; fluctuating parameter Appl. Sci. 2019, 9, 367; doi:10.3390/app9030367 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 367 2 of 22 1. Introduction Typhoons are highly destructive and disastrous weather systems and one of the major catastrophic weather systems that affect China. Approximately 35% of the typhoons in the entire Northwest Pacific Ocean land in China. Further attention should be paid to the harmful vibration of high-rise buildings caused by typhoons to ensure the structural safety and the comfort of residents. Therefore, analysis the typhoon characteristics, including wind field distribution and its evolution, to estimate the dynamic environment parameters and the engineering design of disaster prevention and mitigation is very important [1]. Given the particularity of each typhoon, they are difficult to simulate in the laboratory; consequently, field measurement is the most effective method and has increasingly become as an important basic and long-term direction in the study of structural wind resistance [2]. Countries with developed wind engineering research have successively established a database of wind characteristics in the region and obtained relatively complete analysis results through large-scale observations. Davenport proposed the popular Davenport spectrum [3] and several concepts of the atmospheric boundary layer, such as gradient wind, exponential law, and ground roughness, by which different terrain types are described [4] based on the statistics of the horizontal component of gust in approximately 70 spectra in strong winds. Jackson, Lösslein, Bowen, Kato et al. revealed the effects of height, ground roughness and wind speed on wind characteristics by performing a series of observations of the Gust factor, turbulence and integral length scale measured at different heights [5–8]. Li and Gu have the experimental studies of wind characteristics in China, they have monitored representative super-high-rise buildings in China to investigate wind characteristics at the top of buildings, such as mean wind speed and direction, turbulence intensity, gust factor, turbulence integral scale, wind speed spectrum and correlation [9–11]. An et al. have investigated the relationship between different pulsating parameters and between the pulsating parameters and gust duration by using an anemometer at the top of a building [12]. Several field measurements have been carried out on the top of high-rise buildings in Guangzhou and Shanghai, the wind characteristics, such as mean wind speed, mean wind direction, turbulence intensity, gust factor, turbulence integral length scale, probability distribution of fluctuating wind speed, and wind speed spectrum, are analyzed. These super-tall buildings are all urban landmark buildings, and their high-altitude wind characteristics are representative. However, the plane size of a single high-rise building is relatively limited, so it is difficult to conduct multi-point synchronous observation. At present, research on multi-point simultaneous observation of wind fields is generally only found in the study of extra-large bridge projects. Such as field measurement of the Great Belt Bridge in Danish [13]. Toriumi made field measurements of natural wind conducted at the Ohnaruto Bridge and the Akashi-Kaikyo Bridge [14]. For the purpose of investigating the turbulent characteristics of strong wind during a typhoon landing period, two 3-dimensional ultrasonic anemometer stations are set up 30 m horizontally apart on the Macao Friendship Bridge [15]. However, these field studies are limited to the wind field characteristics under the condition of relatively open topography near the ground, and with the continuous increase in the height of high-rise buildings being built, more attention is paid to the multi-point wind characteristics at heights above 100 m. Although researchers have exerted considerable effort in the measurement of typhoon wind characteristics and structure response under the action of typhoons, the understanding of typhoon wind characteristics remains unclear due to the high cost, long period, and difficulty of field measurement. Thus, the study of strong wind characteristics in China is relatively insufficient in general. Insufficient field-measured data have become the main factor hindering the study of wind characteristics, especially the research on wind characteristics at the top of several adjacent high-rise buildings. Given that typhoons often affect Xiamen, the field measurement of typhoon wind characteristics in Xiamen for studying wind characteristics in Eastern China is vital. This study maintains a process monitoring record of strong wind characteristics at the top of three adjacent super-high-rise buildings in Xiamen under the action of typhoon ‘Moranti’ (2016). Through a statistical Appl. Sci. 2018, 8, x 3 of 23 96 2. Field Measurements 97 The three high-rises buildings (A, B, and C) monitored in this study are approximately 500 m 98 from the beach, as shown in Figure 1. Three buildings have plane size approximately 60 m × 30 m. 99 Buildings A and B are in the northern side and face the same direction; the maximum heights are 100 102.9 and 110.7 m, respectively. The distance between the two buildings is 20.5 m. The height of 101 building C is 149.8 m, as shown in Figure 2(b). 102 The terrain around the building cluster is shown in Figure 1. The coordinates of the 103 measurement point at the origin aids in illustrating the ground roughness in each incoming flow 104 direction. It begins from north (set as 0°) changing clockwise to the east (set as 90°). There is a city 105 with super high-rise buildings located between 0° and 25°. There is a town between 25° and 70°, a sea 106 between 70° and 90°, an island at 90°~140°, and an ocean at 140°~195°. The terrain at an interval 107 between each wind direction within 30 km of the measurement point is categorized into three types, 108 namely; metropolis, open land, and ocean, as shown in Figure 1(a). The measured high-rises and the 109 surrounding environments are shown in Figure 1(b), and several low-rise buildings and a coastal 110 highway are located between the beach and building cluster. Six low-rise buildings are located next 111 to the building cluster, and an open land is situated in the distance. The south contains a music school 112 and high-rises that are barely arranged in a row, a 258 m super high-rise building is 165 m away from 113 the northern side of high-rise A. The remaining residential areas are mainly low-rise or multi-storey Appl. Sci. 2019, 9, 367 3 of 22 114 buildings. The terrain around the measurement location is generally flat and open, and the 115 experimental building is not disturbed in several incoming directions. 116 Typhoons are monitored using three R.M. YOUNG propeller anemometers (R. M. Young analysis of the pulsating characteristics during typhoons, this work can be a reference for wind-resistant 117 Company, Michigan, US) mounted on the mast on the roof of each building. The mast is installed 4.2 design of super-high-rise buildings in the future. 118 m above a 3 m high fence in the east corner of the roof (Figure 2(a)). The height difference of the 2. Field Measurements 119 anemometers is equal to the height difference of the buildings, and the distances between two 120 buildings are approximately 80 and 130 m. The location and wind direction of each anemometer are The three high-rises buildings (A, B, and C) monitored in this study are approximately 500 m 121 shown in Figure 2(b). The included angle between high-rise A/B and the north direction is 39°, and from the beach, as shown in Figure 1. Three buildings have plane size approximately 60 m 30 m. 122 that between the long side of high-rise C and the long side of high-rise A/B is 90°. Judging from the Buildings A and B are in the northern side and face the same direction; the maximum heights are 102.9 123 direction of the building and the location of the anemometer, the wind fields on the roofs of high- and 110.7 m, respectively. The distance between the two buildings is 20.5 m. The height of building C 124 rises A and B are less disturbed when the northeast wind is dominant. Meanwhile, the wind field on is 149.8 m, as shown in Figure 2b. 125 the roof of high-rise C is less disturbed when the southeast wind is dominant. (b) (a) Figure 1. Satellite view of the measurement point and the building monitored. (a) Diagram of ground 126 Figure 1. Satellite view of the measurement point and the building monitored. (a) Diagram of ground Appl. Sci. roughness 2018, 8, x in different directions. (b) Actual measurements of the building and its surrounding 4 of 23 127 roughness in different directions. (b) Actual measurements of the building and its surrounding environment. 128 environment. North Mast 39° East Fence Wind 05103V R.M. Young's propeller anemometers (a) (b) Figure 2. Arrangement of the R.M. Young propeller anemometers. (a) Installation diagram and mast. 129 (Figure 2. b) Layout Arra plan ngement of the R.M of the building and . Young propeller anemo wind direction. meters. (a) Installation diagram and mast. 130 (b) Layout plan of the building and wind direction. The terrain around the building cluster is shown in Figure 1. The coordinates of the measurement point at the origin aids in illustrating the ground roughness in each incoming flow direction. It begins 131 As reported by the Central Meteorological Observatory, at 2:00 PM on 10th September, 2016 from north (set as 0 ) changing clockwise to the east (set as 90 ). There is a city with super high-rise 132 (local time), Typhoon Meranti (14th typhoon in 2016) was generated on the Pacific Northwest. Its buildings located between 0 and 25 . There is a town between 25 and 70 , a sea between 70 and 90 , 133 intensity was initially that of a tropical storm, but it rapidly increased in the next few days. On 13th an island at 90 ~140 , and an ocean at 140 ~195 . The terrain at an interval between each wind direction 134 September, Typhoon Meranti turned into a super typhoon with the highest wind speed of within 30 km of the measurement point is categorized into three types, namely; metropolis, open 135 approximately 75 m/s in the centre and landed in Xiamen at 3:15 AM on 15th September, and the land, and ocean, as shown in Figure 1a. The measured high-rises and the surrounding environments 136 distance between the experimental building and the landing point is 10.6 km. Typhoon Meranti (2016) 137 continued to move northwest with speed of 20 km/h toward to the northern direction and eventually 138 weakened into a tropical depression in Jiangxi at 5:00 PM on the same day, and 8.4 km away from 139 the experimental building, as shown in Figure 3. The wind speed and direction were simultaneously 140 monitored on the roofs, and the sampling frequency was 25.6 Hz. The measurement began at 2:50 141 AM on 14th September and stopped at 3:00 AM on 15th September due to the power failure of the 142 experimental building caused by the typhoon. The measured data were continuously recorded for 24 143 h. The measurement of building B stopped at 8:50 PM on 14th September, and data were continuously 144 recorded for 18 h. The maximum instantaneous wind speed recorded was 68.2 m/s, which was 145 measured on the roof of building C at 3:00 AM on 15th September. (a) (b) 146 Figure 3. Path of Typhoon Meranti (2016) provided by the Regional Specialized Meteorological Center 147 Tokyo. (a) The moving track during Typhoon Meranti; (b) The relationship between experimental site 148 and typhoon 4.2m 3m Appl. Sci. 2018, 8, x 4 of 23 Appl. Sci. 2019, 9, 367 4 of 22 are shown in Figure 1b, and several low-rise buildings and a coastal highway are located between the beach and building cluster. Six low-rise buildings are located next to the Nor building th cluster, and an open land is situated in the distance. The south contains a music school and high-rises that are barely arranged in a row, a 258 m super high-rise building is 165 m away from the northern side of high-rise Mast 39° A. The remaining residential areas are mainly low-rise or multi-storey buildings. The terrain around the measurement location is generally flat and open, and the experimental building is not disturbed in several incoming directions. East Fence Typhoons are monitored using three R.M. YOUNG propeller anemometers (R. M. Young Company, Wind Michigan, US) mounted on the mast on the roof of each building. The mast is installed 4.2 m above a 3 m high fence in the east corner of the roof (Figure 2a). The height difference of the anemometers is equal 05103V R.M. Young's to the height difference of the buildings, and the distances between two buildings are approximately 80 propeller anemometers and 130 m. The location and wind direction of each anemometer are shown in Figure 2b. The included angle between high-rise A/B and the north direction is 39 , and that between the long side of high-rise (a) (b) C and the long side of high-rise A/B is 90 . Judging from the direction of the building and the location of the anemometer, the wind fields on the roofs of high-rises A and B are less disturbed when the 129 Figure 2. Arrangement of the R.M. Young propeller anemometers. (a) Installation diagram and mast. northeast wind is dominant. Meanwhile, the wind field on the roof of high-rise C is less disturbed 130 (b) Layout plan of the building and wind direction. when the southeast wind is dominant. As reported by the Central Meteorological Observatory, at 2:00 PM on 10th September, 2016 (local 131 As reported by the Central Meteorological Observatory, at 2:00 PM on 10th September, 2016 time), Typhoon Meranti (14th typhoon in 2016) was generated on the Pacific Northwest. Its intensity 132 (local time), Typhoon Meranti (14th typhoon in 2016) was generated on the Pacific Northwest. Its was initially that of a tropical storm, but it rapidly increased in the next few days. On 13th September, 133 intensity was initially that of a tropical storm, but it rapidly increased in the next few days. On 13th Typhoon Meranti turned into a super typhoon with the highest wind speed of approximately 75 m/s 134 September, Typhoon Meranti turned into a super typhoon with the highest wind speed of in the centre and landed in Xiamen at 3:15 AM on 15th September, and the distance between the 135 approximately 75 m/s in the centre and landed in Xiamen at 3:15 AM on 15th September, and the experimental building and the landing point is 10.6 km. Typhoon Meranti (2016) continued to move 136 distance between the experimental building and the landing point is 10.6 km. Typhoon Meranti (2016) northwest with speed of 20 km/h toward to the northern direction and eventually weakened into a 137 continued to move northwest with speed of 20 km/h toward to the northern direction and eventually tropical depression in Jiangxi at 5:00 PM on the same day, and 8.4 km away from the experimental 138 weakened into a tropical depression in Jiangxi at 5:00 PM on the same day, and 8.4 km away from building, as shown in Figure 3. The wind speed and direction were simultaneously monitored on the 139 the experimental building, as shown in Figure 3. The wind speed and direction were simultaneously roofs, and the sampling frequency was 25.6 Hz. The measurement began at 2:50 AM on 14th September 140 monitored on the roofs, and the sampling frequency was 25.6 Hz. The measurement began at 2:50 and stopped at 3:00 AM on 15th September due to the power failure of the experimental building 141 AM on 14th September and stopped at 3:00 AM on 15th September due to the power failure of the caused by the typhoon. The measured data were continuously recorded for 24 h. The measurement 142 experimental building caused by the typhoon. The measured data were continuously recorded for 24 of building B stopped at 8:50 PM on 14th September, and data were continuously recorded for 18 h. 143 h. The measurement of building B stopped at 8:50 PM on 14th September, and data were continuously The maximum instantaneous wind speed recorded was 68.2 m/s, which was measured on the roof of 144 recorded for 18 h. The maximum instantaneous wind speed recorded was 68.2 m/s, which was building C at 3:00 AM on 15th September. 145 measured on the roof of building C at 3:00 AM on 15th September. (a) (b) 146 Figure 3. Figure 3. Path Pathof Typhoon Meranti (2016) provide of Typhoon Meranti (2016) provided d by th by the e Re Regional gional Specia Specialized lized Meteoro Meteorological logical Center Center 147 Tokyo Tokyo.. ( (a a) ) The The moving track moving track du during ring Typhoon Typhoon Meranti; Meranti; ( (b b) ) T The he relati relationship onship between experi between experimental mental site site 148 and typhoon and typhoon. 4.2m 3m Appl. Sci. 2018, 8, x 5 of 23 Appl. Sci. 2019, 9, 367 5 of 22 149 3. Research Method for Wind Characteristics An anemometer can simultaneously measure the x and y axial wind speeds at a certain point, 3. Research Method for Wind Characteristics ut ut which are denoted as () and () , respectively. The wind speed statistical process in this x y An anemometer can simultaneously measure the x and y axial wind speeds at a certain point, study uses the vector decomposition method [16] to obtain the longitudinal and transverse horizontal which are denoted as u t and u t , respectively. The wind speed statistical process in this study uses ( ) ( ) x y components, as shown in Figure 4. Ten min is selected as the basic time interval in the statistical the vector decomposition method [16] to obtain the longitudinal and transverse horizontal components, analysis, the mean horizontal wind speed U and mean horizontal wind direction angle are as as shown in Figure 4. Ten min is selected as the basic time interval in the statistical analysis, the mean follows: horizontal wind speed U and mean horizontal wind direction angle f are as follows: Uu=+ ()t 2 u ()t 2 (1) xy U = u (t) + u (t) (1) x y cos(φ ) =ut ( ) /U (2) cos(f) = u (t)/U (2) where u (t) and u (t) are the mean values of the u (t) and u (t) samples at the basic time x x x y where ut () and ut () are the mean values of the ut and ut samples at the basic time () () x x x y interval, respectively. interval, respectively. Figure 4. Sketch map of wind speeds and directions. Figure 4. Sketch map of wind speeds and directions In the basic time interval, the horizontal longitudinal pulsating wind speed ut and In the basic time interval, the horizontal longitudinal pulsating wind speed u(t) and horizontal () longitudinal pulsating wind speed v(t) can be calculated using Formulas (3) and (4): vt horizontal longitudinal pulsating wind speed () can be calculated using Formulas (3) – (4): u(t) = u (t) cos f + u (t) sin f U (3) x y ut ()=+ u ()t cosφφ u (t)sin−U (3) xy v(t) = u (t) sin f + u (t) cos f (4) x y vt () =−u ()t sinφφ +u (t)cos (4) xy Turbulence intensity describes the degree to which wind speed changes with time and space, Turbulence intensity describes the degree to which wind speed changes with time and space, indicating the relative strength of pulsating wind. Turbulence intensity is often defined as the ratio of the indistandar cating the rela d deviation tive strength of of pulsating pul wind satinspe g wi ed nd. to Turbul the mean ence horizontal intensity is of wind ten speed defined u in a the s the ra 10 min tio of the standard deviation of pulsating wind speed to the mean horizontal wind speed u in the 10 min time interval. time interval. I = (i = u, v) (5) In the formula, s (I = u, v) is the standard deviation i of pulsating wind speeds u(t) and v(t) in the I==(, iuv) (5) analysis time interval. The gust factor reflects the ratio of gust wind speed to the mean wind speed and is often defined σ ut vt In the formula, (i = u, v) is the standard deviation of pulsating wind speeds () and () as the t ratio of the maximum mean wind speed in the gust duration (generally 3 s) to the mean horizontal in the analysis ti wind me speed interval u in the . analysis time interval (10 min), that is, The gust factor reflects the ratio of gust wind speed to the mean wind speed and is often defined max(u(t )) as the ratio of the maximum meaG n wind (t ) = spee 1 +d in the gust duration (generally 3 s) to the mean (6a) u g horizontal wind speed u in the analysis time interval (10 min), that is, max(v(t )) G (t ) = (6b) v g max(ut ( )) Gt()=+ 1 (6a) ug U Appl. Sci. 2019, 9, 367 6 of 22 where max(u(t )) and max(v(t )) represent the mean maximum wind speeds in the along-wind and g g cross-wind directions at time t , respectively. u(t ) = u(t) (7a) i=1 v(t ) = v(t) (7b) i=1 where N is the number of samples at time t . The turbulence integral scale is a measure of the mean size of the vortex in the air stream. On the basis of the Taylor hypothesis [17], this scale is expressed as L = R(t)dt (8) s 0 where L is the turbulent integral scale at the i(i = u, v) direction, m denotes the upper limit of the integral obtained from the point where the correlation coefficient drops to 0.05 and R(t) represents the autocorrelation functions of the pulsating wind speed. 4. Analysis of the Measured Fluctuating Wind Speed Data 4.1. Mean Wind Speed and Wind Direction Relevant 2D data on wind speed and direction are collected using R.M. Young 05103V-type propeller anemometers (R. M. Young Company, Michigan, US). The original data of high-rises A, B, and C are segmented into 146, 109, and 146 sub-samples based on the mean time interval of 10 min. Mean wind speed U and wind direction q are given in Figure 5. The mean wind speed and direction measured by the three anemometers were close, and the wind direction was discrete when the wind speed was low. The mean wind speed has a lower value 18 h before the typhoon landed, and it slowly fluctuates and increases. The wind direction was stable 6 h before the typhoon landed and the landing point of Typhoon Meranti (2016) was Xiamen. Northern hemisphere tropical cyclones rotate counter clockwise, and the wind direction slowly changed from northeast to north due to the landing location of the typhoon. The variation in the measured wind direction was consistent with this condition. As shown in the diagram, the maximum mean wind speeds measured on high-rises A, B, and C were 27.2, 15.6, and 28.9 m/s, respectively, with the mean wind directions ranging from 20 to 70 . Appl. Sci. 2018, 8, x 7 of 23 Appl. Sci. 2019, 9, 367 7 of 22 (a) (b) Figure 5. Comparison of the three high-rises in terms of their mean wind speed and direction with a 194 Figure 5. Comparison of the three high-rises in terms of their mean wind speed and direction with a time interval of 10 min. (a) Mean wind speed in 10 min; (b) Mean wind direction in 10 min. 195 time interval of 10 min. (a) Mean wind speed in 10 min; (b) Mean wind direction in 10 min. 4.2. Turbulence Intensity 196 4.2. Turbulence Intensity A comparison of the three high-rises in terms of turbulence in the along-wind and across-wind 197 A comparison of the three high-rises in terms of turbulence in the along-wind and across-wind directions (I and I ) is shown in Figure 6. Before 9:00 am on 14th September, the turbulence of buildings u v 198 directions (Iu and Iv) is shown in Figure 6. Before 9:00 am on 14th September, the turbulence of A and B was discrete, and the typhoon was far from the experimental building and had no effect on 199 buildings A and B was discrete, and the typhoon was far from the experimental building and had no it at that time. The three high-rises had similar turbulence in the middle stage, but the turbulence of 200 effect on it at that time. The three high-rises had similar turbulence in the middle stage, but the high-rise A increased in the late stage because the wind direction slowly moved northward, and a 201 turbulence of high-rise A increased in the late stage because the wind direction slowly moved super high-rise is located north of high-rise A. This super high-rise produced an interference effect on 202 northward, and a super high-rise is located north of high-rise A. This super high-rise produced an the three high-rises. 203 interference effect on the three high-rises. 204 Figures 7 and 8 show the relationships between turbulence intensity and mean wind speed and 205 between turbulence intensity and mean wind direction, respectively. The left side of the figures 206 presents the synchronously recorded data of buildings A, B, and C. The right side of the figures Appl. Sci. 2018, 8, x 8 of 23 207 displays the synchronously recorded data of buildings A and C when building B experienced power 208 outage. The upper right corner of the figures exhibits the sample chart of wind speed and direction. 209 The left side of Figure 7 shows that when U < 10 m/s, the turbulence intensity of buildings A and 210 B decreases with the increase in mean wind speed, whereas the turbulence intensity of building C 211 does not change with the increase in mean wind speed. When U ≥ 10 m/s, the turbulence intensity of 212 the three buildings changes by the same law and decreases with the increase in mean wind speed. 213 The right side of Figure 7 indicates that the turbulence intensity of building A increases with the wind 214 speed. When the mean wind speed reaches 19 m/s, the turbulence intensity does not change with the 215 increase in mean wind speed. When the mean wind speed reaches 25 m/s, the turbulence intensity 216 decreases with the increase in mean wind speed. The turbulence intensity of building C decreases 217 with the increase in wind speed. At 19 m/s < U < 25 m/s, the turbulence intensity does not change 218 with the increase in mean wind speed, and the mean values of the longitudinal and transverse 219 turbulence intensity are 0.14 and 0.11, respectively. When U ≥ 25 m/s, the turbulence intensity 220 increases with the mean wind speed, and the along-wind and cross-wind turbulence intensities are 221 0.19 and 0.15, respectively. In this process, the wind direction angle slowly changes from 55° to 20°, 222 and the wind speed slowly increases. Meanwhile, the law of building A is completely different from 223 that of building C because a super high-rise building is situated north of building A, imposing an 224 interference effect of the upstream building, which will be considered in the next work through a 225 wind tunnel test. 226 The left side of Figure 8 shows that the turbulence intensity of buildings A and B does not change 227 with the increase in mean wind direction angle, thereby presenting a great dispersion. The turbulence 228 intensity of building C increases with the mean wind direction angle θ. Between θ ∈ (40°, 45°), 229 buildings A and C have further intersections at the turbulence intensity sample. The right side of 230 Figure 8 indicates that the turbulence of building A decreases with the increase in mean wind 231 direction angle θ, and the turbulence intensity remains stable and constant when θ > 40°. The 232 turbulence intensity of building C decreases first and then increases with the mean wind direction 233 angle. The inflection point interval is located between the wind direction angles θ∈ (35°, 45°). The 234 mean values of the along-wind and cross-wind turbulence intensity of building A are 0.14 and 0.13, 235 respectively, whereas those of building C are 0.15 and 0.13, respectively. 236 Table 1 shows the comparison of along-wind direction turbulence intensity between Chinese 237 code (GB50009-2012) and field measurements, respectively. The turbulence intensity in the along- 238 wind direction of three high-rises ranged from 17.7% to 30.8%, which is greater than the value 239 specified in a relevant standard (GB50009-2012) in China when the terrain category changed from Appl. Sci. 2019, 9, 367 8 of 22 240 Class A to Class D. This change can be explained by the interference in the building cluster. Appl. Sci. 2018, 8, x 9 of 23 (a) (b) Figure 6. Comparison of wind fields on the roofs of the three high-rises in terms of turbulence. (a) 241 Figure 6. Comparison of wind fields on the roofs of the three high-rises in terms of turbulence. (a) Longitudinal turbulence intensities; (b) Lateral turbulence intensities. 242 Longitudinal turbulence intensities; (b) Lateral turbulence intensities. Figures 7 and 8 show the relationships between turbulence intensity and mean wind speed and between turbulence intensity and mean wind direction, respectively. The left side of the figures presents the synchronously recorded data of buildings A, B, and C. The right side of the figures displays the synchronously recorded data of buildings A and C when building B experienced power outage. The upper right corner of the figures exhibits the sample chart of wind speed and direction. The left side of Figure 7 shows that when U < 10 m/s, the turbulence intensity of buildings A and B decreases with the increase in mean wind speed, whereas the turbulence intensity of building C does not change with the increase in mean wind speed. When U 10 m/s, the turbulence intensity of the three buildings changes by the same law and decreases with the increase in mean wind speed. The right side of Figure 7 indicates that the turbulence intensity of building A increases with the wind speed. When the mean wind speed reaches 19 m/s, the turbulence intensity does not change with the increase in mean wind speed. When the mean wind speed reaches 25 m/s, the turbulence intensity decreases with the increase in mean wind speed. The turbulence intensity of building C decreases with (a) (b) 243 Figure 7. Variation in turbulence intensities with 10 min mean wind speed. (a) Longitudinal 244 turbulence intensities; (b) Lateral turbulence intensities. Appl. Sci. 2018, 8, x 9 of 23 Appl. Sci. 2019, 9, 367 9 of 22 the increase in wind speed. At 19 m/s < U < 25 m/s, the turbulence intensity does not change with the increase in mean wind speed, and the mean values of the longitudinal and transverse turbulence intensity are 0.14 and 0.11, respectively. When U 25 m/s, the turbulence intensity increases with the mean wind speed, and the along-wind and cross-wind turbulence intensities are 0.19 and 0.15, (b) respectively. In this process, the wind direction angle slowly changes from 55 to 20 , and the wind speed slowly increases. Meanwhile, the law of building A is completely different from that of building 241 Figure 6. Comparison of wind fields on the roofs of the three high-rises in terms of turbulence. (a) C because a super high-rise building is situated north of building A, imposing an interference effect of 242 Longitudinal turbulence intensities; (b) Lateral turbulence intensities. the upstream building, which will be considered in the next work through a wind tunnel test. (a) (b) 243 Figure 7. Variation in turbulence intensities with 10 min mean wind speed. (a) Longitudinal Figure 7. Variation in turbulence intensities with 10 min mean wind speed. (a) Longitudinal turbulence 244 turbulence intensities; (b) Lateral turbulence intensities. intensities; (b) Lateral turbulence intensities. The left side of Figure 8 shows that the turbulence intensity of buildings A and B does not change with the increase in mean wind direction angle, thereby presenting a great dispersion. The turbulence intensity of building C increases with the mean wind direction angle q. Between q 2 (40 , 45 ), buildings A and C have further intersections at the turbulence intensity sample. The right side of Figure 8 indicates that the turbulence of building A decreases with the increase in mean wind direction angle q, and the turbulence intensity remains stable and constant when q > 40 . The turbulence intensity of building C decreases first and then increases with the mean wind direction angle. The inflection point interval is located between the wind direction angles q 2 (35 , 45 ). The mean values of the along-wind and cross-wind turbulence intensity of building A are 0.14 and 0.13, respectively, whereas those of building C are 0.15 and 0.13, respectively. Table 1 shows the comparison of along-wind direction turbulence intensity between Chinese code (GB50009-2012) and field measurements, respectively. The turbulence intensity in the along-wind direction of three high-rises ranged from 17.7% to 30.8%, which is greater than the value specified in a Appl. Sci. 2019, 9, 367 10 of 22 relevant standard (GB50009-2012) in China when the terrain category changed from Class A to Class Appl. Sci. 2018, 8, x 10 of 23 D. This change can be explained by the interference in the building cluster. (a) (b) 245 Figure Figure 8. 8. Variation Variation in tu in turbulence rbulence intensit intensities ies with 10 m with 10 min in m mean ean wind direction. wind direction. (a) (a Lo ) Longitud ngitudinal inal 246 turbulence intensities; (b) Lateral turbulence intensities. turbulence intensities; (b) Lateral turbulence intensities. Table 1. Comparison of longitudinal turbulence intensity between Chinese load code for the design of 247 Table 1. Comparison of longitudinal turbulence intensity between Chinese load code for the design building and field measurements. 248 of building and field measurements. Mean Longitudinal Class D Class C Class B Class A Periods Building Samples Mean longitudinal Class D Class C Class B Class A Turbulence Intensity Terrain Terrain Terrain Terrain Periods Building Samples turbulence intensity Terrain Terrain Terrain Terrain Building A 109 30.4% Building 109 30.4% Building B 109 30.8% Three sites Building C 109 19.4% 17.3% 12.6% 9.3% 8.6% Three Building 109 30.8% Building A 37 20.3% sites B Two sites Building C 37 17.7% Building 109 19.4% 17.3% 12.6% 9.3% 8.6% 4.3. Gust Factor Building 37 20.3% Two A Figures 9 and 10 present the relationship between gust factors and mean wind speed and between sites Building 37 17.7% gust factors and mean wind direction, respectively. The left side of the figure shows the synchronously recorded data of buildings A, B, and C. The right side of the figure exhibits the synchronously recorded 249 4.3. Gust Factor data of buildings A and C when building B experiences power outage. The line with an ordinate of 1 is used to distinguish the longitudinal and transverse gust factors (G and G ). In the selected u v 250 Figure 9 and 10 present the relationship between gust factors and mean wind speed and between samples, the gust duration is 3 s, and Table 2 shows the mean of the gust factors of the three buildings 251 gust factors and mean wind direction, respectively. The left side of the figure shows the in two phases. 252 synchronously recorded data of buildings A, B, and C. The right side of the figure exhibits the 253 synchronously recorded data of buildings A and C when building B experiences power outage. The 254 line with an ordinate of 1 is used to distinguish the longitudinal and transverse gust factors (Gu and Appl. Sci. 2018, 8, x 11 of 23 Appl. Sci. 2018, 8, x 11 of 23 255 Gv). In the selected samples, the gust duration is 3 s, and Table 2 shows the mean of the gust factors 255 Gv). In the selected samples, the gust duration is 3 s, and Table 2 shows the mean of the gust factors 256 of the three buildings in two phases. 256 of the three buildings in two phases. 257 The left side of Figure 9 illustrates that the change law of gust factor with the mean wind speed 257 The left side of Figure 9 illustrates that the change law of gust factor with the mean wind speed 258 258 UU is ne is ne ar ar ly ly id id entical with t entical with t hh at of turbule at of turbulen nce. When ce. When U U < < 10 m/s, the 10 m/s, the gust gust factor factors o s off bu build ilding ingss A A and B and B 259 259 decrease with decrease with the increase the increase in mean win in mean win d d speed, wher speed, where ea as s t th he e g gu us st t f fa ac ct to or r o of f b bu uiilld diin ng g C C d do o e e s s n n o o tt c c h h a a n n g g ee 260 260 with with the incr the incr ease ease in in me me an an wind speed. When wind speed. When U U ≥≥ 1 10 0 m m//s s,, t th he e c ch ha an ng ge e lla aw w o off g gu usstt f fa acctto orr i in n t th hee t thhrr ee ee 261 261 build build ing ing s s is is c c oo nsist nsist ee nt nt and and decrea decrea ses ses wit wit h h incre increa as siing ng mean w mean wi ind nd s sp peed, b eed, bu ut t t th he e change change speed speed is is s s ll ow. ow. 262 The right side of Figure 9 shows that the along-wind gust factor of building A increases first and then 262 The right side of Figure 9 shows that the along-wind gust factor of building A increases first and then 263 decreases, and the maximum value is 1.73 when U = 19 m/s. The cross-wind gust factor of building 263 decreases, and the maximum value is 1.73 when U = 19 m/s. The cross-wind gust factor of building 264 A, the along-wind gust factor of building C and the cross-wind gust factor do not change with the 264 A, the along-wind gust factor of building C and the cross-wind gust factor do not change with the 265 increase in mean wind speed. Figure 10 indicates that the change law of gust factor with the mean 265 increase in mean wind speed. Figure 10 indicates that the change law of gust factor with the mean 266 wind speed is nearly identical with the change law of turbulence. 266 wind speed is nearly identical with the change law of turbulence. 267 The analysis of Figures 7–10 presents that the turbulence and gust factors obtained by 267 The analysis of Figures 7–10 presents that the turbulence and gust factors obtained by 268 investigating the samples at U ≥ 10 m/s are reasonable. The gust factors that meet the requirements 268 investigating the samples at U ≥ 10 m/s are reasonable. The gust factors that meet the requirements 269 are evaluated statistically. The mean longitudinal and transverse gust coefficients at the top of 269 are evaluated statistically. The mean longitudinal and transverse gust coefficients at the top of 270 building A (102 samples) are 1.428 and 0.356, those at the top of building B (63 samples) are 1.485 and 270 building A (102 samples) are 1.428 and 0.356, those at the top of building B (63 samples) are 1.485 and Appl. Sci. 2019, 9, 367 11 of 22 271 0.351 and those at the top of building C (96 samples) are 1.319 and 0.225, respectively. 271 0.351 and those at the top of building C (96 samples) are 1.319 and 0.225, respectively. 273 Figure 9. Variation in gust factor with 10 min mean wind direction. Figure 9. Variation in gust factor with 10 min mean wind direction. 273 Figure 9. Variation in gust factor with 10 min mean wind direction. Figure 10. Variation in gust factor with 10 min mean wind direction. 275 Figure 10. Variation in gust factor with 10 min mean wind direction. 275 Figure 10. Variation in gust factor with 10 min mean wind direction. Table 2. Mean gust factor of two periods. 276 Table 2. Mean gust factor of two periods. 276 Table 2. Mean gust factor of two periods. Mean Longitudinal Mean Lateral Periods Building Samples Mean Longitudinal Gust Factor Mean Lateral Gust Factor Periods Building Samples Gust Factor Gust Factor Three site Periods s Building Building A Samples 65 Mean Longitudinal G 1.64 ust Factor Mean Lateral 0.44Gust Factor Building A 65 1.64 0.44 Three sites Building A 65 1.64 0.44 Building B 63 1.59 0.40 Three sites Building C 59 1.35 0.24 Building A 37 1.42 0.35 Two sites Building C 37 1.28 0.20 The left side of Figure 9 illustrates that the change law of gust factor with the mean wind speed U is nearly identical with that of turbulence. When U < 10 m/s, the gust factors of buildings A and B decrease with the increase in mean wind speed, whereas the gust factor of building C does not change with the increase in mean wind speed. When U 10 m/s, the change law of gust factor in the three buildings is consistent and decreases with increasing mean wind speed, but the change speed is slow. The right side of Figure 9 shows that the along-wind gust factor of building A increases first and then decreases, and the maximum value is 1.73 when U = 19 m/s. The cross-wind gust factor of building A, the along-wind gust factor of building C and the cross-wind gust factor do not change with the increase in mean wind speed. Figure 10 indicates that the change law of gust factor with the mean wind speed is nearly identical with the change law of turbulence. The analysis of Figures 7–10 presents that the turbulence and gust factors obtained by investigating the samples at U 10 m/s are reasonable. The gust factors that meet the requirements are Appl. Sci. 2018, 8, x 12 of 23 Appl. Sci. 2019, 9, 367 12 of 22 Building B 63 1.59 0.40 Building C 59 1.35 0.24 evaluated statistically. The mean longitudinal and transverse gust coefficients at the top of building A Building A 37 1.42 0.35 (102 samples) are 1.428 and 0.356, those at the top of building B (63 samples) are 1.485 and 0.351 and Two sites Building C 37 1.28 0.20 those at the top of building C (96 samples) are 1.319 and 0.225, respectively. 277 4.4. Turbulence Integral Scale 4.4. Turbulence Integral Scale 278 The turbulent integral length scale statistical analysis of the data of mean wind speed U ≥ 10 m/s The turbulent integral length scale statistical analysis of the data of mean wind speed U 10 m/s 279 was performed as shown in Figures 11 and 12. Table 3 presents the mean value of the turbulent was performed as shown in Figures 11 and 12. Table 3 presents the mean value of the turbulent integral 280 integral scale for the two cycles. The along-wind turbulent integral scale distribution area of building scale for the two cycles. The along-wind turbulent integral scale distribution area of building A is 281 A is (115 m, 636 m), that of building B is (10 m, 524 m), and that of building C is (102 m, 403 m). All (115 m, 636 m), that of building B is (10 m, 524 m), and that of building C is (102 m, 403 m). All of them 282 of them show a large dispersion. No relevant provisions in the Chinese specification can be used to show a large dispersion. No relevant provisions in the Chinese specification can be used to predict 283 predict the turbulence integral length scales, but the values estimated by ASCE-7 and AIJ-2004 are the turbulence integral length scales, but the values estimated by ASCE-7 and AIJ-2004 are 277.9 m 1/8 0.5 284 277.9 m (Sea, Lu = 198.12 x (150/10) = 277.9 m) and 223.6 m (Lu = 100 x (150/30) = 223.6 m), 1/8 0.5 (Sea, Lu = 198.12 x (150/10) = 277.9 m) and 223.6 m (Lu = 100 x (150/30) = 223.6 m), respectively. 285 respectively. These values are comparable to the measured values of buildings A and C. The left side These values are comparable to the measured values of buildings A and C. The left side of Figure 12 286 of Figure 12 shows that the mean wind direction angle of building B is θ ∈ (39°, 51°), and no shows that the mean wind direction angle of building B is q 2 (39 , 51 ), and no interference in the 287 interference in the upstream of building B exists within this wind direction angle. According to Kwok upstream of building B exists within this wind direction angle. According to Kwok and Khandurid, 288 and Khandurid, when the plane size of the building is similar, aerodynamic interference occurs when the plane size of the building is similar, aerodynamic interference occurs between buildings, and 289 between buildings, and the plane size of the three buildings are the same [18-19]. Building B is in the 290 themiddle position, which expla plane size of the three buildings ins why areit the s turb same ulence [18,integra 19]. Building l scale iB s smal is in ler than those of the other the middle position, which 291 explains two build why ing its s. turbulence integral scale is smaller than those of the other two buildings. (a) (b) Figure 11. Variation in turbulence integral length scales with 10 min mean wind speed. (a) Longitudinal turbulence intensities; (b) Lateral turbulence intensities. Appl. Sci. 2018, 8, x 13 of 23 292 Figure 11. Variation in turbulence integral length scales with 10 min mean wind speed. (a) 293 Longitudinal turbulence intensities; (b) Lateral turbulence intensities. Appl. Sci. 2019, 9, 367 13 of 22 (a) (b) 294 Figure Figure 12. 12. Variation in tu Variation in turbulence rbulence integ integral ral leng length th scale scaless with with 10 m 10 min in m mean ean wind di wind dirrection. ection. (a (a) ) 295 Longitudinal Longitudinal t turbulence urbulence intensities intensities;; ((b) b) Lateral Lateral turbulence intensities. turbulence intensities. Table 3. Mean gust factor of two periods. 296 Table 3. Mean gust factor of two periods. Mean Longitudinal Mean Lateral Mean longitudinal turbulence Mean lateral turbulence Periods Building Samples Periods Building Samples Turbulence Integral Turbulence Integral integral length scales (m) integral length scales (m) Length Scales (m) Length Scales (m) Building 65 306 130 Building A 65 306 130 Three sites Building B 63 164 46 Three Building 63 164 46 Building C 59 231 49 sites B Building A 37 260 149 Building Two sites 59 231 49 Building C 37 224 55 Building 37 260 149 5. Analysis of Fluctuating Parameters Two sites Building 37 224 55 Continuous strong wind data from 9:00 AM on 14th September to 3:00 AM on 15th September are analyzed in detail. These data with high wind speed can help explain the turbulence characteristics. An environment with a low mean speed is conducive for free convection, which may introduce 297 5. Analysis of Fluctuating Parameters additional turbulence records and increase the deviation from the mean value. Moreover, several requirements should be met to obtain reasonable results. Based on the results of the previous analysis, data are selected for analysis at the mean wind speed U 10 m/s. When three measuring points are Appl. Sci. 2019, 9, 367 14 of 22 collected at the same time, three the mean wind speed is U < 16 m/s, and the samples of Building A, B, and C are 11, 10, and 9, respectively; when only two measuring points are collected at the same time, there are two samples of mean wind speed of Building A; 10 m/s U < 16 m/s, 4 samples of U 16 m/s; and 2 samples of Building C; 10 m/s U < 16 m/s, and 4 samples with U 16 m/s. Therefore, in Section 5, the main components of 10 m/s U <16 m/s and U 16 m/s are analyzed. Under the conditions determined by long time interval (1 h), the low wind speed section (10 m/s U < 16 m/s) and high wind speed section (U 16 m/s) are discussed. The difference in the observation period of the three buildings is not considered in Section 5, mainly because the low-speed section contained the whole process of simultaneous acquisition of three measuring points, while the high-speed section only had two simultaneous measuring points. 5.1. Relations Between Fluctuating Parameters Turbulence intensity and Gust factor are two important parameters in determining the fluctuating wind speed component. On the basis of the wind field of the typhoon investigated by Choi [20] and Ishizaki [21], Cao et al. established a standardized empirical expression for describing the relations between the gust factor and longitudinal turbulence intensity [1], which is: T T k 1 k 1 2 4 G t = 1 + k I ln , G t = k I ln (9) u g v g 1 u 3 v t t g g where k and k are two parameters and average time interval T is set to 10 min. Choi suggested that k = 0.62 and k = 1.27, whereas Ishizaki stated that k = 0.5 and k = 1.0. 1 2 1 2 Many field measurements have revealed linear relations between the gust factor and longitudinal turbulence intensity, which means k = 1.0 is widely accepted [22–25]. Gu et al. [23] conducted a statistical analysis by comparing fitting parameter k with Equation (9) or the constant 1, and the results show that the calculations of the two methods are nearly identical. In this study, a linear fitting method was used to determine the relations amongst the gust factors, longitudinal turbulence intensity, and lateral turbulence intensity, which are defined as follows: T T G t = 1 + k I ln , G t = k I ln (10) u g u u v g v v t t g g The fitting results of Equations (9) and (10) are shown in Figure 13, and the fitting parameters are shown in Table 4. As indicated in the graph, the Gust factor increased with turbulence intensity, and the fitting curve patterns of Equations (9) and (10) are not very different. However, the fitting curve patterns of Equation (9) are different from the values given by Choi and Ishizaki. By contrast, Equation (10) only considers a single parameter, and the fitting parameters of the three high-rises are in good agreement with the value of 0.42 proposed by Erich [26]. Thus, the relations between the gust factor and turbulence can be easily fitted using Equation (10). The mean values of k and k are 0.356 and u v 0.342, respectively. Table 4. Fitted parameters of the two equations. Building Equation (1) Equation (2) A k = 0.333 k = 1.851 k = 0.382 1 2 longitudinal B k = 0.349 k = 1.978 k = 0.357 1 2 C k = 0.380 k = 2.087 k = 0.330 1 2 A K = 0.258 K = 1.711 k = 0.397 3 4 v B K = 0.300 K = 1.898 k = 0.348 lateral 3 4 v C K = 0.200 K = 1.814 k = 0.282 3 4 v Appl. Sci. 2018, 8, x 15 of 23 Appl. Sci. 2019, 9, 367 15 of 22 (a) (b) 335 Figure Figure 13. 13. ( (a a, , b) b) T Tu urbulence rbulence intensity intensityagainst againstgust gust factor: factor: ( (a) a) and and (b) (b) are are sca scatter tter plot plots s an and d f fitting itting resu results lts 336 r respectiv espective e for for t the he long longitudinal itudinal and la and lateral teral dir dir ection. ection. 5.2. Relations Between Fluctuating Parameters and Gust Duration 337 Table 4. Fitted parameters of the two equations. There are limited field measurements studying the relations between the fluctuating parameters Building Equation (1) Equation (2) and gust duration. Durst revealed the statistical relations between turbulence intensity and gust factor A k1 = 0.333 k2 = 1.851 ku = 0.382 under different gust durations and the corresponding mean hourly wind speeds for open and flat longitudinal B k1 = 0.349 k2 = 1.978 ku = 0.357 terrains [27]. Krayer and Marshall determined the variation in longitudinal turbulence intensity with C k1 = 0.380 k2 = 2.087 ku = 0.330 time interval based on measured results [28]. Yu and Gan obtained the Gust factor and turbulence for a A K3 = 0.258 K4 = 1.711 kv = 0.397 subsurface tropical cyclone and evaluated the variations with terrain roughness and gust duration [29]. lateral B K3 = 0.300 K4 = 1.898 kv = 0.348 On the basis of wind field records on the roof of Shanghai World Financial Centre, An et al. presented C K3 = 0.200 K4 = 1.814 kv = 0.282 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, 338 5.2. Relations Between Fluctuating Parameters and Gust Duration such as turbulence intensity, gust factor, and peak factor, with the long-time interval (T). The expression 339 There are limited field measurements studying the relations between the fluctuating parameters for the longitudinal gust factor and turbulence intensity for a specific short-time interval is 340 and gust duration. Durst revealed the statistical relations between turbulence intensity and gust 341 factor under different gust durations and the corresponding mean hourly wind speeds for open and Appl. Sci. 2019, 9, 367 16 of 22 G (T, t) = u (T, t)/U(T) (11) u max u (t)/(N 1) i=1 SD (T, t) = (12) U(T) In Equation (11), u T, t indicates the longitudinal fluctuating wind within basic time interval ( ) max 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 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 T, t approximates turbulence I , as previously described. In addition, in G T, t and SD T, t , ( ) ( ) ( ) u u u u 0 0 by replacing u with v , the gust factor in the across-wind direction G (T, t) and turbulence SD (T, t) v v 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 and G ) are shown in Figures 14 and 15. u u 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. Appl. Sci. 2018, 8, x 17 of 23 Appl. Sci. 2019, 9, 367 17 of 22 (a) (b) 373 Figure 14. Comparison of the three high-rises with turbulence and gust factor varying with gust Figure 14. Comparison of the three high-rises with turbulence and gust factor varying with gust duration and wind speed. (a) Estimated values of SSD D (T() T , t,)t; (b) Estimated values of SSD D (T() T , t,)t. u v u v 374 duration and wind speed. (a) Estimated values of ; (b) Estimated values of . Appl. Sci. 2018, 8, x 18 of 23 Appl. Sci. 2019, 9, 367 18 of 22 (a) (b) 375 Figure 15. Comparison of the three high-rises with turbulence and gust factor varying with gust Figure 15. Comparison of the three high-rises with turbulence and gust factor varying with gust GT ,t GT ,t duration and wind speed. (a) Estimated values of G (T() , t), (b) Estimated values of G (T() , t). u v u v 376 duration and wind speed. (a) Estimated values of , (b) Estimated values of . 5.3. Wind Speed Spectrum 377 5.3. Wind Speed Spectrum Successive measured data at the same time with U 10 m/s are given in Figure 4 to plot the 378 Successive measured data at the same time with U ≥ 10 m/s are given in Figure 4(a) to plot the fluctuating wind speed spectrum. In this study, a Welch power spectrum estimation method is 379 fluctuating wind speed spectrum. In this study, a Welch power spectrum estimation method is adopted for the analysis. The longitudinal wind speed spectrum of the three high-rises is shown 380 adopted for the analysis. The longitudinal wind speed spectrum of the three high-rises is shown in in Figure 16. The x-axis coordinate indicates the reference frequency (fz/u), and the y-coordinate 381 Figure 16. The x-axis coordinate indicates the reference frequency (fz/u), and the y-coordinate indicates the normalized fluctuating wind speed spectrum. The spectrum is compared with the 382 indicates the normalized fluctuating wind speed spectrum. The spectrum is compared with the von von Karman fluctuating wind speed spectrum. The results show that the fluctuating wind speed 383 Karman fluctuating wind speed spectrum. The results show that the fluctuating wind speed spectra spectra of buildings A and C in the along-wind direction effectively fitted the von Karman model. 384 of buildings A and C in the along-wind direction effectively fitted the von Karman model. The The fluctuating wind speed spectrum of building B in the along-wind direction is higher than that of 385 fluctuating wind speed spectrum of building B in the along-wind direction is higher than that of the the von Karman model when the reference frequency is larger than 0.2. This phenomenon results from 386 von Karman model when the reference frequency is larger than 0.2. This phenomenon results from the interference of building B being located between building A and C. This finding will be discussed in subsequent studies. Appl. Sci. 2018, 8, x 20 of 24 Appl. Sci. 2019, 9, 367 19 of 22 (a) (b) (c) Figure 16. Wind speed spectra of the three high-rises in the along-wind direction. (a) Building A; (b) Building B; (c) Building C. Appl. Sci. 2018, 8, x 20 of 23 (c) 389 Figure 16. Wind speed spectra of the three high-rises in the along-wind direction. (a) Building A; (b) 390 Building B; (c) Building C. Appl. Sci. 2019, 9, 367 20 of 22 391 5.4. Relativity of Wind Turbulence 5.4. Relativity of Wind Turbulence The relativity of wind speed at two spatial points may be described with the spatial correlation The relativity of wind speed at two spatial points may be described with the spatial correlation Coh n coefficient. In this study, spatial correlation coefficient and coherence function () x x xx AB AB coefficient. In this study, spatial correlation coefficient r and coherence function Coh n on ( ) x x x x A B A B on the roofs of high-rises A and B are investigated and defined as follows: the roofs of high-rises A and B are investigated and defined as follows: Exx [ ] A B ρ = E[x x ] xx A B (13) A B r = p (13) x x Exx E x x A B [] [ ] AA B B E[x x ]E[x x ] A A B B E ⋅ where, x can be substituted by two corresponding fluctuating speed components u, v and [ ] is where, x can be substituted by two corresponding fluctuating speed components u, v and E[] is the the calculation symbol of the average. calculation symbol of the average. 397 With the mean wind speed on the roof of building A as a reference, the relations between With the mean wind speed on the roof of building A as a reference, the relations between building 398 building A and B in the spatial correlation coefficient for wind speed and mean wind speed are shown A and B in the spatial correlation coefficient for wind speed and mean wind speed are shown in 399 in Figure 17. The spatial correlation coefficient for the fluctuating wind speed in the along-wind Figure 17. The spatial correlation coefficient for the fluctuating wind speed in the along-wind direction 400 direction increased with the mean wind speed. The data within the upper and lower boundaries in increased with the mean wind speed. The data within the upper and lower boundaries in the graph 401 the graph are fitted in linearly, the spatial correlation coefficient for the fluctuating wind speed in the are fitted in linearly, the spatial correlation coefficient for the fluctuating wind speed in the across-wind 402 across-wind direction hardly changed with the mean wind speed, and the linearly-fitted slope direction hardly changed with the mean wind speed, and the linearly-fitted slope approached zero. 403 approached zero. The correlation coefficient for the wind speed in the along-wind direction The correlation coefficient for the wind speed in the along-wind direction depended on the wind speed, 404 depended on the wind speed, and the higher the wind speed is, the greater the correlation coefficient and the higher the wind speed is, the greater the correlation coefficient is. However, the correlation 405 is. However, the correlation coefficient in the across-wind direction was basically irrelevant to the coefficient in the across-wind direction was basically irrelevant to the wind speed, and the mean 406 wind speed, and the mean value of the spatial correlation coefficient for the wind speed on the roofs value of the spatial correlation coefficient for the wind speed on the roofs of building A and B in the 407 of building A and B in the across-wind direction is approximately 0.10. across-wind direction is approximately 0.10. (a) (b) 408 Figure 17. Relations between spatial correlation coefficients for wind speed on the roofs of high-rises Figure 17. Relations between spatial correlation coefficients for wind speed on the roofs of high-rises 409 A and B and mean wind speed. (a) Longitudinal spatial correlation coefficient; (b) Lateral spatial A and B and mean wind speed. (a) Longitudinal spatial correlation coefficient; (b) Lateral spatial 410 correlation coefficient. correlation coefficient. 411 6. Conclusions 6. Conclusions 412 The wind fields characteristics on the roofs of three adjacent buildings were measured during The wind fields characteristics on the roofs of three adjacent buildings were measured during 413 Typhoon Meranti on the east coast of Xiamen, China to analyze the fluctuating features of the selected Typhoon Meranti on the east coast of Xiamen, China to analyze the fluctuating features of the 414 strong wind data in detail and investigate the relations among the high-rises in wind speed. The selected strong wind data in detail and investigate the relations among the high-rises in wind speed. 415 conclusions of this study are summarized as follows: The conclusions of this study are summarized as follows: 416 (1) The three high-rise buildings have similar mean values of measured mean wind speed and (1) The three high-rise buildings have similar mean values of measured mean wind speed and 417 direction, which enabled a comparison of the wind characteristics. The maximum mean wind speeds direction, which enabled a comparison of the wind characteristics. The maximum mean wind speeds 418 on the roofs of the buildings are 27.2, 15.6, and 28.9 m/s, respectively. on the roofs of the buildings are 27.2, 15.6, and 28.9 m/s, respectively. (2) The analysis period was divided into two parts. The characteristics of the winds were investigated separately of part one for the three sites (A, B, C) and part two for two sites (A, C). Reasonable results of turbulence intensity and gust factor were obtained based on the statistics of Appl. Sci. 2019, 9, 367 21 of 22 sampling with mean wind speed higher than 10 m/s. When U 10m/s of the synchronously recorded of buildings A, B, and C, the turbulence intensity of the three buildings changed by the same law and decreased with the increase of mean wind speed. When buildings A and C were synchronously recorded, the wind direction angle slowly changed from 55 to 20 , and the wind speed slowly increased. Meanwhile, the law of building A is completely different from building C because of a super high-rise building situated north of building A. This imposed an interference effect on the upstream building, which will be considered in the next work through a wind tunnel test. The turbulence intensity on the roof of three high-rises in the along-wind direction are between 17.7% and 30.8% and greater than the terrain as specified in a relevant Chinese load (GB50009-2012) changing from Class A to D. This result can be explained by the interference in the building cluster. The mean longitudinal and lateral gust factors for building A were 1.428 and 0.356, 1.485 and 0.351 for building B, and 1.319 and 0.225 for building C. The along-wind turbulent integral scale distribution area of building A is (115 m, 636 m), building B is (10 m, 524 m), and building C is (102 m, 403 m). The measured values of buildings A and C were consistent with the values estimated by ASCE-7 and AIJ-2004. When the plane size of the buildings is similar, aerodynamic interference occurs between buildings, and the plane size of the three buildings are the same. Building B is between two buildings which explains its small turbulence integral scale. (3) The relations between gust factor and turbulence intensity were investigated. The gust factor increases with increasing turbulence intensity. The relations are fitted by using two methods, and small differences are observed. The parameters for the linear fitting method are simple and easy to compare with other results. In addition, the variations in turbulence intensity and gust factor with gust duration were evaluated. The fitting parameters k and k , recommended as 0.356 and 0.342, are mainly affected u v by short-term wind fluctuation. (4) The wind spectrum of two high-rises is plotted and compared with the von Karman model. The wind spectrum in the longitudinal direction agrees with the von Karman model. (5) The spatial correlation in wind speed between buildings A and B is evaluated. Wind speed remarkably affected the spatial correlation coefficient for longitudinal fluctuating wind speed. 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