- Email: [email protected]
Field measurement study on turbulence field by wind tower and Windcube Lidar in mountain valley
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
Contents lists available at ScienceDirect
Journal of Wind Engineering & Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia
Field measurement study on turbulence field by wind tower and Windcube Lidar in mountain valley Haili Liao a, b, Hongmiao Jing a, Cunming Ma a, b, *, Qiyu Tao c, Zhiguo Li a, b a b c
Research Center for Wind Engineering, Southwest Jiaotong University, Chengdu, China Wind Engineering Key Laboratory of Sichuan Province, Chengdu, China Highway Planning, Survey, Design and Research Institute, Department of Transport, Sichuan Province, Chengdu, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Field measurement Ultrasonic anemometer Windcube Lidar Bridge site in mountain valley Turbulence intensity Turbulent spectrum Spatial coherence
Due to the complexity of turbulence in mountain valley and lack of research focusing on such type of turbulence fields, which are critical for both buffeting response and vortex induced vibration (VIV) in slender structures, this paper aims to enhance the understanding of turbulence fields in mountain valley by investigating field measurement wind data obtained by a wind tower and a Windcube Lidar. Turbulence intensity, turbulent spectrum and vertical spatial coherence are obtained and analyzed according to the continuous measured data, which are significantly influenced by mountain terrain. Some of these characteristics are compared with current recommended specifications, standards and empirical formulas. The results indicate that turbulence intensity (e.g. probability density function (PDF) distribution, variation with mean wind speed and height) in mountain valley are very different from those recommended by the specifications and standards. It is identified that the Simiu and Panofsky spectral models could induce large discrepancies for mountain valley terrain in China Southwest, while the von Karman spectral models can still well indicate such terrains. Furthermore, the vertical spatial coherences can be accurately expressed by some empirical coherence formulas for a mountain valley, but it is not feasible to adopt empirical coherence formulas with fixed parameters to represent the realistic coherence at different heights in a mountain valley. Meanwhile, the results have a general applicability for the determination of wind characteristics in the mountain areas of China Southwest.
1. Introduction It is of great interest to investigate the wind characteristics of the atmospheric boundary layer (ABL) in mountain areas as the knowledge has applications in many engineering practices. In recent decades, a large number of infra projects (such as long-span bridges and wind turbines) have been built in mountain valleys of southwestern China, and wind loads have been regarded as one of the dominant factors determining their safety and serviceability. Furthermore, since bridge girders and towers for bridges crossing mountain valleys tend to be respectively very long and tall, they are relatively weak and sensitive to wind effects (Ma et al., 2018, 2019; Wang et al., 2019; Wu et al., 2020). For example, the turbulence intensity, which plays a key role in buffeting response and VIV for slender structures, could be relatively large and variable due to the complex mountain terrain. In particular, vertical variation of turbulence intensity is strongly related to the buffeting response of high-rise structures such as bridge towers and wind turbines built in mountain valleys
(Li et al., 2019). For convenience, winds within ABL are usually divided into two parts: mean wind and fluctuating wind. Mean wind is associated with aerodynamic stability, while fluctuating wind, including turbulence intensity, spectrum and coherence, is mostly related to quasi-static and dynamic load effects (dynamic response). It should be noted that most windresistant design focus primarily on mean wind static stability, while design for quasi-static and dynamic load effects are relatively conservative due to lack of a systematic and comprehensive understanding of fluctuating wind. In many countries, wind field characteristic parameters for windresistant design are widely specified and presented in the specifications or codes. For instance, along-wind turbulence intensity have already been specified with empirical formulas under some design standards (Lin et al., 2018), such as USA (ASCE7-10) (ASCE/SEI 7–10, 2010), Japan (AIJ-RLB-2004) (AIJ-RLB-2004, 2004), China (GB50009-2012) (JTG/T 3360-01, 2018), ESDU (ESDU82031, 2012) and Australia/New Zealand
* Corresponding author. Research Center for Wind Engineering, Southwest Jiaotong University, Chengdu, China. E-mail address: [email protected] (C. Ma). https://doi.org/10.1016/j.jweia.2019.104090 Received 15 July 2019; Received in revised form 21 October 2019; Accepted 29 December 2019 Available online xxxx 0167-6105/© 2020 Elsevier Ltd. All rights reserved.
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
(AS/NZS1170.2) (AS/NZS1170.2, 2011). However, wind field characteristics within ABL are too complicated to be completely specified by limited standards. Moreover, the aforementioned specifications or codes may not be suitable for special regions or weather, such as mountain areas and typhoon climates. Therefore, lots of research in recent years has extensively investigated wind characteristics under extreme conditions through numerical simulations, terrain model wind tunnel tests and field measurements. El-Sayed Abd-Elaal et al. (2018) and Matthew Haines et al. (Haines and Taylor, 2018) used numerical simulations to investigate downburst wind flow over real topography and low rise buildings, respectively, and they acquired relatively accurate wind field characteristics. Jubayer C. M. et al. (Jubayer and Hangan, 2018) obtained relevant wind parameters via terrain model wind tunnel tests, and the test results indicated that the simplified code would generally result in higher design wind speeds for structures in complex terrain. Through a terrain model wind tunnel experiment and field measurement campaign, Fernando Bastos et al. (2018) obtained the wind characteristics for a bridge crossing a steep volcanic breach. He found that the mean wind component derived from field measurements is significantly less than that recommended under design code, but the turbulence intensity is much larger due to the roughness and orography upstream from the bridge site. Hui et al. (2009a) comprehensively studied wind turbulence characteristics through field measurements and terrain model wind tunnel tests and provided important wind parameters for wind-resistant design of Stonecutters Bridge. It found that the average turbulence intensity profiles obtained from field measurements were close to design profiles, and the expression under Power Law in relevant specifications was proper. Li Lin et al. (2018) analyzed wind characteristics under a typhoon located on China southeast coast. In many countries’ design specifications, it is indicated that the turbulence intensity calculated based on measurement data is more appropriate for engineering applications than power law. Wang et al. (2013) also noted that design specification was not completely suitable for Su-tong bridge site located on China east coast. Actually, several papers (Fenerci et al., 2017; Lystad et al., 2018; Jing et al., 2019, 2020; Ma et al., 2019) have studied wind characteristics for bridge sites located at mountain valleys and provided important wind characteristic parameters for wind-resistant design of bridges located in such terrain. It should be noted that wind characteristics in mountain areas are different from those in flat terrain like typhoon as well strong winds. Firstly, mountain wind is mainly disturbed by rugged terrain, while for extreme wind in flat terrain is mostly influenced by air convection. Based on Chinese specification (JTG/T 3360-01, 2018), the terrain studied in this paper is obviously belong to D-type exposure with terrain roughness
Fig. 2. The equipment: (a) ultrasonic anemometer (b) windcube Lidar.
coefficient of 0.3. However, under high wind velocity conditions, wind directions measured in mountain valleys (Fenerci et al., 2017; Yu et al., 2019) are always consistent with the direction of the canyon. Meanwhile, the terrain along the canyon is relatively flat so that the D-type exposure with terrain roughness coefficient of 0.3 is no longer applicable for the profile of wind velocity. Moreover, some research (Bastos et al., 2018; Fenerci and Øiseth, 2018) indicate that the ratio between longitudinal, lateral, and vertical turbulence intensities in mountain areas is different from that of 1:0.88:0.50 recommended in the specification (JTG/T 3360-01, 2018), which is suitable for strong winds in flat terrain. The turbulent spectra and spatial coherence (including decay parameter) might be also different from that in a flat terrain, like typhoon and strong winds. Therefore, it is very necessary to carry out the field measurement study of turbulence field in mountain valley. A lot of research has extensively reported observations regarding turbulence fields, however, the studies have generally been conducted regarding special weather in coastal regions. Though some researchers have carried out activities to characterize winds in mountainous topography to meet engineering need, the turbulence intensity, spectrum and coherence have not been systematically investigated or summarized. The purpose of this paper is to enhance the understanding on turbulence intensity, spectrum and coherence in mountain valley regions and provide appropriate turbulent parameters for wind-resistant design practice use in mountain areas. Therefore, a series of data, including long-term data obtained from mast measurements comprising two ultrasonic anemometers and short-term from Windcube Lidar, is analyzed for study use. The subsequent contents of this paper are organized as follows: Section 2 introduces the bridge site, equipment and data processing method; Section 3 presents the results of turbulence intensity (i.e. PDF distribution,
Fig. 1. The topographic map of the bridge site. 2
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
Fig. 4. Wind speed history.
so the loss of data is so heavy that they are removed. Moreover, 12 measuring points are installed from 40 m to 280 m, and recorded measuring data show that the loss of data increases with height. Therefore, data at the lower 9 measuring levels ranging from 40 m to 210 m, are selected for this study, to minimize data missing. In fact, only data at high levels might be lost, and there is almost no loss of data at lower levels. Wind data collected via Windcube Lidar is divided by time interval of 10 min, to derive average wind speed and standard deviation over 10 min easily. Similarly, the ultrasonic anemometers are also sensitive to unfavorable weather such as thunderstorms. Unlike results from Windcube Lidar, wind data at some levels recorded by ultrasonic anemometers are larger than the average. So abnormal wind data at those levels are removed from the datasets in this study. Wind data obtained from ultrasonic anemometers is also divided by 10-min intervals. In addition, wind data collected from ultrasonic anemometers is mainly used to analyze the characteristics of turbulence intensity at a single measurement level, owing to the higher sampling frequency. Meanwhile, the variation in turbulence intensity with height is analyzed by wind data obtained from Windcube Lidar, taking advantage of its ability to simultaneously collect wind data at different heights. Crosschecking of data between anemometer and Lidar is important. However, the measuring period of anemometer and Lidar is different. Data measured by anemometer is about two months, while data measured by Lidar is only two weeks, and they are not in the same time. Meanwhile, we have studied relevant paper (Qiaoqiao et al., 2013). Their result indicate that the correlation coefficients of wind speed measured by anemometer and Lidar are up to more than 99%, and the average deviation of turbulence intensity is 0.009. Therefore, it can say that the data measured by anemometer and Lidar is reliable. Strictly speaking, wind speed measured in mountain area shows to some extent the non-stationary characteristics reported in much of the literature (Jiang et al., 2019). Y. L. Xu et al. (Lystad et al., 2018) and Chen et al. (2007) have documented the non-stationary characteristics of wind speed data collected at a bridge site located in Hong Kong and proposed corresponding wind data processing approaches for non-stationary wind. However, the wind characteristics (e.g. turbulence intensity, wind spectrum, gust factor, etc.) resulting from the above reference are almost the same as those obtained from traditional wind data processing method adopted by this paper. Moreover, Y. L. Xu et al. (Lystad et al., 2018) directly pointed that if a 10-min duration was used in identifying the wind characteristics, nearly the same results would be obtained due to the fact that non-stationarity is not as significant in recordings of 10 min duration. Tao et al., 2016a, 2016b have studied wind characteristics of a strong wind event and a tropical storm based on stationary and non-stationary models. Their result show that the longitudinal turbulence intensity shows much stronger non-stationarity, and PSDs estimated by stationary and non-stationary models are almost the same, except low-frequency range. For mountain area wind, the maximum wind speed recorded in this study is only approximate 18 m/s. Meanwhile, the wind speed history series show that high wind speed always
Fig. 3. The location of the measurement system.
variation with wind speed and height), turbulent spectrum and vertical spatial coherence, some of which are compared with current recommended design specifications, standards or empirical formulas; Section 4 lists the major conclusions on field measurement study. 2. Equipment and data processing Wind measuring devices are installed at the bridge site located on the bank of the Ya-lung River, southwest to Xichang City, Sichuan Province, China (Fig. 1). The bridge site (N 27 420 1600 , E 102 00 5400 ) consists of typical mountainous terrain in China southwest. It is surrounded by high mountains with altitudes of approximate 3000 m, except along the deep valley that the Ya-lung River goes by. A wind measurement system is consisted of two ultrasonic anemometers (as shown in Fig. 2a) and a Windcube Lidar (as shown in Fig. 2b). The two ultrasonic anemometers are installed on wind tower at heights of 30 m and 50 m respectively. The ultrasonic anemometers can collect data regarding scalar wind speed, azimuth angle and elevation angle. According to relative specifications, wind speed ranging from 0 to 40 m/s can be captured by ultrasonic anemometer with both 0.01 m/s resolution and threshold, 1% (30 m/s) to 3% (40 m/s) accuracy, and 10 Hz sampling frequency. As shown in Fig. 3, Windcube Lidar is installed in the vicinity of wind tower, which can provide wind measurements at twelve points ranging from 40 m to approximate 300 m above ground. To ensure collect reliable data, the measuring levels should be set between 40 m and 210 m under three different increments 10 m, 25 m and 20 m. Moreover, wind speed ranging from 0 to 60 m/s can be measured by Windcube Lidar with both 0.02 m/s resolution and threshold, 0.1 m/s accuracy, and 1 Hz sampling frequency. Total 12 different levels ranging from 40 m to 300 m are measured by the installed Windcube Lidar. It should be noted that, as Windcube Lidar makes use of light scattered by atmospheric aerosols, the wind data could be compromised in special weather conditions such as heavy precipitation, fog or excessively clean air. Sometimes, birds or flying debris can also affect Windcube Lidar data collection. Empirically, wind data may be null at some measurement levels. Based on recorded data, it is found that the proportion of the loss of data is 4.28%, which is small enough, so linear interpolation is adopted to generate the missing data. It also noted that the weather is particularly bad (for instance, heavy fog in the morning) for a few days, 3
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
Fig. 5. PSDs at different time.
3. Results and discussions
happen in the afternoon, and wind speed changes slowly with time. In addition, based on the study by Huang et al. (2015) and Tao et al. (Tao and Wang, 2019), we also calculate the evolutionary power spectral density (EPSD) using 2 h’ wind data, which changes more sharply from 1 m/s to 16 m/s. The variation of wind speed with time is illustrated in Fig. 4, and the EPSDs are plotted in Fig. 5. It should be noted that the frequency and spectra are all normalized for comparison. As can be seen from the result, there are minor variations in PSDs, and they are almost unchanged with time on the whole. Therefore, wind can be treated as stationary in the view of EPSD. In a word, the traditional wind data processing method, which is fast and simple, is suitable in this study. It is also critical to derive accurate fluctuating wind speeds (u, v and w components) from the raw wind data. However, raw wind data collected by the ultrasonic anemometer and Windcube Lidar adopt different types of coordinate systems, i.e. Spherical system (U, α and β) and Cartesian system (Ux , Uy and Uz ), respectively. Thus, for ultrasonic wind data under Spherical system, the fluctuating wind speed can be obtained according to the following formulas:
α’ ¼ α α
β’ ¼ β β
u ¼ U cos α’cos β’ U
v ¼ U cos α’sin β’
For a better understanding of the turbulence in mountain valleys, turbulence intensity, turbulent spectrum and coherence are investigated. They are key parameters for calculating buffeting response of structures. 3.1. Turbulence intensity The turbulence intensity characterizes wind speed fluctuations and is defined as the ratio between standard deviation of fluctuating wind components and mean wind speed (this paper adoptes a 10 min mean wind speed) as follows:
σi
Ii ¼ ; ði ¼ u; v; wÞ U
Where, Ii denotes turbulence intensity;σ i denotes standard deviation of fluctuating wind component; U denotes mean wind speed. Turbulence intensity is one of the most important wind field characteristics in structural design, especially critical to buffeting response in long-span bridges. For example, turbulence not only has a significant influence on VIV, but also on aeroelastic stability. Due to the fact that low wind velocity is responsible for VIV and high wind velocity takes major on aeroelastic stability, so turbulence intensity should be investigated at both low and high wind velocities. A comprehensive investigation on turbulence intensity in a mountain valley is carried out in this section. The ultrasonic anemometers were continuously operated for 2 months to provide wind data, while the Windcube Lidar was used to collect wind data for half a month.
(1) w ¼ U sin α’
(2)
Where, α and β denote the attack and yaw angles, respectively; u, v and w denote the longitudinal, lateral and vertical fluctuating wind speeds, respectively. Meanwhile, for Lidar wind data under Cartesian coordinates, the fluctuating wind speed can be calculated using the following equations: qffiffiffiffiffiffiffi 2 2 Ux þ Uy
(3)
qffiffiffiffiffiffiffi 2 2 2 U ¼ Ux þ Uy þ Uz
(4)
Uh ¼
cosα ¼
cosβ ¼
Uh U
sinα ¼
Ux Uh
sinβ ¼
Uz U
(5)
Uy Uh
(6)
u ¼ Ux cosβ þ Uy sinβ cosα þ Uz sinα Uv ¼ Ux sinβ þ Uy cosβw ¼ Ux cosβ þ Uy sinβ sinα þ Uz cosα
(8)
3.1.1. PDF distribution A large amount of research (Lystad et al., 2018) and specifications (AIJ-RLB-2004, 2004) indicate that the PDF distribution of turbulence intensity aligns well with lognormal distribution, which is expressed as follows: f ðxÞ ¼
1 pffiffiffiffiffie xσ 2π
ðln xμÞ2 2σ 2
;x > 0
(9)
where μ denotes mean of the natural logarithm of variable x; σ denotes the standard deviation of the natural logarithm of variable x. However, the turbulence in mountain valley is so complicated that it is difficult to know if the above expression can be applied here. Therefore, wind data collected from the two ultrasonic anemometers (two levels of 30 m and 50 m above the ground) are further analyzed to investigate the PDF distribution. Moreover, to investigate the influence of mean wind speed on the distribution parameters, the wind data are divided by different mean wind speed, i.e. mean speed 1–4 m/s, 4–8 m/s, 8–12 m/s, and above 12 m/s. By doing this, we get parameters in the
(7)
Where, Ux , Uy and Uz usually denote the east, south and erective wind speeds, respectively; Uh and U denote the horizontal and total wind speeds, respectively.
4
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
Fig. 6. PDF distribution of turbulence intensity (height ¼ 50 m, U ¼ 1–4 m/s).
Fig. 7. PDF distribution of turbulence intensity (height ¼ 50 m, U ¼ 4–8 m/s).
increase of wind speed. However, σ, Expectations and standard deviations fall very slowly with wind speed, while μ drops more rapidly. The results are of great significance for investigation and wind-resistant design of structures in mountain valleys. The ratio amongst turbulence intensity’s tree components is listed in Table 1. It is indicated that the ratio varies greatly with wind speed and there is no fixed value. As can be seen from Table 1, ratios get smaller as mean wind speed increases. When mean wind velocity are larger than 12 m/s, the ratios amongst each component at heights of 50 m and 30 m are 1:0.667:0.722 and 1:0.694:0.574, respectively. As known, some specifications and standards have proposed ratios amongst each component for the turbulence intensity. For example, the Chinese code (JTG/T 3360-01,
lognormal distribution that are functions of the mean wind velocity. The PDF of turbulence intensity at heights of 50 m and 30 m under different mean wind speed are illustrated in Figs. 6–13. Meanwhile, the fitted parameters, μ and σ, as well as mathematical expectations and standard deviations derived from μ and σ according to lognormal distribution property, are also shown in above figures. As can be seen, under different mean wind speed and heights (50 and 30 m), PDF distributions are all in a good agreement with lognormal distribution. It implies that PDF distribution in mountain valley can be expressed by lognormal distribution with appropriate parameters. In addition, the variations of these fitted parameters at heights of 50 m and 30 m are illustrated in Figs. 14 and 15, respectively. The results show that all these parameters decrease with the
Fig. 8. PDF distribution of turbulence intensity (height ¼ 50 m, U ¼ 8–12 m/s).
Fig. 9. PDF distribution of turbulence intensity (height ¼ 50 m, U > 12 m/s). 5
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
Fig. 10. PDF distribution of turbulence intensity (height ¼ 30 m, U ¼ 1–4 m/s).
Fig. 11. PDF distribution of turbulence intensity (height ¼ 30 m, U ¼ 4–8 m/s).
3.1.2. Variation with wind speed From above section, it can find that the mean and standard deviations of turbulence intensity decrease with the growing of mean wind speed. According to Eq. (1), the turbulence intensity also drops with the mean wind speed increasing. However, in order to further understand the variation in turbulence intensity with the wind speed in mountain valley, the mean wind speed threshold of 1 m/s is adopted to calculate the turbulence intensity, as shown in Figs. 16 and 17. These two figures indicate that the turbulence intensity decreases with the increase of wind speed, and each component (Iu, Iv and Iw) obviously tends to have a fixed value.
2018) proposes the ratio of 1:0.88:0.50. It can also be seen from Table 1 that the proposed ratios vary a lot from that obtained under measurements. It can be concluded that it is inappropriate to directly apply the specifications and standards to mountain valley. However, the ratios listed in the specifications and standards are not completely unuseful in mountainous valley. Owing to the complicated topographical conditions and mean wind speed threshold, the ratios obtained from the measurement may be close to the values recommended by the specifications and standards under certain conditions. It is important to note that it is necessary to obtain turbulence intensity in mountainous valley by on-site measurements or other methods.
Fig. 12. PDF distribution of turbulence intensity (height ¼ 30 m, U ¼ 8–12 m/s).
Fig. 13. PDF distribution of turbulence intensity (height ¼ 30 m, U > 12 m/s). 6
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
Fig. 14. Fitted parameters at height of 50 m.
Fig. 15. Fitted parameters at height of 30 m.
Additionally, as can be seen from Figs. 16 and 17, with the increase of wind speed, the three turbulence intensity components, Iu, Iv and Iw, tend to reach approximately 0.092, 0.054 and 0.065 respectively, and the ratios shall be close to 1:0.59:0.71, which is very different from the ratios of 1:0.88:0.50 recommended by the Chinese code (JTG/T 3360-01, 2018). Therefore, under high wind speed conditions, it is inappropriate to apply the ratio proposed by specifications and standards for the wind-resistant design of structures located in mountain valleys. As mentioned in Introduction, the turbulence intensity is not only critical for buffeting response in structures under high wind speeds, but also plays key role on structure VIV at low wind speeds. The ratios amongst the three turbulence intensity components at low wind speeds are not yet statistically in agreement with the recommended values. Therefore, more attention should be paid to the actual turbulence intensity for wind-resistant design of structures (e.g. long-span bridges and wind turbos) located in mountain valley.
Table 1 Ratio amongst components of turbulence intensity. Height
Threshold
Iu: Iv: Iw
50 m
1–4 m/s 4–8 m/s 8–12 m/s >12 m/s 1–4 m/s 4–8 m/s 8–12 m/s >12 m/s
1:0.920:0.751 1:0.829:0.720 1:0.805:0.760 1:0.667:0.722 1:0.931:0.709 1:0.825:0.669 1:0.812:0.656 1:0.694:0.574
30 m
Although there are 20 m level difference between the two measuring heights, the scattered pattern of the turbulence intensity under the two heights are very close. However, the scattered pattern of different turbulence intensity components are not identical. Comparing with the scale of the terrain, the 20 m height difference is too small to substantially affect the scattered pattern. Besides, the height of the measuring points is higher than the ground vegetation, which has an important influence on the turbulence intensity. According to the different distribution patterns under the three turbulence intensity components, as illustrated in Figs. 16 and 17, it can be concluded that the turbulence intensity presents significant three-dimensional behavior in mountain valley.
3.1.3. Variation with height It is difficult to obtain turbulence intensity at all desired positions (e.g. long-span bridge girders and bridge tower tops) for structures located in mountain valley through field measurements. In most cases, the turbulence intensity can only be obtained for a few points near the site at specific heights above the ground. In order to further understand
Fig. 16. The variation in turbulence intensity with wind speed at a height of 50 m. 7
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
Fig. 17. The variation in turbulence intensity with wind speed at a height of 30 m.
Fig. 20. The variation in turbulence intensity of Iv with height.
Iu ðzÞ ¼ I10
(11)
Where, α is terrain roughness coefficient; I10 is nominal turbulence intensity at a height of 10 m (Lin et al., 2018). For convenience, the above empirical formula has been adopted in analysis for turbulence intensity in mountain valley. The recorded turbulence intensity is fitted by least squares method using the empirical formula so as to obtain the parameters of c and d (I10 and α). Two technical routines (A and B) are employed during data processing and illustrated in Fig. 18. The purpose of technical routine A is to investigate how turbulence intensity varies with height in mountain valley; the results are plotted in Figs. 19–21. Additionally, the PDF distribution for fitted parameters c and d are illustrated in Figs. 23–25, and the mean and standard deviations are listed in Table 2. It should be noted that, owing to very limited wind data taken from Windcube Lidar, no threshold wind speed is adopted during wind data
Fig. 18. The diagram of the technical routines A and B.
how turbulence intensity varies with height and how it affect the structures, a set of wind data with sampling frequency of 1 Hz, collected by the Windcube Lidar, is analyzed. Some specifications (ASCE/SEI 7–10, 2010; AIJ-RLB-2004, 2004; JTG/T 3360-01, 2018) proposed that the turbulence intensity in the along-wind direction of Iu ðzÞ could be expressed by a power law (Lin et al., 2018). The empirical formula is as follows: d 10 Iu ðzÞ ¼ c z
α 10 z
(10)
The empirical formula in Chinese Code GB50009-2012 (JTG/T 3360-01, 2018) has been specifically defined as:
Fig. 21. The variation in turbulence intensity of Iw with height. Fig. 19. The variation in turbulence intensity of Iu with height. 8
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
processing. As mentioned in Section 2, though the measuring height can reach up to 300 m, a large amount of wind data at higher measuring levels are unable to be properly collected due to complex site conditions such as precipitation, heavy fog and dust. Therefore, only wind data from nine measuring levels, 40, 50, 60, 85, 110, 135, 160, 185 and 210 m above ground, are adopted for analysis. As can be seen from Figs. 19–21, profiles of turbulence intensity align well with the aforementioned empirical formula. It can be concluded that Table 2 The mean and standard deviations for fitted parameters c and d. Component
Parameter
Mean
Std
Iu
c/I10 d/α c/I10 d/α c/I10 d/α
0.4470 0.0814 0.4303 0.0108 0.2053 0.0364
0.5040 0.3756 0.4518 0.4275 0.2321 0.3796
Iv Iw
Fig. 22. The correlation coefficients of turbulence intensity at different heights.
Fig. 23. The PDF of c and d for Iu .
Fig. 24. The PDF of c and d for Iv .
Fig. 25. The PDF of c and d for Iw . 9
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
Fig. 26. Parameter d.
energy distribution in the frequency domain. In the previous studies, varies empirical expressions for turbulent wind speed spectra have been developed in many countries. For example, Chinese Codes employ the Simiu spectrum (Simiu and Scanlan 1996) to depict the longitudinal and lateral wind spectra and Panofsky spectrum (Panofsky and Mccormick, 1960) to the vertical (Yu et al., 2019). The empirical formulas are as follows: For longitudinal wind spectrum, the Simiu spectrum is
it is reasonable to apply the power law proposed by the aforementioned specifications and standards to the description of the variation in turbulence intensity with height in mountain valley. However, the fitted parameters of c and d (I10 and α) are very different from those recommended by specifications or standards. Moreover, turbulence intensities listed in Figs. 19–21 are all larger than those obtained from the ultrasonic anemometers. This may be due to the fact that actual wind speed was relatively small during Windcube Lidar’s recording period. In addition, it can be seen that the turbulence intensity observed in the middle part of power law curves are slightly smaller than that at the top and bottom levels. Owing to the speed-up effect caused by the hill where the Windcube Lidar and mast were located, there is a higher wind speed in the middle, which results in a smaller turbulence intensity, as mentioned in subsection 3.2. Meanwhile, it can also be seen from Figs. 19–21 that the standard deviations of the turbulence intensity are all very large and slightly changes with height. Meanwhile, the correlation of the turbulence intensity in the different points above ground are also studied, due to the significant scatter of turbulence intensity is shown in Figs. 19–21. The correlation coefficients of turbulence intensity are presented in Fig. 22. As can be seen from the result, there is strong correlation for turbulence intensity with height. Moreover, the lateral and vertical turbulence intensities are relatively stronger than longitudinal turbulence intensity. Although the magnitudes of the three turbulence intensity components are very different, their correlation coefficients with height are almost identical. It implies that the turbulence intensity in mountain valley can be predicted with a function in height. The PDF parameter c complies with the lognormal distribution very well, as shown in Figs. 23–25. According to Chinese Code GB50009-2012 (JTG/T 3360-01, 2018), the parameter of c is I10 that matching the lognormal distribution as in subsection 3.1.1. Comparing with parameter of c, the PDF of the parameter d aligns well with Gaussian distribution (normal distribution). In other words, the PDF of the terrain roughness coefficient, α/d, clearly follows Gaussian distribution in mountain valley. Relevant studies (Kikumoto et al., 2017) show that d varies with wind speed, and the shape of PDF obtained in this manuscript is consistent with that given in reference (Kikumoto et al., 2017). However, the terrain roughness coefficient α is too small to represent reality. The more reasonable parameter α might be obtained at high wind speeds. Therefore, the variation in parameter of d with wind speed is illustrated in Fig. 26. The results indicate that parameter d will converge to be a fixed value, approximate 0.2, as the wind speed increases. These results are different from those illustrated in Figs. 19–21, since the latter are calculated from all wind speed. The parameters c and d for turbulence profiles should be thus selected according to wind speed. It is also indicated that, in mountain valley, the parameters should be calculated based on measured data rather than the specifications or standards, which would be more appropriate for engineering applications.
f Su ðf ; zÞ 200fz ¼ 5=3 u2* 1 þ 50fz
(12)
For lateral wind spectrum, the following modified spectrum is recommended by Simiu and Scanlan (1996): f Sv ðf ; zÞ 15fz ¼ 5=3 u2* 1 þ 9:5fz
(13)
For vertical wind spectrum, the Panofsky spectrum is f Sw ðf ; zÞ 6fz ¼ 2 u2* 1 þ 4fz
(14)
Where f is the frequency in Hz; Su;v;w ðf ; zÞ is the turbulent wind spectrum at height z above ground; u* is the friction speed; fz is the nondimensional reduced frequency, which is expressed as follows: fz ¼
f z UðzÞ
(15)
Where UðzÞ is the mean wind speed at height z above ground. Moreover, according to much research on field measurement, the von Karman spectrum is deemed to be one of the most suitable wind spectra to represent the fluctuating wind speed at high wind speed (Panofsky and Mccormick, 1960; Cao et al., 2009; Hui et al., 2009b). The von Karman spectrum is expressed as follows: f Su ðf ; zÞ
σ 2u
f Sv;w ðf ; zÞ
σ 2v;w
4Lu f U
¼
2 5=6 1 þ 70:8 LuU f
4Lv;w f U
(16)
2 1 þ 755 Lv;wU f
¼ 2 11=6 1 þ 283 Lv;wU f
(17)
Where, Lu , Lv and Lw are the longitudinal, lateral and vertical turbulent integral length scales, respectively; σ u , σ v and σ w are the standard deviations of the longitudinal, lateral and vertical turbulent components, respectively; U is the mean wind speed.
3.2. Turbulent spectrum
3.2.1. Field measurement spectrum Given the complex wind environment in mountain valley located in
The turbulent wind spectrum is an argument to describe the turbulent 10
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
Fig. 27. Turbulent wind spectra calculated by the pwelch and pyulear functions, respectively.
China Southwest, the turbulent wind spectrum may not be represented appropriately by the Simiu spectrum, Panofsky spectrum or von Karman spectrum. Therefore, the turbulent wind spectra derived from field measurement recorded by the Windcube Lidar are investigated, since turbulent wind play an important role in calculation of structural buffeting response. The recorded field measurement spectrum is calculated using MATLAB’s pyulear function in order to obtain a smooth spectral curve. Moreover, the pyulear function can, with an appropriate order, return a useful autoregressive power spectral density estimate. The recorded field measurement spectrum can also be calculated via MATLAB’s pwelch function. However, the resulted wind spectral curve is not smooth. The order inputted in the pyulear function is set to 15 during data processing. To verify that the order of 15 is appropriate, a set of raw wind data is simultaneously processed by the pyulear and pwelch functions. The results are illustrated in Fig. 27. It can be seen that the two types of wind spectra are almost the same except at low frequency domain. However, the wind spectrum obtained from pyulear function is more smooth than that obtained from pwelch function, and it is very convenient for obtaining the peak frequency. Due to missing of raw wind data at low frequency domain, the two power spectral estimate methods resulted in difference at low frequency domain. In addition, the spectrum at low frequency domain can be neglected when considering wind effect on structures. In order to investigate the applicability of the aforementioned spectral models, the fitted Simiu, Panofsky and von Karman spectra are also illustrated together with the corresponding field measurement spectra. In order to unify coordinates, the height is used to normalize the frequency. Meanwhile, the fitted turbulence integral scale and friction speed are also supplemented in the results. It should be noted that data used for spectral analysis is measured by Windcube Lidar, due to its ability to simultaneously measure wind data at multiple levels. There are total two weeks (14 days) of data collected by the Windcube Lidar. However, due to the complex field environment and weather conditions, for instance heavy fog in the morning, such data on these days is removed. Eventually, there are approximate 9 days’ data used for the spectral analysis. These data is divide into a series of 10-min segments, then the average field measurement spectra and fitted spectra at heights of 40 m, 85 m and 185 m are shown in Figs. 28–30, respectively. As can be seen from the figures, the von K arm an spectral models can accurately represent the field measurement spectra at the three heights of 40 m, 85 m and 185 m. In contrast, the Simiu and Panofsky spectral models, which are employed by Chinese Code, vary too much from the measured spectra and not applicable at all, except for some spectra. Objectively speaking, only in the lateral and vertical direction at specific heights the Simiu and Panofsky spectral models are in agreement with the realistic spectra. From the analysis of relevant research, it found that the Simiu spectrum can fit the
Fig. 28. The field measurement spectra and fitted spectra at a height of 40 m.
measured results very well at certain height above ground in mountain areas. However, it is not applicable for all vertical levels. In addition, the data used for spectral analysis is measured from Windcube Lidar, and the sampling frequency is only 1 Hz, which resulting in the high-frequency region of the spectra is missed. Therefore, these reasons maybe lead to the fitted Simiu spectrum significantly differ from the measured results in the longitudinal direction. It is also indicated that the Simiu and Panofsky spectral models recommended by Chinese code are not applicable for mountain valley in China Southwest, while the von Karman spectral models still have significant applicability for these terrains. The values of fitted parameters are also supplemented in Figs. 28–30. The turbulence integral length scale fitted by von Karman spectrum is approximate 50 m at the heights of 40, 85 and 185 m, and they are almost identical in the three directions (longitudinal, lateral and vertical). Meanwhile, the friction velocity of u* fitted by Simiu spectrum in lateral direction is approximate 0.3–0.4. 3.2.2. Variation with height Due to the high complexity of the mountain valley, the blockage effect 11
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
Fig. 29. The field measurement spectra and fitted spectra at a height of 85 m. Fig. 30. The field measurement spectra and fitted spectra at a height of 185 m.
of the terrain can have a significant influence on the turbulent spectra near the ground surface. This effect might get weaken as the height above ground surface increases. To further understand the variations in turbulent spectra with height, the field measurement spectra at ten different heights (40 m, 50 m, 60 m, 85 m, 110 m, 135 m, 160 m, 185 m and 210 m and 235 m above ground) are calculated from the raw wind data and illustrated in Figs. 31–33. The above Figs. 28–30 also reflect, to some extent, the changes in the turbulent wind spectra with height. The shape of the longitudinal, lateral and vertical component spectra are basically unchanged at different heights, as shown in Figs. 28–30. However, slight variation can still be observed. Figs. 31–33 show that the high energy zones of all dimensionless spectra move to high frequency domain, and the magnitudes slightly reduced. This may relate to the fact that the airflow at higher positions is less likely to be disturbed (due to squeezing, cutting effects, etc.) than that on ground surface due to terrain roughness, resulting in fluctuating wind amplitude to slightly decrease. Therefore, it is inappropriate to adopt just one spectrum with fixed parameters to calculate the buffeting response for structures located in mountain valley. In many conditions, although certain two points in a mountainous valley might be at the same level, their heights above ground surface is different. Consequently, the turbulent wind spectra at
the two points are also different, which calls for concern when calculating the buffeting response in horizontal structures located in a mountainous valley. In general, wind spectrum should be selected very carefully when calculating the structural buffeting response in mountain valley. 3.3. Vertical spatial coherence The statistical dependence of the fluctuating wind speed at any two points can be described by the coherence function in the frequency domain. It is usually defined as the ratio between the cross-spectral density and the auto-spectral density of turbulent wind speed at any two points (Panofsky and Mccormick, 1960; Peng et al., 2018). In this paper, the vertical coherence functions for measured data are calculated using MATLAB’s mscohere function with NFFT ¼ 10240 and Hanning Window. The definition is as follows: Pxy ðf Þ 2 Cxy ðf Þ ¼ Pxx ðf ÞPyy ðf Þ
(18)
Where Cxy denotes the coherence estimates of the fluctuating wind 12
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
Fig. 31. The longitudinal field measurement spectra along the height.
f Δ Cohðf Þ ¼ exp C U
speeds xðtÞ and yðtÞ using Welch’s averaged modified periodogram method; Pxy denotes the cross-spectral density of fluctuating wind speeds xðtÞ and yðtÞ; Pxx and Pyy denote the auto-spectral density of fluctuating wind speeds xðtÞ and yðtÞ, respectively. Many empirical formulas regarding spatial coherence have been proposed in previous research. Davenport (1961) recommended the following coherence formula in exponential format to represent the horizontal and vertical coherences:
(19)
where C is the decay coefficient; Δ is the separation distance between the two points. However, based on more field measurement research, the coherence is not equal to unity when the frequency approaches zero. Later, Mann (Mann et al., 1991) had improved the above formula to better fit the measured data. The improved formula is expressed as Eq. (20). Furthermore, for the purpose of concision, a modified coherence
Fig. 32. The lateral field measurement spectra along the height.
Fig. 33. The vertical field measurement spectra along the height. 13
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
As can be seen from Figs. 34–36, Eq. (21) can be a good representation of the realistic measured coherences. Moreover, when the reduced frequency approaches zero, the measured coherences are not actually equal to unity. For different turbulent components of the same two points, the fitted values K and C are not yet identical. The fitted values of K decrease as the vertical distance of the two points increase, to the contrary, the fitted values of C increase. For the same vertical distance and different heights, the fitted values of K and C are not identical, which indicates that it is inappropriate to adopt coherence model with fixed parameters to represent the real coherence at different heights in mountain valley. However, the measured coherences indicate that the longitudinal and lateral coherence are basically similar, and they are both smaller and drop faster than the vertical coherence. This may be caused by the heavy disturbance of the longitudinal and lateral turbulent wind arising from the rugged terrain. The impact to the vertical turbulent wind is relatively small. When the reduced frequency approaches zero and the threshold value of coherence is set to 0.4, it can be found that both the longitudinal and lateral effective distance for coherence are both approximate 50 m, while the vertical effective distance is up to 80 m. Furthermore, as shown in Figs. 35 and 36, when the distance between the two points is a constant, even if their measuring height changes, either up or down, the coherence in each component is basically identical. This indicates that the turbulent vortices remain basically uniform at different heights in the canyon. This conclusion also has been proved in section 3.2. The measured spectra align well with von Karman spectral model, which is
Table 3 The measured coherences for investigation. Coherence
Height of z1
Height of z2
Cohxxðz1 ; z2 Þðxx ¼ uu; vv; wwÞ
40 m 85 m 160 m
50 m, 60 m, 85 m 110 m, 135 m, 160 m 185 m, 210 m
formula is developed from Eq. (20) and written as Eq. (21) (Hui et al., 2009b). Cohðf Þ ¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Δ f Δ exp C 1 B z U
f Δ Cohðf Þ ¼ K exp C U
(20)
(21)
where B and K are parameters to be fitted; z is height above ground. In general, due to the complex wind environment in a canyon, the aforementioned coherence formulas may not be applicable. Therefore, to verify whether the aforementioned coherence formula (Eq. (21)) can be employed to represent the coherence in mountain valley, a comparison between measured data and the above coherence model is carried out. In addition, the coherence functions for measured data are also studied to further reveal the variation in coherence with height. The coherences for measured data at two vertical levels are conducted as given in Table 3.
Fig. 34. The measured coherence functions (z1 ¼ 40 m; z2 ¼ 50 m, 60 m, 85 m). 14
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
Fig. 35. The measured coherence functions (z1 ¼ 85 m; z2 ¼ 110 m, 135 m, 160 m).
Fig. 36. The measured coherence functions (z1 ¼ 160 m; z2 ¼ 185 m, 210 m). 15
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
Fig. 37. The variation in parameter K with distance at different heights.
Fig. 38. The variation in parameter C with distance at different heights.
derived from homogeneous turbulence field. However, it should be noted that the maximum measuring height in this paper is only 235 m, which is much lower than the surrounding mountain. To study the variation of these parameters, K and C, with distance, the results are illustrated in Figs. 37 and 38. As can be seen from the results, the parameter K almost decrease linearly with distance. It is noted that parameter K in vertical direction is always larger than that in longitudinal and lateral direction, and the latter two parameters are almost identical. In addition, the parameter C gets larger as the distance between the two points increases, and C dispersion also rise up. In general, these parameters of K and C are approximately unchanged with the height of z1, but sharply varied with vertical distance between z1 and z2, and relevant parameters could be selected from Figs. 37 and 38 for engineering applications.
intensity with height in mountainous valleys, and the power law index is approximate 0.2 under high wind speed condition. (2) The Simiu and Panofsky spectral models are no longer applicable to mountainous valleys in Southwest China, but the von Karman spectral models still have significant applicability for this type of terrain. The turbulence integral length scales obtained by fitting von Karman spectrum are approximate 50 m in the valley, and they are basically uniform in different heights and directions. The line types of the longitudinal, lateral and vertical component spectra remain basically unchanged as the height increases, but the high energy zones of all the dimensionless spectra move to the high frequency domain, and their values are slightly reduced. (3) The empirical coherence formula can be a good representation of the vertical spatial coherences in mountainous valleys. When the reduced frequency approaches zero, the measured coherences are approximate 0.8 when distance is 20 m. When the threshold value of coherence is set to 0.4, the longitudinal and lateral effective distances for coherence are both approximate 50 m, while the vertical effective distance is up to 80 m.
4. Concluding remarks Owing to the complexity of turbulence and the lack of literature focusing on it in mountainous valleys, this paper carried out a comprehensive investigation of the turbulence in a mountainous valley using field measured wind data from a wind tower and a Windcube Lidar. The turbulence intensity, turbulent spectra and vertical spatial coherence were comprehensively studied by statistical methods. The results were also compared with the specifications and standards of many countries. The major conclusions of this study can be summarized as follows:
Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
(1) The PDF distribution of turbulence intensity in a mountainous valley can be characterized by lognormal distribution with appropriate parameters, which are approximate 2.4 and 0.4 for μ and σ when the mean wind speed is larger than 12 m/s. Moreover, the ratio of the components of turbulence intensity proposed by the specifications or standards cannot be applied to mountainous valleys, which are approximate 1:0.68:0.65 when the mean wind speed is larger than 12 m/s. Furthermore, it is reasonable to apply the power law to the description of the variation in turbulence
Acknowledgement The work described in this paper was fully supported by the National Natural Science Foundation of China (No. 51778545). References Abd-Elaal, El-Sayed, Mills, Julie E., Ma, Xing, 2018. Numerical simulation of downburst wind flow over real topography. J. Wind Eng. Ind. Aerodyn. 172, 85–95. AIJ-RLB-2004, 2004. Recommendations for Loads on Building-Wind Loads. Architectural Institute of Japan, Tokyo. 16
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090 Li, M., Li, M., Yang, Y., 2019. Strategy for the determination of unsteady aerodynamic forces on elongated bodies in grid-generated turbulent flow. Exp. Therm. Fluid Sci. 109939. Lin, Li, Chen, Kai, Xia, Dandan, Wang, Huaifeng, Hu, Haitao, He, Fuqiang, 2018. Analysis on the wind characteristics under typhoon climate at the southeast coast of China. J. Wind Eng. Ind Aerod. 182, 37–48. Lystad, T.M., Fenerci, A., Øiseth, O., 2018. Evaluation of mast measurements and wind tunnel terrain models to describe spatially variable wind field characteristics for longspan bridge design. J. Wind Eng. Ind. Aerodyn. 179, 558–573. Ma, C., Duan, Q., Li, Q., Liao, H., Tao, Q., 2019. Aerodynamic characteristics of a longspan cable-stayed bridge under construction. Eng. Struct. 184, 232–246. Ma, C., Wang, J., Li, Q., et al., 2018. Vortex-induced vibration performance and suppression mechanism for a long suspension bridge with wide twin-box girder. J. Struct. Eng. 144 (11), 4018202. Ma, C., Wang, J., Li, Q., et al., 2019. 3D aerodynamic admittances of streamlined box bridge decks. Eng. Struct. 179, 321–331. Mann, J., Kristensen, L., Courtney, M.S., 1991. The Great Belt Coherence Experiment: A Study of Atmospheric Turbulence over Water. Risø National Laboratory. Panofsky, H.A., Mccormick, R.A., 1960. The spectrum of vertical velocity near the surface. Q. J. R. Meteorol. Soc. 86, 495–503. Peng, Yongbo, Wang, Shifeng, Li, Jie, 2018. Field measurement and investigation of spatial coherence for near-surface strong winds in Southeast China. J. Wind Eng. Ind. Aerod. 172, 423–440. Qiaoqiao, W., Xiuzhi, Z., Shangkun, W., 2013. Comparison between windcube laser radar and wind tower data. Meteorol. Sci. Technol. 41 (1), 20–26. Simiu, E., Scanlan, R.H., 1996. In: Winds Effects on Structures: Fundamentals and Applications to Design, 3 edition. Wiley-Interscience, New York. Tao, T., Wang, H., 2019. Modelling of longitudinal evolutionary power spectral density of typhoon winds considering high-frequency subrange. J. Wind Eng. Ind. Aerodyn. 193, 103957. Tao, T., Wang, H., Wu, T., 2016. Comparative study of the wind characteristics of a strong wind event based on stationary and nonstationary models. J. Struct. Eng. 143 (5), 04016230. Tao, T., Wang, H., Li, A., 2016. Stationary and nonstationary analysis on the wind characteristics of a tropical storm. Smart Struct. Syst. 17 (6), 1067–1085. Wang, Hao, Li, Aiqun, Niu, Jie, Zong, Zhouhong, Li, Jian, 2013. Long-term monitoring of wind characteristics at Sutong Bridge site. J. Wind Eng. Ind Aerod 115, 39–47. Wang, J., Ma, C., Li, M., et al., 2019. Experimental and numerical studies of the vortexinduced vibration behavior of an asymmetrical composite beam bridge. Adv. Struct. Eng. 22 (10), 2236–2249. Wu, B., Chen, X., Wang, Q., et al., 2020. Characterization of vibration amplitude of nonlinear bridge flutter from section model test to full bridge estimation. J. Wind Eng. Ind. Aerodyn. 197, 104048. Yu, Chuanjin, Li, Yongle, Zhang, Mingjin, Zhang, Yi, Zhai, Guanghao, 2019. Wind characteristics along a bridge catwalk in a deep-cutting gorge from field measurements. J. Wind Eng. Ind. Aerodyn. 186, 94–104.
AS/NZS1170.2, 2011. Structural Design Actions, Part 2: Wind Actions. Jointly published by SAI Global Limited under license from Standards Australia Limited. ASCE/SEI 7–10, 2010. Minimum Design Loads for Buildings and Other Structures. American Society of Civil Engineers, Reston, VA. Bastos, Fernando, Caetano, Elsa, Cunha, Alvaro, Cespedes, Xavier, Flamand, Olivier, 2018. Characterisation of the wind properties in the Grande Ravine viaduct. J. Wind Eng. Ind. Aerodyn. 173, 112–131. Cao, S., Tamura, Y., Kikuchi, N., Saito, M., Nakayama, I., Matsuzaki, Y., 2009. Wind characteristics of a strong typhoon. J. Wind Eng. Ind. Aerodyn. 97 (1), 11–21. Chen, Jun, Hui, Michael C.H., Xu, Y.L., 2007. A comparative study of stationary and nonstationary wind models using field measurements. Boundary-Layer Meteorol. 122, 105–121. Jubayer, Chowdhury Mohammad, Hangan, Horia, 2018. A hybrid approach for evaluating wind flow over a complex terrain. J. Wind Eng. Ind. Aerodyn. 175, 65–76. Davenport, A.G., 1961. The spectrum of horizontal gustiness near the ground in high winds. Q. J. R. Meteorol. Soc. 87, 194–211. ESDU82031, 2012. Paraboloidal Antennas: Wind Loading. Part 1: Mean Forces and Moments. Fenerci, A., Øiseth, O., 2018. Strong wind characteristics and dynamic response of a longspan suspension bridge during a storm. J. Wind Eng. Ind. Aerodyn. 172, 116–138. Fenerci, A., Øiseth, O., Rønnquist, A., 2017. Long-term monitoring of wind field characteristics and dynamic response of a long-span suspension bridge in complex terrain. Eng. Struct. 147, 269–284. Haines, Matthew, Taylor, Ian, 2018. Numerical investigation of the flow field around low rise buildings due to a downburst event using large eddy simulation. J. Wind Eng. Ind. Aerodyn. 172, 12–30. Huang, G., Zheng, H., Xu, Y.L., Li, Y., 2015. Spectrum models for nonstationary extreme winds. J. Struct. Eng. 141 (10), 04015010. Hui, M.C.H., Larsen, A., Xiang, H.F., 2009a. Wind turbulence characteristics study at the Stonecutters Bridge site: Part I—mean wind and turbulence intensities. J. Wind Eng. Ind. Aerodyn. 97, 22–36. Hui, M.C.H., Larsen, A., Xiang, H.F., 2009b. Wind turbulence characteristics study at the Stonecutters Bridge site: Part II-Wind power spectra, integral length scales and coherences. J. Wind Eng. Ind. Aerodyn. 97, 48–59. Jiang, Y., Zhao, N., Peng, L., Liu, S., 2019. A new hybrid framework for probabilistic wind speed prediction using deep feature selection and multi-error modification. Energy Convers. Manag. 199, 111981. Jing, H., Liao, H., Ma, C., et al., 2020. Field measurement study of wind characteristics at different measuring positions in a mountainous valley. Exp. Therm. Fluid Sci. 112, 109991. Jing, H., Liao, H., Ma, C., Chen, K., 2019. Influence of elevated water levels on wind field characteristics at a bridge site. Adv. Struct. Eng. 22 (7), 1783–1795. JTG/T 3360-01, 2018. Wind-resistant Design Specification for Highway Bridges. Ministry of Communications of the People’s Republic of China, Beijing, China. Kikumoto, H., Ooka, R., Sugawara, H., Lim, J., 2017. Observational study of power-law approximation of wind profiles within an urban boundary layer for various wind conditions. J. Wind Eng. Ind. Aerodyn. 164, 13–21.
17
Contents lists available at ScienceDirect
Journal of Wind Engineering & Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia
Field measurement study on turbulence field by wind tower and Windcube Lidar in mountain valley Haili Liao a, b, Hongmiao Jing a, Cunming Ma a, b, *, Qiyu Tao c, Zhiguo Li a, b a b c
Research Center for Wind Engineering, Southwest Jiaotong University, Chengdu, China Wind Engineering Key Laboratory of Sichuan Province, Chengdu, China Highway Planning, Survey, Design and Research Institute, Department of Transport, Sichuan Province, Chengdu, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Field measurement Ultrasonic anemometer Windcube Lidar Bridge site in mountain valley Turbulence intensity Turbulent spectrum Spatial coherence
Due to the complexity of turbulence in mountain valley and lack of research focusing on such type of turbulence fields, which are critical for both buffeting response and vortex induced vibration (VIV) in slender structures, this paper aims to enhance the understanding of turbulence fields in mountain valley by investigating field measurement wind data obtained by a wind tower and a Windcube Lidar. Turbulence intensity, turbulent spectrum and vertical spatial coherence are obtained and analyzed according to the continuous measured data, which are significantly influenced by mountain terrain. Some of these characteristics are compared with current recommended specifications, standards and empirical formulas. The results indicate that turbulence intensity (e.g. probability density function (PDF) distribution, variation with mean wind speed and height) in mountain valley are very different from those recommended by the specifications and standards. It is identified that the Simiu and Panofsky spectral models could induce large discrepancies for mountain valley terrain in China Southwest, while the von Karman spectral models can still well indicate such terrains. Furthermore, the vertical spatial coherences can be accurately expressed by some empirical coherence formulas for a mountain valley, but it is not feasible to adopt empirical coherence formulas with fixed parameters to represent the realistic coherence at different heights in a mountain valley. Meanwhile, the results have a general applicability for the determination of wind characteristics in the mountain areas of China Southwest.
1. Introduction It is of great interest to investigate the wind characteristics of the atmospheric boundary layer (ABL) in mountain areas as the knowledge has applications in many engineering practices. In recent decades, a large number of infra projects (such as long-span bridges and wind turbines) have been built in mountain valleys of southwestern China, and wind loads have been regarded as one of the dominant factors determining their safety and serviceability. Furthermore, since bridge girders and towers for bridges crossing mountain valleys tend to be respectively very long and tall, they are relatively weak and sensitive to wind effects (Ma et al., 2018, 2019; Wang et al., 2019; Wu et al., 2020). For example, the turbulence intensity, which plays a key role in buffeting response and VIV for slender structures, could be relatively large and variable due to the complex mountain terrain. In particular, vertical variation of turbulence intensity is strongly related to the buffeting response of high-rise structures such as bridge towers and wind turbines built in mountain valleys
(Li et al., 2019). For convenience, winds within ABL are usually divided into two parts: mean wind and fluctuating wind. Mean wind is associated with aerodynamic stability, while fluctuating wind, including turbulence intensity, spectrum and coherence, is mostly related to quasi-static and dynamic load effects (dynamic response). It should be noted that most windresistant design focus primarily on mean wind static stability, while design for quasi-static and dynamic load effects are relatively conservative due to lack of a systematic and comprehensive understanding of fluctuating wind. In many countries, wind field characteristic parameters for windresistant design are widely specified and presented in the specifications or codes. For instance, along-wind turbulence intensity have already been specified with empirical formulas under some design standards (Lin et al., 2018), such as USA (ASCE7-10) (ASCE/SEI 7–10, 2010), Japan (AIJ-RLB-2004) (AIJ-RLB-2004, 2004), China (GB50009-2012) (JTG/T 3360-01, 2018), ESDU (ESDU82031, 2012) and Australia/New Zealand
* Corresponding author. Research Center for Wind Engineering, Southwest Jiaotong University, Chengdu, China. E-mail address: [email protected] (C. Ma). https://doi.org/10.1016/j.jweia.2019.104090 Received 15 July 2019; Received in revised form 21 October 2019; Accepted 29 December 2019 Available online xxxx 0167-6105/© 2020 Elsevier Ltd. All rights reserved.
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
(AS/NZS1170.2) (AS/NZS1170.2, 2011). However, wind field characteristics within ABL are too complicated to be completely specified by limited standards. Moreover, the aforementioned specifications or codes may not be suitable for special regions or weather, such as mountain areas and typhoon climates. Therefore, lots of research in recent years has extensively investigated wind characteristics under extreme conditions through numerical simulations, terrain model wind tunnel tests and field measurements. El-Sayed Abd-Elaal et al. (2018) and Matthew Haines et al. (Haines and Taylor, 2018) used numerical simulations to investigate downburst wind flow over real topography and low rise buildings, respectively, and they acquired relatively accurate wind field characteristics. Jubayer C. M. et al. (Jubayer and Hangan, 2018) obtained relevant wind parameters via terrain model wind tunnel tests, and the test results indicated that the simplified code would generally result in higher design wind speeds for structures in complex terrain. Through a terrain model wind tunnel experiment and field measurement campaign, Fernando Bastos et al. (2018) obtained the wind characteristics for a bridge crossing a steep volcanic breach. He found that the mean wind component derived from field measurements is significantly less than that recommended under design code, but the turbulence intensity is much larger due to the roughness and orography upstream from the bridge site. Hui et al. (2009a) comprehensively studied wind turbulence characteristics through field measurements and terrain model wind tunnel tests and provided important wind parameters for wind-resistant design of Stonecutters Bridge. It found that the average turbulence intensity profiles obtained from field measurements were close to design profiles, and the expression under Power Law in relevant specifications was proper. Li Lin et al. (2018) analyzed wind characteristics under a typhoon located on China southeast coast. In many countries’ design specifications, it is indicated that the turbulence intensity calculated based on measurement data is more appropriate for engineering applications than power law. Wang et al. (2013) also noted that design specification was not completely suitable for Su-tong bridge site located on China east coast. Actually, several papers (Fenerci et al., 2017; Lystad et al., 2018; Jing et al., 2019, 2020; Ma et al., 2019) have studied wind characteristics for bridge sites located at mountain valleys and provided important wind characteristic parameters for wind-resistant design of bridges located in such terrain. It should be noted that wind characteristics in mountain areas are different from those in flat terrain like typhoon as well strong winds. Firstly, mountain wind is mainly disturbed by rugged terrain, while for extreme wind in flat terrain is mostly influenced by air convection. Based on Chinese specification (JTG/T 3360-01, 2018), the terrain studied in this paper is obviously belong to D-type exposure with terrain roughness
Fig. 2. The equipment: (a) ultrasonic anemometer (b) windcube Lidar.
coefficient of 0.3. However, under high wind velocity conditions, wind directions measured in mountain valleys (Fenerci et al., 2017; Yu et al., 2019) are always consistent with the direction of the canyon. Meanwhile, the terrain along the canyon is relatively flat so that the D-type exposure with terrain roughness coefficient of 0.3 is no longer applicable for the profile of wind velocity. Moreover, some research (Bastos et al., 2018; Fenerci and Øiseth, 2018) indicate that the ratio between longitudinal, lateral, and vertical turbulence intensities in mountain areas is different from that of 1:0.88:0.50 recommended in the specification (JTG/T 3360-01, 2018), which is suitable for strong winds in flat terrain. The turbulent spectra and spatial coherence (including decay parameter) might be also different from that in a flat terrain, like typhoon and strong winds. Therefore, it is very necessary to carry out the field measurement study of turbulence field in mountain valley. A lot of research has extensively reported observations regarding turbulence fields, however, the studies have generally been conducted regarding special weather in coastal regions. Though some researchers have carried out activities to characterize winds in mountainous topography to meet engineering need, the turbulence intensity, spectrum and coherence have not been systematically investigated or summarized. The purpose of this paper is to enhance the understanding on turbulence intensity, spectrum and coherence in mountain valley regions and provide appropriate turbulent parameters for wind-resistant design practice use in mountain areas. Therefore, a series of data, including long-term data obtained from mast measurements comprising two ultrasonic anemometers and short-term from Windcube Lidar, is analyzed for study use. The subsequent contents of this paper are organized as follows: Section 2 introduces the bridge site, equipment and data processing method; Section 3 presents the results of turbulence intensity (i.e. PDF distribution,
Fig. 1. The topographic map of the bridge site. 2
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
Fig. 4. Wind speed history.
so the loss of data is so heavy that they are removed. Moreover, 12 measuring points are installed from 40 m to 280 m, and recorded measuring data show that the loss of data increases with height. Therefore, data at the lower 9 measuring levels ranging from 40 m to 210 m, are selected for this study, to minimize data missing. In fact, only data at high levels might be lost, and there is almost no loss of data at lower levels. Wind data collected via Windcube Lidar is divided by time interval of 10 min, to derive average wind speed and standard deviation over 10 min easily. Similarly, the ultrasonic anemometers are also sensitive to unfavorable weather such as thunderstorms. Unlike results from Windcube Lidar, wind data at some levels recorded by ultrasonic anemometers are larger than the average. So abnormal wind data at those levels are removed from the datasets in this study. Wind data obtained from ultrasonic anemometers is also divided by 10-min intervals. In addition, wind data collected from ultrasonic anemometers is mainly used to analyze the characteristics of turbulence intensity at a single measurement level, owing to the higher sampling frequency. Meanwhile, the variation in turbulence intensity with height is analyzed by wind data obtained from Windcube Lidar, taking advantage of its ability to simultaneously collect wind data at different heights. Crosschecking of data between anemometer and Lidar is important. However, the measuring period of anemometer and Lidar is different. Data measured by anemometer is about two months, while data measured by Lidar is only two weeks, and they are not in the same time. Meanwhile, we have studied relevant paper (Qiaoqiao et al., 2013). Their result indicate that the correlation coefficients of wind speed measured by anemometer and Lidar are up to more than 99%, and the average deviation of turbulence intensity is 0.009. Therefore, it can say that the data measured by anemometer and Lidar is reliable. Strictly speaking, wind speed measured in mountain area shows to some extent the non-stationary characteristics reported in much of the literature (Jiang et al., 2019). Y. L. Xu et al. (Lystad et al., 2018) and Chen et al. (2007) have documented the non-stationary characteristics of wind speed data collected at a bridge site located in Hong Kong and proposed corresponding wind data processing approaches for non-stationary wind. However, the wind characteristics (e.g. turbulence intensity, wind spectrum, gust factor, etc.) resulting from the above reference are almost the same as those obtained from traditional wind data processing method adopted by this paper. Moreover, Y. L. Xu et al. (Lystad et al., 2018) directly pointed that if a 10-min duration was used in identifying the wind characteristics, nearly the same results would be obtained due to the fact that non-stationarity is not as significant in recordings of 10 min duration. Tao et al., 2016a, 2016b have studied wind characteristics of a strong wind event and a tropical storm based on stationary and non-stationary models. Their result show that the longitudinal turbulence intensity shows much stronger non-stationarity, and PSDs estimated by stationary and non-stationary models are almost the same, except low-frequency range. For mountain area wind, the maximum wind speed recorded in this study is only approximate 18 m/s. Meanwhile, the wind speed history series show that high wind speed always
Fig. 3. The location of the measurement system.
variation with wind speed and height), turbulent spectrum and vertical spatial coherence, some of which are compared with current recommended design specifications, standards or empirical formulas; Section 4 lists the major conclusions on field measurement study. 2. Equipment and data processing Wind measuring devices are installed at the bridge site located on the bank of the Ya-lung River, southwest to Xichang City, Sichuan Province, China (Fig. 1). The bridge site (N 27 420 1600 , E 102 00 5400 ) consists of typical mountainous terrain in China southwest. It is surrounded by high mountains with altitudes of approximate 3000 m, except along the deep valley that the Ya-lung River goes by. A wind measurement system is consisted of two ultrasonic anemometers (as shown in Fig. 2a) and a Windcube Lidar (as shown in Fig. 2b). The two ultrasonic anemometers are installed on wind tower at heights of 30 m and 50 m respectively. The ultrasonic anemometers can collect data regarding scalar wind speed, azimuth angle and elevation angle. According to relative specifications, wind speed ranging from 0 to 40 m/s can be captured by ultrasonic anemometer with both 0.01 m/s resolution and threshold, 1% (30 m/s) to 3% (40 m/s) accuracy, and 10 Hz sampling frequency. As shown in Fig. 3, Windcube Lidar is installed in the vicinity of wind tower, which can provide wind measurements at twelve points ranging from 40 m to approximate 300 m above ground. To ensure collect reliable data, the measuring levels should be set between 40 m and 210 m under three different increments 10 m, 25 m and 20 m. Moreover, wind speed ranging from 0 to 60 m/s can be measured by Windcube Lidar with both 0.02 m/s resolution and threshold, 0.1 m/s accuracy, and 1 Hz sampling frequency. Total 12 different levels ranging from 40 m to 300 m are measured by the installed Windcube Lidar. It should be noted that, as Windcube Lidar makes use of light scattered by atmospheric aerosols, the wind data could be compromised in special weather conditions such as heavy precipitation, fog or excessively clean air. Sometimes, birds or flying debris can also affect Windcube Lidar data collection. Empirically, wind data may be null at some measurement levels. Based on recorded data, it is found that the proportion of the loss of data is 4.28%, which is small enough, so linear interpolation is adopted to generate the missing data. It also noted that the weather is particularly bad (for instance, heavy fog in the morning) for a few days, 3
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
Fig. 5. PSDs at different time.
3. Results and discussions
happen in the afternoon, and wind speed changes slowly with time. In addition, based on the study by Huang et al. (2015) and Tao et al. (Tao and Wang, 2019), we also calculate the evolutionary power spectral density (EPSD) using 2 h’ wind data, which changes more sharply from 1 m/s to 16 m/s. The variation of wind speed with time is illustrated in Fig. 4, and the EPSDs are plotted in Fig. 5. It should be noted that the frequency and spectra are all normalized for comparison. As can be seen from the result, there are minor variations in PSDs, and they are almost unchanged with time on the whole. Therefore, wind can be treated as stationary in the view of EPSD. In a word, the traditional wind data processing method, which is fast and simple, is suitable in this study. It is also critical to derive accurate fluctuating wind speeds (u, v and w components) from the raw wind data. However, raw wind data collected by the ultrasonic anemometer and Windcube Lidar adopt different types of coordinate systems, i.e. Spherical system (U, α and β) and Cartesian system (Ux , Uy and Uz ), respectively. Thus, for ultrasonic wind data under Spherical system, the fluctuating wind speed can be obtained according to the following formulas:
α’ ¼ α α
β’ ¼ β β
u ¼ U cos α’cos β’ U
v ¼ U cos α’sin β’
For a better understanding of the turbulence in mountain valleys, turbulence intensity, turbulent spectrum and coherence are investigated. They are key parameters for calculating buffeting response of structures. 3.1. Turbulence intensity The turbulence intensity characterizes wind speed fluctuations and is defined as the ratio between standard deviation of fluctuating wind components and mean wind speed (this paper adoptes a 10 min mean wind speed) as follows:
σi
Ii ¼ ; ði ¼ u; v; wÞ U
Where, Ii denotes turbulence intensity;σ i denotes standard deviation of fluctuating wind component; U denotes mean wind speed. Turbulence intensity is one of the most important wind field characteristics in structural design, especially critical to buffeting response in long-span bridges. For example, turbulence not only has a significant influence on VIV, but also on aeroelastic stability. Due to the fact that low wind velocity is responsible for VIV and high wind velocity takes major on aeroelastic stability, so turbulence intensity should be investigated at both low and high wind velocities. A comprehensive investigation on turbulence intensity in a mountain valley is carried out in this section. The ultrasonic anemometers were continuously operated for 2 months to provide wind data, while the Windcube Lidar was used to collect wind data for half a month.
(1) w ¼ U sin α’
(2)
Where, α and β denote the attack and yaw angles, respectively; u, v and w denote the longitudinal, lateral and vertical fluctuating wind speeds, respectively. Meanwhile, for Lidar wind data under Cartesian coordinates, the fluctuating wind speed can be calculated using the following equations: qffiffiffiffiffiffiffi 2 2 Ux þ Uy
(3)
qffiffiffiffiffiffiffi 2 2 2 U ¼ Ux þ Uy þ Uz
(4)
Uh ¼
cosα ¼
cosβ ¼
Uh U
sinα ¼
Ux Uh
sinβ ¼
Uz U
(5)
Uy Uh
(6)
u ¼ Ux cosβ þ Uy sinβ cosα þ Uz sinα Uv ¼ Ux sinβ þ Uy cosβw ¼ Ux cosβ þ Uy sinβ sinα þ Uz cosα
(8)
3.1.1. PDF distribution A large amount of research (Lystad et al., 2018) and specifications (AIJ-RLB-2004, 2004) indicate that the PDF distribution of turbulence intensity aligns well with lognormal distribution, which is expressed as follows: f ðxÞ ¼
1 pffiffiffiffiffie xσ 2π
ðln xμÞ2 2σ 2
;x > 0
(9)
where μ denotes mean of the natural logarithm of variable x; σ denotes the standard deviation of the natural logarithm of variable x. However, the turbulence in mountain valley is so complicated that it is difficult to know if the above expression can be applied here. Therefore, wind data collected from the two ultrasonic anemometers (two levels of 30 m and 50 m above the ground) are further analyzed to investigate the PDF distribution. Moreover, to investigate the influence of mean wind speed on the distribution parameters, the wind data are divided by different mean wind speed, i.e. mean speed 1–4 m/s, 4–8 m/s, 8–12 m/s, and above 12 m/s. By doing this, we get parameters in the
(7)
Where, Ux , Uy and Uz usually denote the east, south and erective wind speeds, respectively; Uh and U denote the horizontal and total wind speeds, respectively.
4
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
Fig. 6. PDF distribution of turbulence intensity (height ¼ 50 m, U ¼ 1–4 m/s).
Fig. 7. PDF distribution of turbulence intensity (height ¼ 50 m, U ¼ 4–8 m/s).
increase of wind speed. However, σ, Expectations and standard deviations fall very slowly with wind speed, while μ drops more rapidly. The results are of great significance for investigation and wind-resistant design of structures in mountain valleys. The ratio amongst turbulence intensity’s tree components is listed in Table 1. It is indicated that the ratio varies greatly with wind speed and there is no fixed value. As can be seen from Table 1, ratios get smaller as mean wind speed increases. When mean wind velocity are larger than 12 m/s, the ratios amongst each component at heights of 50 m and 30 m are 1:0.667:0.722 and 1:0.694:0.574, respectively. As known, some specifications and standards have proposed ratios amongst each component for the turbulence intensity. For example, the Chinese code (JTG/T 3360-01,
lognormal distribution that are functions of the mean wind velocity. The PDF of turbulence intensity at heights of 50 m and 30 m under different mean wind speed are illustrated in Figs. 6–13. Meanwhile, the fitted parameters, μ and σ, as well as mathematical expectations and standard deviations derived from μ and σ according to lognormal distribution property, are also shown in above figures. As can be seen, under different mean wind speed and heights (50 and 30 m), PDF distributions are all in a good agreement with lognormal distribution. It implies that PDF distribution in mountain valley can be expressed by lognormal distribution with appropriate parameters. In addition, the variations of these fitted parameters at heights of 50 m and 30 m are illustrated in Figs. 14 and 15, respectively. The results show that all these parameters decrease with the
Fig. 8. PDF distribution of turbulence intensity (height ¼ 50 m, U ¼ 8–12 m/s).
Fig. 9. PDF distribution of turbulence intensity (height ¼ 50 m, U > 12 m/s). 5
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
Fig. 10. PDF distribution of turbulence intensity (height ¼ 30 m, U ¼ 1–4 m/s).
Fig. 11. PDF distribution of turbulence intensity (height ¼ 30 m, U ¼ 4–8 m/s).
3.1.2. Variation with wind speed From above section, it can find that the mean and standard deviations of turbulence intensity decrease with the growing of mean wind speed. According to Eq. (1), the turbulence intensity also drops with the mean wind speed increasing. However, in order to further understand the variation in turbulence intensity with the wind speed in mountain valley, the mean wind speed threshold of 1 m/s is adopted to calculate the turbulence intensity, as shown in Figs. 16 and 17. These two figures indicate that the turbulence intensity decreases with the increase of wind speed, and each component (Iu, Iv and Iw) obviously tends to have a fixed value.
2018) proposes the ratio of 1:0.88:0.50. It can also be seen from Table 1 that the proposed ratios vary a lot from that obtained under measurements. It can be concluded that it is inappropriate to directly apply the specifications and standards to mountain valley. However, the ratios listed in the specifications and standards are not completely unuseful in mountainous valley. Owing to the complicated topographical conditions and mean wind speed threshold, the ratios obtained from the measurement may be close to the values recommended by the specifications and standards under certain conditions. It is important to note that it is necessary to obtain turbulence intensity in mountainous valley by on-site measurements or other methods.
Fig. 12. PDF distribution of turbulence intensity (height ¼ 30 m, U ¼ 8–12 m/s).
Fig. 13. PDF distribution of turbulence intensity (height ¼ 30 m, U > 12 m/s). 6
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
Fig. 14. Fitted parameters at height of 50 m.
Fig. 15. Fitted parameters at height of 30 m.
Additionally, as can be seen from Figs. 16 and 17, with the increase of wind speed, the three turbulence intensity components, Iu, Iv and Iw, tend to reach approximately 0.092, 0.054 and 0.065 respectively, and the ratios shall be close to 1:0.59:0.71, which is very different from the ratios of 1:0.88:0.50 recommended by the Chinese code (JTG/T 3360-01, 2018). Therefore, under high wind speed conditions, it is inappropriate to apply the ratio proposed by specifications and standards for the wind-resistant design of structures located in mountain valleys. As mentioned in Introduction, the turbulence intensity is not only critical for buffeting response in structures under high wind speeds, but also plays key role on structure VIV at low wind speeds. The ratios amongst the three turbulence intensity components at low wind speeds are not yet statistically in agreement with the recommended values. Therefore, more attention should be paid to the actual turbulence intensity for wind-resistant design of structures (e.g. long-span bridges and wind turbos) located in mountain valley.
Table 1 Ratio amongst components of turbulence intensity. Height
Threshold
Iu: Iv: Iw
50 m
1–4 m/s 4–8 m/s 8–12 m/s >12 m/s 1–4 m/s 4–8 m/s 8–12 m/s >12 m/s
1:0.920:0.751 1:0.829:0.720 1:0.805:0.760 1:0.667:0.722 1:0.931:0.709 1:0.825:0.669 1:0.812:0.656 1:0.694:0.574
30 m
Although there are 20 m level difference between the two measuring heights, the scattered pattern of the turbulence intensity under the two heights are very close. However, the scattered pattern of different turbulence intensity components are not identical. Comparing with the scale of the terrain, the 20 m height difference is too small to substantially affect the scattered pattern. Besides, the height of the measuring points is higher than the ground vegetation, which has an important influence on the turbulence intensity. According to the different distribution patterns under the three turbulence intensity components, as illustrated in Figs. 16 and 17, it can be concluded that the turbulence intensity presents significant three-dimensional behavior in mountain valley.
3.1.3. Variation with height It is difficult to obtain turbulence intensity at all desired positions (e.g. long-span bridge girders and bridge tower tops) for structures located in mountain valley through field measurements. In most cases, the turbulence intensity can only be obtained for a few points near the site at specific heights above the ground. In order to further understand
Fig. 16. The variation in turbulence intensity with wind speed at a height of 50 m. 7
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
Fig. 17. The variation in turbulence intensity with wind speed at a height of 30 m.
Fig. 20. The variation in turbulence intensity of Iv with height.
Iu ðzÞ ¼ I10
(11)
Where, α is terrain roughness coefficient; I10 is nominal turbulence intensity at a height of 10 m (Lin et al., 2018). For convenience, the above empirical formula has been adopted in analysis for turbulence intensity in mountain valley. The recorded turbulence intensity is fitted by least squares method using the empirical formula so as to obtain the parameters of c and d (I10 and α). Two technical routines (A and B) are employed during data processing and illustrated in Fig. 18. The purpose of technical routine A is to investigate how turbulence intensity varies with height in mountain valley; the results are plotted in Figs. 19–21. Additionally, the PDF distribution for fitted parameters c and d are illustrated in Figs. 23–25, and the mean and standard deviations are listed in Table 2. It should be noted that, owing to very limited wind data taken from Windcube Lidar, no threshold wind speed is adopted during wind data
Fig. 18. The diagram of the technical routines A and B.
how turbulence intensity varies with height and how it affect the structures, a set of wind data with sampling frequency of 1 Hz, collected by the Windcube Lidar, is analyzed. Some specifications (ASCE/SEI 7–10, 2010; AIJ-RLB-2004, 2004; JTG/T 3360-01, 2018) proposed that the turbulence intensity in the along-wind direction of Iu ðzÞ could be expressed by a power law (Lin et al., 2018). The empirical formula is as follows: d 10 Iu ðzÞ ¼ c z
α 10 z
(10)
The empirical formula in Chinese Code GB50009-2012 (JTG/T 3360-01, 2018) has been specifically defined as:
Fig. 21. The variation in turbulence intensity of Iw with height. Fig. 19. The variation in turbulence intensity of Iu with height. 8
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
processing. As mentioned in Section 2, though the measuring height can reach up to 300 m, a large amount of wind data at higher measuring levels are unable to be properly collected due to complex site conditions such as precipitation, heavy fog and dust. Therefore, only wind data from nine measuring levels, 40, 50, 60, 85, 110, 135, 160, 185 and 210 m above ground, are adopted for analysis. As can be seen from Figs. 19–21, profiles of turbulence intensity align well with the aforementioned empirical formula. It can be concluded that Table 2 The mean and standard deviations for fitted parameters c and d. Component
Parameter
Mean
Std
Iu
c/I10 d/α c/I10 d/α c/I10 d/α
0.4470 0.0814 0.4303 0.0108 0.2053 0.0364
0.5040 0.3756 0.4518 0.4275 0.2321 0.3796
Iv Iw
Fig. 22. The correlation coefficients of turbulence intensity at different heights.
Fig. 23. The PDF of c and d for Iu .
Fig. 24. The PDF of c and d for Iv .
Fig. 25. The PDF of c and d for Iw . 9
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
Fig. 26. Parameter d.
energy distribution in the frequency domain. In the previous studies, varies empirical expressions for turbulent wind speed spectra have been developed in many countries. For example, Chinese Codes employ the Simiu spectrum (Simiu and Scanlan 1996) to depict the longitudinal and lateral wind spectra and Panofsky spectrum (Panofsky and Mccormick, 1960) to the vertical (Yu et al., 2019). The empirical formulas are as follows: For longitudinal wind spectrum, the Simiu spectrum is
it is reasonable to apply the power law proposed by the aforementioned specifications and standards to the description of the variation in turbulence intensity with height in mountain valley. However, the fitted parameters of c and d (I10 and α) are very different from those recommended by specifications or standards. Moreover, turbulence intensities listed in Figs. 19–21 are all larger than those obtained from the ultrasonic anemometers. This may be due to the fact that actual wind speed was relatively small during Windcube Lidar’s recording period. In addition, it can be seen that the turbulence intensity observed in the middle part of power law curves are slightly smaller than that at the top and bottom levels. Owing to the speed-up effect caused by the hill where the Windcube Lidar and mast were located, there is a higher wind speed in the middle, which results in a smaller turbulence intensity, as mentioned in subsection 3.2. Meanwhile, it can also be seen from Figs. 19–21 that the standard deviations of the turbulence intensity are all very large and slightly changes with height. Meanwhile, the correlation of the turbulence intensity in the different points above ground are also studied, due to the significant scatter of turbulence intensity is shown in Figs. 19–21. The correlation coefficients of turbulence intensity are presented in Fig. 22. As can be seen from the result, there is strong correlation for turbulence intensity with height. Moreover, the lateral and vertical turbulence intensities are relatively stronger than longitudinal turbulence intensity. Although the magnitudes of the three turbulence intensity components are very different, their correlation coefficients with height are almost identical. It implies that the turbulence intensity in mountain valley can be predicted with a function in height. The PDF parameter c complies with the lognormal distribution very well, as shown in Figs. 23–25. According to Chinese Code GB50009-2012 (JTG/T 3360-01, 2018), the parameter of c is I10 that matching the lognormal distribution as in subsection 3.1.1. Comparing with parameter of c, the PDF of the parameter d aligns well with Gaussian distribution (normal distribution). In other words, the PDF of the terrain roughness coefficient, α/d, clearly follows Gaussian distribution in mountain valley. Relevant studies (Kikumoto et al., 2017) show that d varies with wind speed, and the shape of PDF obtained in this manuscript is consistent with that given in reference (Kikumoto et al., 2017). However, the terrain roughness coefficient α is too small to represent reality. The more reasonable parameter α might be obtained at high wind speeds. Therefore, the variation in parameter of d with wind speed is illustrated in Fig. 26. The results indicate that parameter d will converge to be a fixed value, approximate 0.2, as the wind speed increases. These results are different from those illustrated in Figs. 19–21, since the latter are calculated from all wind speed. The parameters c and d for turbulence profiles should be thus selected according to wind speed. It is also indicated that, in mountain valley, the parameters should be calculated based on measured data rather than the specifications or standards, which would be more appropriate for engineering applications.
f Su ðf ; zÞ 200fz ¼ 5=3 u2* 1 þ 50fz
(12)
For lateral wind spectrum, the following modified spectrum is recommended by Simiu and Scanlan (1996): f Sv ðf ; zÞ 15fz ¼ 5=3 u2* 1 þ 9:5fz
(13)
For vertical wind spectrum, the Panofsky spectrum is f Sw ðf ; zÞ 6fz ¼ 2 u2* 1 þ 4fz
(14)
Where f is the frequency in Hz; Su;v;w ðf ; zÞ is the turbulent wind spectrum at height z above ground; u* is the friction speed; fz is the nondimensional reduced frequency, which is expressed as follows: fz ¼
f z UðzÞ
(15)
Where UðzÞ is the mean wind speed at height z above ground. Moreover, according to much research on field measurement, the von Karman spectrum is deemed to be one of the most suitable wind spectra to represent the fluctuating wind speed at high wind speed (Panofsky and Mccormick, 1960; Cao et al., 2009; Hui et al., 2009b). The von Karman spectrum is expressed as follows: f Su ðf ; zÞ
σ 2u
f Sv;w ðf ; zÞ
σ 2v;w
4Lu f U
¼
2 5=6 1 þ 70:8 LuU f
4Lv;w f U
(16)
2 1 þ 755 Lv;wU f
¼ 2 11=6 1 þ 283 Lv;wU f
(17)
Where, Lu , Lv and Lw are the longitudinal, lateral and vertical turbulent integral length scales, respectively; σ u , σ v and σ w are the standard deviations of the longitudinal, lateral and vertical turbulent components, respectively; U is the mean wind speed.
3.2. Turbulent spectrum
3.2.1. Field measurement spectrum Given the complex wind environment in mountain valley located in
The turbulent wind spectrum is an argument to describe the turbulent 10
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
Fig. 27. Turbulent wind spectra calculated by the pwelch and pyulear functions, respectively.
China Southwest, the turbulent wind spectrum may not be represented appropriately by the Simiu spectrum, Panofsky spectrum or von Karman spectrum. Therefore, the turbulent wind spectra derived from field measurement recorded by the Windcube Lidar are investigated, since turbulent wind play an important role in calculation of structural buffeting response. The recorded field measurement spectrum is calculated using MATLAB’s pyulear function in order to obtain a smooth spectral curve. Moreover, the pyulear function can, with an appropriate order, return a useful autoregressive power spectral density estimate. The recorded field measurement spectrum can also be calculated via MATLAB’s pwelch function. However, the resulted wind spectral curve is not smooth. The order inputted in the pyulear function is set to 15 during data processing. To verify that the order of 15 is appropriate, a set of raw wind data is simultaneously processed by the pyulear and pwelch functions. The results are illustrated in Fig. 27. It can be seen that the two types of wind spectra are almost the same except at low frequency domain. However, the wind spectrum obtained from pyulear function is more smooth than that obtained from pwelch function, and it is very convenient for obtaining the peak frequency. Due to missing of raw wind data at low frequency domain, the two power spectral estimate methods resulted in difference at low frequency domain. In addition, the spectrum at low frequency domain can be neglected when considering wind effect on structures. In order to investigate the applicability of the aforementioned spectral models, the fitted Simiu, Panofsky and von Karman spectra are also illustrated together with the corresponding field measurement spectra. In order to unify coordinates, the height is used to normalize the frequency. Meanwhile, the fitted turbulence integral scale and friction speed are also supplemented in the results. It should be noted that data used for spectral analysis is measured by Windcube Lidar, due to its ability to simultaneously measure wind data at multiple levels. There are total two weeks (14 days) of data collected by the Windcube Lidar. However, due to the complex field environment and weather conditions, for instance heavy fog in the morning, such data on these days is removed. Eventually, there are approximate 9 days’ data used for the spectral analysis. These data is divide into a series of 10-min segments, then the average field measurement spectra and fitted spectra at heights of 40 m, 85 m and 185 m are shown in Figs. 28–30, respectively. As can be seen from the figures, the von K arm an spectral models can accurately represent the field measurement spectra at the three heights of 40 m, 85 m and 185 m. In contrast, the Simiu and Panofsky spectral models, which are employed by Chinese Code, vary too much from the measured spectra and not applicable at all, except for some spectra. Objectively speaking, only in the lateral and vertical direction at specific heights the Simiu and Panofsky spectral models are in agreement with the realistic spectra. From the analysis of relevant research, it found that the Simiu spectrum can fit the
Fig. 28. The field measurement spectra and fitted spectra at a height of 40 m.
measured results very well at certain height above ground in mountain areas. However, it is not applicable for all vertical levels. In addition, the data used for spectral analysis is measured from Windcube Lidar, and the sampling frequency is only 1 Hz, which resulting in the high-frequency region of the spectra is missed. Therefore, these reasons maybe lead to the fitted Simiu spectrum significantly differ from the measured results in the longitudinal direction. It is also indicated that the Simiu and Panofsky spectral models recommended by Chinese code are not applicable for mountain valley in China Southwest, while the von Karman spectral models still have significant applicability for these terrains. The values of fitted parameters are also supplemented in Figs. 28–30. The turbulence integral length scale fitted by von Karman spectrum is approximate 50 m at the heights of 40, 85 and 185 m, and they are almost identical in the three directions (longitudinal, lateral and vertical). Meanwhile, the friction velocity of u* fitted by Simiu spectrum in lateral direction is approximate 0.3–0.4. 3.2.2. Variation with height Due to the high complexity of the mountain valley, the blockage effect 11
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
Fig. 29. The field measurement spectra and fitted spectra at a height of 85 m. Fig. 30. The field measurement spectra and fitted spectra at a height of 185 m.
of the terrain can have a significant influence on the turbulent spectra near the ground surface. This effect might get weaken as the height above ground surface increases. To further understand the variations in turbulent spectra with height, the field measurement spectra at ten different heights (40 m, 50 m, 60 m, 85 m, 110 m, 135 m, 160 m, 185 m and 210 m and 235 m above ground) are calculated from the raw wind data and illustrated in Figs. 31–33. The above Figs. 28–30 also reflect, to some extent, the changes in the turbulent wind spectra with height. The shape of the longitudinal, lateral and vertical component spectra are basically unchanged at different heights, as shown in Figs. 28–30. However, slight variation can still be observed. Figs. 31–33 show that the high energy zones of all dimensionless spectra move to high frequency domain, and the magnitudes slightly reduced. This may relate to the fact that the airflow at higher positions is less likely to be disturbed (due to squeezing, cutting effects, etc.) than that on ground surface due to terrain roughness, resulting in fluctuating wind amplitude to slightly decrease. Therefore, it is inappropriate to adopt just one spectrum with fixed parameters to calculate the buffeting response for structures located in mountain valley. In many conditions, although certain two points in a mountainous valley might be at the same level, their heights above ground surface is different. Consequently, the turbulent wind spectra at
the two points are also different, which calls for concern when calculating the buffeting response in horizontal structures located in a mountainous valley. In general, wind spectrum should be selected very carefully when calculating the structural buffeting response in mountain valley. 3.3. Vertical spatial coherence The statistical dependence of the fluctuating wind speed at any two points can be described by the coherence function in the frequency domain. It is usually defined as the ratio between the cross-spectral density and the auto-spectral density of turbulent wind speed at any two points (Panofsky and Mccormick, 1960; Peng et al., 2018). In this paper, the vertical coherence functions for measured data are calculated using MATLAB’s mscohere function with NFFT ¼ 10240 and Hanning Window. The definition is as follows: Pxy ðf Þ 2 Cxy ðf Þ ¼ Pxx ðf ÞPyy ðf Þ
(18)
Where Cxy denotes the coherence estimates of the fluctuating wind 12
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
Fig. 31. The longitudinal field measurement spectra along the height.
f Δ Cohðf Þ ¼ exp C U
speeds xðtÞ and yðtÞ using Welch’s averaged modified periodogram method; Pxy denotes the cross-spectral density of fluctuating wind speeds xðtÞ and yðtÞ; Pxx and Pyy denote the auto-spectral density of fluctuating wind speeds xðtÞ and yðtÞ, respectively. Many empirical formulas regarding spatial coherence have been proposed in previous research. Davenport (1961) recommended the following coherence formula in exponential format to represent the horizontal and vertical coherences:
(19)
where C is the decay coefficient; Δ is the separation distance between the two points. However, based on more field measurement research, the coherence is not equal to unity when the frequency approaches zero. Later, Mann (Mann et al., 1991) had improved the above formula to better fit the measured data. The improved formula is expressed as Eq. (20). Furthermore, for the purpose of concision, a modified coherence
Fig. 32. The lateral field measurement spectra along the height.
Fig. 33. The vertical field measurement spectra along the height. 13
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
As can be seen from Figs. 34–36, Eq. (21) can be a good representation of the realistic measured coherences. Moreover, when the reduced frequency approaches zero, the measured coherences are not actually equal to unity. For different turbulent components of the same two points, the fitted values K and C are not yet identical. The fitted values of K decrease as the vertical distance of the two points increase, to the contrary, the fitted values of C increase. For the same vertical distance and different heights, the fitted values of K and C are not identical, which indicates that it is inappropriate to adopt coherence model with fixed parameters to represent the real coherence at different heights in mountain valley. However, the measured coherences indicate that the longitudinal and lateral coherence are basically similar, and they are both smaller and drop faster than the vertical coherence. This may be caused by the heavy disturbance of the longitudinal and lateral turbulent wind arising from the rugged terrain. The impact to the vertical turbulent wind is relatively small. When the reduced frequency approaches zero and the threshold value of coherence is set to 0.4, it can be found that both the longitudinal and lateral effective distance for coherence are both approximate 50 m, while the vertical effective distance is up to 80 m. Furthermore, as shown in Figs. 35 and 36, when the distance between the two points is a constant, even if their measuring height changes, either up or down, the coherence in each component is basically identical. This indicates that the turbulent vortices remain basically uniform at different heights in the canyon. This conclusion also has been proved in section 3.2. The measured spectra align well with von Karman spectral model, which is
Table 3 The measured coherences for investigation. Coherence
Height of z1
Height of z2
Cohxxðz1 ; z2 Þðxx ¼ uu; vv; wwÞ
40 m 85 m 160 m
50 m, 60 m, 85 m 110 m, 135 m, 160 m 185 m, 210 m
formula is developed from Eq. (20) and written as Eq. (21) (Hui et al., 2009b). Cohðf Þ ¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Δ f Δ exp C 1 B z U
f Δ Cohðf Þ ¼ K exp C U
(20)
(21)
where B and K are parameters to be fitted; z is height above ground. In general, due to the complex wind environment in a canyon, the aforementioned coherence formulas may not be applicable. Therefore, to verify whether the aforementioned coherence formula (Eq. (21)) can be employed to represent the coherence in mountain valley, a comparison between measured data and the above coherence model is carried out. In addition, the coherence functions for measured data are also studied to further reveal the variation in coherence with height. The coherences for measured data at two vertical levels are conducted as given in Table 3.
Fig. 34. The measured coherence functions (z1 ¼ 40 m; z2 ¼ 50 m, 60 m, 85 m). 14
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
Fig. 35. The measured coherence functions (z1 ¼ 85 m; z2 ¼ 110 m, 135 m, 160 m).
Fig. 36. The measured coherence functions (z1 ¼ 160 m; z2 ¼ 185 m, 210 m). 15
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090
Fig. 37. The variation in parameter K with distance at different heights.
Fig. 38. The variation in parameter C with distance at different heights.
derived from homogeneous turbulence field. However, it should be noted that the maximum measuring height in this paper is only 235 m, which is much lower than the surrounding mountain. To study the variation of these parameters, K and C, with distance, the results are illustrated in Figs. 37 and 38. As can be seen from the results, the parameter K almost decrease linearly with distance. It is noted that parameter K in vertical direction is always larger than that in longitudinal and lateral direction, and the latter two parameters are almost identical. In addition, the parameter C gets larger as the distance between the two points increases, and C dispersion also rise up. In general, these parameters of K and C are approximately unchanged with the height of z1, but sharply varied with vertical distance between z1 and z2, and relevant parameters could be selected from Figs. 37 and 38 for engineering applications.
intensity with height in mountainous valleys, and the power law index is approximate 0.2 under high wind speed condition. (2) The Simiu and Panofsky spectral models are no longer applicable to mountainous valleys in Southwest China, but the von Karman spectral models still have significant applicability for this type of terrain. The turbulence integral length scales obtained by fitting von Karman spectrum are approximate 50 m in the valley, and they are basically uniform in different heights and directions. The line types of the longitudinal, lateral and vertical component spectra remain basically unchanged as the height increases, but the high energy zones of all the dimensionless spectra move to the high frequency domain, and their values are slightly reduced. (3) The empirical coherence formula can be a good representation of the vertical spatial coherences in mountainous valleys. When the reduced frequency approaches zero, the measured coherences are approximate 0.8 when distance is 20 m. When the threshold value of coherence is set to 0.4, the longitudinal and lateral effective distances for coherence are both approximate 50 m, while the vertical effective distance is up to 80 m.
4. Concluding remarks Owing to the complexity of turbulence and the lack of literature focusing on it in mountainous valleys, this paper carried out a comprehensive investigation of the turbulence in a mountainous valley using field measured wind data from a wind tower and a Windcube Lidar. The turbulence intensity, turbulent spectra and vertical spatial coherence were comprehensively studied by statistical methods. The results were also compared with the specifications and standards of many countries. The major conclusions of this study can be summarized as follows:
Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
(1) The PDF distribution of turbulence intensity in a mountainous valley can be characterized by lognormal distribution with appropriate parameters, which are approximate 2.4 and 0.4 for μ and σ when the mean wind speed is larger than 12 m/s. Moreover, the ratio of the components of turbulence intensity proposed by the specifications or standards cannot be applied to mountainous valleys, which are approximate 1:0.68:0.65 when the mean wind speed is larger than 12 m/s. Furthermore, it is reasonable to apply the power law to the description of the variation in turbulence
Acknowledgement The work described in this paper was fully supported by the National Natural Science Foundation of China (No. 51778545). References Abd-Elaal, El-Sayed, Mills, Julie E., Ma, Xing, 2018. Numerical simulation of downburst wind flow over real topography. J. Wind Eng. Ind. Aerodyn. 172, 85–95. AIJ-RLB-2004, 2004. Recommendations for Loads on Building-Wind Loads. Architectural Institute of Japan, Tokyo. 16
H. Liao et al.
Journal of Wind Engineering & Industrial Aerodynamics 197 (2020) 104090 Li, M., Li, M., Yang, Y., 2019. Strategy for the determination of unsteady aerodynamic forces on elongated bodies in grid-generated turbulent flow. Exp. Therm. Fluid Sci. 109939. Lin, Li, Chen, Kai, Xia, Dandan, Wang, Huaifeng, Hu, Haitao, He, Fuqiang, 2018. Analysis on the wind characteristics under typhoon climate at the southeast coast of China. J. Wind Eng. Ind Aerod. 182, 37–48. Lystad, T.M., Fenerci, A., Øiseth, O., 2018. Evaluation of mast measurements and wind tunnel terrain models to describe spatially variable wind field characteristics for longspan bridge design. J. Wind Eng. Ind. Aerodyn. 179, 558–573. Ma, C., Duan, Q., Li, Q., Liao, H., Tao, Q., 2019. Aerodynamic characteristics of a longspan cable-stayed bridge under construction. Eng. Struct. 184, 232–246. Ma, C., Wang, J., Li, Q., et al., 2018. Vortex-induced vibration performance and suppression mechanism for a long suspension bridge with wide twin-box girder. J. Struct. Eng. 144 (11), 4018202. Ma, C., Wang, J., Li, Q., et al., 2019. 3D aerodynamic admittances of streamlined box bridge decks. Eng. Struct. 179, 321–331. Mann, J., Kristensen, L., Courtney, M.S., 1991. The Great Belt Coherence Experiment: A Study of Atmospheric Turbulence over Water. Risø National Laboratory. Panofsky, H.A., Mccormick, R.A., 1960. The spectrum of vertical velocity near the surface. Q. J. R. Meteorol. Soc. 86, 495–503. Peng, Yongbo, Wang, Shifeng, Li, Jie, 2018. Field measurement and investigation of spatial coherence for near-surface strong winds in Southeast China. J. Wind Eng. Ind. Aerod. 172, 423–440. Qiaoqiao, W., Xiuzhi, Z., Shangkun, W., 2013. Comparison between windcube laser radar and wind tower data. Meteorol. Sci. Technol. 41 (1), 20–26. Simiu, E., Scanlan, R.H., 1996. In: Winds Effects on Structures: Fundamentals and Applications to Design, 3 edition. Wiley-Interscience, New York. Tao, T., Wang, H., 2019. Modelling of longitudinal evolutionary power spectral density of typhoon winds considering high-frequency subrange. J. Wind Eng. Ind. Aerodyn. 193, 103957. Tao, T., Wang, H., Wu, T., 2016. Comparative study of the wind characteristics of a strong wind event based on stationary and nonstationary models. J. Struct. Eng. 143 (5), 04016230. Tao, T., Wang, H., Li, A., 2016. Stationary and nonstationary analysis on the wind characteristics of a tropical storm. Smart Struct. Syst. 17 (6), 1067–1085. Wang, Hao, Li, Aiqun, Niu, Jie, Zong, Zhouhong, Li, Jian, 2013. Long-term monitoring of wind characteristics at Sutong Bridge site. J. Wind Eng. Ind Aerod 115, 39–47. Wang, J., Ma, C., Li, M., et al., 2019. Experimental and numerical studies of the vortexinduced vibration behavior of an asymmetrical composite beam bridge. Adv. Struct. Eng. 22 (10), 2236–2249. Wu, B., Chen, X., Wang, Q., et al., 2020. Characterization of vibration amplitude of nonlinear bridge flutter from section model test to full bridge estimation. J. Wind Eng. Ind. Aerodyn. 197, 104048. Yu, Chuanjin, Li, Yongle, Zhang, Mingjin, Zhang, Yi, Zhai, Guanghao, 2019. Wind characteristics along a bridge catwalk in a deep-cutting gorge from field measurements. J. Wind Eng. Ind. Aerodyn. 186, 94–104.
AS/NZS1170.2, 2011. Structural Design Actions, Part 2: Wind Actions. Jointly published by SAI Global Limited under license from Standards Australia Limited. ASCE/SEI 7–10, 2010. Minimum Design Loads for Buildings and Other Structures. American Society of Civil Engineers, Reston, VA. Bastos, Fernando, Caetano, Elsa, Cunha, Alvaro, Cespedes, Xavier, Flamand, Olivier, 2018. Characterisation of the wind properties in the Grande Ravine viaduct. J. Wind Eng. Ind. Aerodyn. 173, 112–131. Cao, S., Tamura, Y., Kikuchi, N., Saito, M., Nakayama, I., Matsuzaki, Y., 2009. Wind characteristics of a strong typhoon. J. Wind Eng. Ind. Aerodyn. 97 (1), 11–21. Chen, Jun, Hui, Michael C.H., Xu, Y.L., 2007. A comparative study of stationary and nonstationary wind models using field measurements. Boundary-Layer Meteorol. 122, 105–121. Jubayer, Chowdhury Mohammad, Hangan, Horia, 2018. A hybrid approach for evaluating wind flow over a complex terrain. J. Wind Eng. Ind. Aerodyn. 175, 65–76. Davenport, A.G., 1961. The spectrum of horizontal gustiness near the ground in high winds. Q. J. R. Meteorol. Soc. 87, 194–211. ESDU82031, 2012. Paraboloidal Antennas: Wind Loading. Part 1: Mean Forces and Moments. Fenerci, A., Øiseth, O., 2018. Strong wind characteristics and dynamic response of a longspan suspension bridge during a storm. J. Wind Eng. Ind. Aerodyn. 172, 116–138. Fenerci, A., Øiseth, O., Rønnquist, A., 2017. Long-term monitoring of wind field characteristics and dynamic response of a long-span suspension bridge in complex terrain. Eng. Struct. 147, 269–284. Haines, Matthew, Taylor, Ian, 2018. Numerical investigation of the flow field around low rise buildings due to a downburst event using large eddy simulation. J. Wind Eng. Ind. Aerodyn. 172, 12–30. Huang, G., Zheng, H., Xu, Y.L., Li, Y., 2015. Spectrum models for nonstationary extreme winds. J. Struct. Eng. 141 (10), 04015010. Hui, M.C.H., Larsen, A., Xiang, H.F., 2009a. Wind turbulence characteristics study at the Stonecutters Bridge site: Part I—mean wind and turbulence intensities. J. Wind Eng. Ind. Aerodyn. 97, 22–36. Hui, M.C.H., Larsen, A., Xiang, H.F., 2009b. Wind turbulence characteristics study at the Stonecutters Bridge site: Part II-Wind power spectra, integral length scales and coherences. J. Wind Eng. Ind. Aerodyn. 97, 48–59. Jiang, Y., Zhao, N., Peng, L., Liu, S., 2019. A new hybrid framework for probabilistic wind speed prediction using deep feature selection and multi-error modification. Energy Convers. Manag. 199, 111981. Jing, H., Liao, H., Ma, C., et al., 2020. Field measurement study of wind characteristics at different measuring positions in a mountainous valley. Exp. Therm. Fluid Sci. 112, 109991. Jing, H., Liao, H., Ma, C., Chen, K., 2019. Influence of elevated water levels on wind field characteristics at a bridge site. Adv. Struct. Eng. 22 (7), 1783–1795. JTG/T 3360-01, 2018. Wind-resistant Design Specification for Highway Bridges. Ministry of Communications of the People’s Republic of China, Beijing, China. Kikumoto, H., Ooka, R., Sugawara, H., Lim, J., 2017. Observational study of power-law approximation of wind profiles within an urban boundary layer for various wind conditions. J. Wind Eng. Ind. Aerodyn. 164, 13–21.
17