Comparison of wind characteristics at different heights of deep-cut canyon based on field measurement

Abstract

The typical U-shaped deep-cut canyon is widely distributed in the western mountainous areas of China, especially in Sichuan province and Yunnan province. The deep-cut canyon has the characteristics of the high drop in elevation, high-temperature difference, and complex wind environment. A 50 m high meteorological mast with a total of eight anemometers was erected in such topography, and a long-span suspension bridge will be constructed in the area where the meteorological mast is located. Based on the long-term monitor data, the wind characteristic parameters including average and fluctuating wind characteristics and coherence between different heights are investigated. The results are as follows. The dominant wind direction which depends on the topography is north–south. The attack angle of wind is mainly less than zero, and its probability distribution obeys the hypothetical Gaussian distribution. Both the increases in height of anemometer and in wind speed reduce the dispersion of the attack angle of wind. The gust factor has a similar change law of attack angle of wind. Turbulence intensities are affected by the height of the anemometer and the wind speed, and they are different from the recommended value of China Codes. In terms of turbulence integral length scale, the value increases with an increase in the height of the anemometer in the same component. The largest value occurs in the longitudinal direction and the smallest occurs in the vertical direction at the same level. The coherence between any two locations is relatively strong, and the longitudinal component is stronger than others. The measured wind power spectrum for longitudinal, lateral, and vertical wind in deep-cut canyon fits the von Kármán model better.

Keywords

deep-cut canyon field measurement meteorological mast power spectra turbulence intensity wind characteristics wind speed

Introduction

Accurate assessment of wind-induced vibration of structures, such as long-span bridges and vehicle operation, is the premise for ensuring the reliability and safety (Chen et al., 2017a, 2018; Zhang, Zhang et al., 2019), and hence the spatial distribution of aerodynamic forces is needed. The accurate evaluation of the wind characteristics of bridge site determines the accurate prediction of its aerodynamic response (Hui et al., 2009a, 2009b). In an early period, pioneer researchers have finished a lot of work on the wind field measurement, laying the foundation for subsequent research (Busch and Panofsky, 1968; Choi, 1978; Monahan and Armendariz, 1971; Naito, 1988; Solari, 1987; Tamura et al., 1993; von Kármán, 1948). These statistical analyses of the wind data put forward a series of formulas, such as the power spectrum and wind coherence.

Overall, there are three common methods to obtain the wind characteristics at the bridge site: wind tunnel tests (Chen et al., 2017b; Yamaguchi et al., 2003), numerical simulation (Ramechecandane and Gravdahl, 2012), and field measurement (Shu et al., 2015). The wind tunnel test is widely used for its advantages such as high efficiency, easy launch, and easy control of test conditions. With the help of wind tunnel tests, reduced-scale wind tunnel tests were carried out to reproduce as much details as possible of the surrounding roughness and site topography, and the wind characteristics, including the effects of local terrain roughness and topography of the terrains, were investigated (Li et al., 2017a, 2017b; Mattuella et al., 2016). With the development of computer science, many research have launched numerical simulation to investigate the local flow parameters of the site’s surrounding topography (Giahi and Jafarian Dehkordi, 2016; Hu et al., 2016; Ramechecandane and Gravdahl, 2012). Based on the numerical simulation method, the variation in wind field characteristics under the influence of thermal effects at a bridge site in a deep-cut canyon with high-altitude and temperature difference was also studied (Zhang et al., 2018). Nevertheless, the wind tunnel tests and numerical simulations still have some limitations. Due to the limitation of the size of the wind tunnel, the scale ratio of the terrain model may be too small, which will affect the accuracy. For numerical methods, the limitations in turbulence and separated flows affect the accuracy as well. Thus, the field measurements are the most direct way to study the wind parameters for the limitations of the other two methods.

In view of the wind characteristics at bridge site area, many researchers have studied it by means of field measurements in recent years. Hui et al. (2009a, 2009b) investigated the wind characteristics at the Stonecutters Bridge site. Wang et al. (2015) studied the wind properties at the Runyang Bridge based on long-term monitor data. Other researchers (Wang et al., 2013; Xu et al., 2000) also made a great deal of contributions on the wind characteristics of bridge sites. Many other pieces of literature discussed the wind characteristics under extreme weather conditions, such as typhoons and cyclones (Li et al., 2015; Song et al., 2012; Wang et al., 2016). Moreover, compared with the coastal area, there are a few studies by means of field measurement methods recently to depict the wind flow characteristics in complex terrains. Bastos et al. (2018) investigated the properties of the atmospheric wind during an abrupt volcanic breach where affected by cyclones frequently and pointed that a deep and shallow ravine would naturally accelerate the local wind and affect the wind-induced response of the bridge. Cheynet et al. (2016) studied the buffeting response of a suspension bridge in complex terrain based on full-scale data, and the effect of the topography was investigated. Fenerci et al. (2017) discussed the relationship between the wind-loading and response processes by using long-term monitoring data of wind properties.

The article concentrates on wind characteristics at the Jin’an Bridge site that can be classified as a U-shaped deep-cut canyon. The deep-cut canyon has the characteristics of the sharp drop in elevation, high-temperature difference, and complex wind environment. In addition, a 50-m high meteorological mast equipped with tri-axial ultrasonic and bi-axial propeller anemometers was erected at the bridge site. The monitor system can supply the information of mean and turbulent wind characteristics.

Background, measurement system, and recorded data

Jin’an Bridge with the main span of 1386 m in the pipeline is located on the G4216 expressway between Chengdu City and Lijiang City, which is one of the most important construction projects in this section. Figure 1 shows the three-dimensional (3D) render map of the bridge after construction. The terrain at the bridge site is shown in Figure 2.

Figure 1.

Jin’an bridge 3D render map.

Figure 2.

Terrain at the bridge site (Captured from Google Earth).

Description of the bridge site

The bridge site area located in the inland of western China is a typical U-shaped deep-cut canyon (local enlarged drawing can be seen in Figure 2), and the depth of the canyon is over 300 m. For west side of the canyon, the slope gradient of the mountain is generally 40°∼50°, and the gradient of some local area is over 50°. On the east, the slope gradient of the mountain is generally 10°∼21°, and steep cliffs with a height of 20∼40 m appear in some local areas. Near the bridge site, a mountain at an altitude of about 3200 m is located at the south of the bridge, while its slope is relatively gentle. Moreover, the lower reaches of the river are meandering and there is rigid topography near the bridge.

Layout of the monitor system

A meteorological mast with a height of 50 m was built at the location of the north near Jin’an Bridge to collect the wind data in order to study the wind characteristics and provide the reference for bridge design and construction. The location illustration of the meteorological mast is shown in Figure 2. Pictures of the actual erected meteorological mast and close-up views of the anemometers are given in Figure 3. The mast includes three tri-axial ultrasonic anemometers (RM Young 81000, 10 Hz sampling rate, measurement range 0∼40 m/s and 1% accuracy when the wind speed is below 30 m/s) installed on the mast at the level of 10, 30, and 50 m, respectively, and five bi-axial propeller anemometers (RM Young 05106 and measurement range 0∼100 m/s) at the level of 10, 20, 30, 40, and 50 m, respectively. The propeller anemometers belong to the mechanical anemometer, which uses a propeller to collect wind speed data. The collected data are 10 min of average wind speed and wind direction. The ultrasonic anemometer measures 3D wind speed based on the transit time of ultrasonic acoustic signals. The sampling frequency of ultrasonic anemometer records is set to 10 Hz, and the data recorded contain instantaneous wind speed in longitudinal (north), lateral (east), and vertical directions. The lateral separation between ultrasonic anemometer and propeller anemometer at the same level is 2.5 m. In the long-term monitor, all the anemometers had been calibrated before the measurement period.

Figure 3.

The actual erected meteorological mast (left) and the close-up views of the anemometers at the 30-m level (upper right) and anemometers (lower right).

The long-term monitored wind data, which were collected from anemometers at 10-, 30-, and 50-m levels, used for this study covered a 14-month period from November 2016 to December 2017. There are over 8000 hourly time wind records from each propeller anemometer and ultrasonic anemometer allowed for analysis.

Wind data characteristics

Wind speed, wind direction, and attack angle

Equation (1) is the formula for calculating wind direction, where $U_{u}$ and $U_{v}$ represent the measured wind speed in two directions, respectively: longitudinal and lateral directions

ϕ = \arccos (\frac{U_{u}}{\sqrt{U_{u}^{2} + U_{v}^{2}}})

(1)

where $ϕ$ is the wind direction, unit: (°). For the definition of wind direction, 0° represents north and 180° represents the south.

The timespan of the data collected by ultrasonic anemometer used for analysis is set as 10 min, which is coordinated with the China Codes. In addition, only samples with wind speed in three directions greater than 3 m/s will be used for analysis. Figure 4(a) to (c) show the 10-min average wind speed and the direction of measured wind during the observation period recorded by propeller anemometers at the 10-, 30-, and 50-m levels, respectively, and plotted in wind rose diagrams with eight cardinal directions. Figure 4(d) to (f) express the same situation but recorded by ultrasonic anemometers at the 10-, 30-, and 50-m levels, respectively. It is seen that the wind speed and direction of measured wind recorded by the propeller anemometers at 10, 30, and 50 m are similar to those recorded by ultrasonic anemometers at the corresponding level. High consistency of data recorded from different anemometers ensures the quality and the reliability of measured data. In the follow-up analysis, the data based on ultrasonic anemometers will be analyzed and discussed.

Figure 4.

Polar diagrams of measured wind data: (a) propeller anemometer at the 10-m level, (b) propeller anemometer at the 30-m level, (c) propeller anemometer at the 50-m level, (d) ultrasonic anemometer at the 10-m level, (e) ultrasonic anemometer at the 30-m level, and (f) ultrasonic anemometer at the 50-m level.

In Figure 5(a) to (c), the ranges of the mean wind direction for 10 min are shown in polar plots of 8 45° sectors at the level of 10, 30, and 50 m, respectively. It can be seen from the figures that the dominant mean wind directions of the measured wind are from South to South-East-South (SES). In addition, as the height of the anemometer increases, the number of samples with mean wind speed greater than 3 m/s increases gradually. Figure 5(d) shows the maximum wind speed in each sector. It is observed that the three large wind speeds are from sector 135-180, sector 180-225, and sector 315-360 and the corresponding wind speeds are 17.87, 15.17, and 13.28 m/s, respectively. It is worth noting that the wind speeds in sectors 180–225 and 315–360 are still large, although the number of samples is very limited. In addition, the sector SES is the sector that is almost parallel to that of the downstream river of the bridge.

Figure 5.

Rose diagrams of sample number of mean wind direction and maximum wind speed: (a) 10-min mean wind direction at the 10-m level, (b) 10-min mean wind direction at the 30-m level, (c) 10-min mean wind direction at the 50-m level, and (d) maximum wind speed of each cardinal direction.

A total of six indicators, including wind speed, maximum value, 90% quartile (P90), median value, 10% quartile (P10), and minimum value, at different levels are shown in Figure 6. As can be seen from the figure, the aforementioned indicators increase with the increase in the height of the anemometer. Moreover, the increase from the 10-m level to the 30-m level is obviously greater than that from the 30-m level to the 50-m level. This is primarily due to the influence of the surrounding terrain, and the acceleration effect of ridges may make the near-surface wind speed to be at a higher value. The similar phenomena also occur in the Dadu River Bridge area (Zhang, Yu et al., 2019).

Figure 6.

The vertical distribution of the mean wind speed.

Equation (2) is the formula for calculating attack angle of wind, where $U_{u}$ , $U_{v}$ , and $U_{w}$ represent the measured wind speed in three directions, respectively: longitudinal, lateral, and vertical directions

α = \arctan (\frac{U_{w}}{\sqrt{U_{u}^{2} + U_{v}^{2}}})

(2)

where $α$ is the attack angle of wind, unit: (°).

Figure 7 shows the relationship between the attack angle of wind and wind speed, probability distribution and count. It can be noted from the results that the probability of a negative angle of attack is much greater than that of a positive angle of attack. It is owed to the fact that the mast is located in the lower part of the canyon and most of the wind in mountain area flows from top to bottom, which leads to the negative angles of attack. The higher probability of negative angle of attack is consistent with the studies of Fenerci et al. (2017; Fenerci and Øiseth, 2018). The relationship between wind speed and attack angle of wind is shown in Figure 7(a) to (c). It can be seen from the diagrams that when the wind speed increases, the dispersion of the angle of attack at the measuring point decreases. Specifically, the larger the wind speed, the smaller the fluctuation of the angle of attack, and its value tends to be stable. The probability distributions and counts of attack angle of wind are displayed in Figure 7(d) to (f). In this part, according to the research of Cao et al. (2009), we assume that the probability distribution of the angle of attack conforms to the Gaussian distribution, and the curves were also fitted. For the data at the 10-m level, the mean root-mean-square error (RMSE) and coefficient of determination ( $R^{2}$ ) values are about 0.0125 and 0.9649, respectively. For the 30-m level, the RMSE and $R^{2}$ values are 0.0035 and 0.9953, respectively, and for the 50-m level, the RMSE and $R^{2}$ values are 0.0038 and 0.9955, respectively. Thus, both RMSE and $R^{2}$ values at the 30- and 50-m levels are superior to the values at the 10-m level. Therefore, the probability distribution of the attack angle of wind accords with the Gaussian distribution, and the higher the probability distribution of anemometers, the better the fitting. To better observe the distribution of the attack angle of wind, the distribution of sample number every 2° is also introduced. As can be seen from Figure 6(d) to (f), the probability distribution and sample number distribution are both mainly between –10° and 0°. Furthermore, as the height of anemometer increases, the attack angle of wind is getting concentrated. Through Gaussian fitting, the mean value of the attack angle of the bridge site is about –4°, which is greater than the plain area.

Figure 7.

Relationship between distribution of attack angle of wind and: (a) wind speed at the 10-m level, (b) wind speed at the 30-m level, (c) wind speed at the 50-m level, (d) frequency distribution and counts at the 10-m level, (e) frequency distribution and counts at the 30-m level, and (f) frequency distribution and counts at the 50-m level.

The relationships between attack angle and wind directions at different levels are shown in Figure 8. The results show that the south wind is dominated by the negative attack angle of wind, and the north wind is dominated by the positive attack angle. In addition, for the samples with higher wind speed, the attack angle of wind is mainly negative and the wind direction is mainly between the south wind and the southeast by south wind. As the height of the anemometer increases, the distribution of wind direction angle is more extensive under the premise of the same attack angle of wind. The distribution law in Figure 8 is consistent with the previous analysis. When the wind speed is high, the wind direction angle is mainly concentrated near 0° (North) and 180° (South), and the attack angle of wind is mainly between –10° and 0°.

Figure 8.

The relationship between wind direction angle and attack angle of wind at the (a) 10-m level, (b) 30-m level, and (c) 50-m level.

Gust factor

The gust factor is defined as the ratio of the maximum mean wind speed in gust duration and the average wind speed in averaging time interval, and it is given as

G_{t, T} = \frac{U_{t}}{U_{T}}

(3)

where U_t is the largest t-averaged wind speed within the averaging interval T, U_T is the mean wind speed over T seconds. Generally, t = 3 s and T = 10 min are selected to calculate the gust factor (Bardal and Sætran, 2016; Choi and Hidayat, 2002).

Figure 9 shows the distribution relationship between gust factor (u component, longitudinal direction) and wind speed. In addition, the wind speed is divided into several segments with the interval of 3 m/s for the purpose of detailed analysis and comparison. The mean value and standard deviation (SD) of gust factor of each segment and the whole are calculated and shown in the diagrams. For the 10-m level, referring to Figure 9(a), with the increase in wind speed, the mean value of gust factor increases slightly, while the SD value decreases. But in such case, the segment with a wind speed greater than 12 m/s, since the number of samples is too small, the mean value and the SD value are limited. For the 30- and 50-m levels, both the mean value and SD value decrease with the increase in wind speed (Figure 9(b) and (c)). Besides, each measurement point has two notable aspects: one is that the overall mean value and SD value are close to those of the first segment (wind speed between 3 and 6 m/s), and the second is that the value and dispersion of gust factors are larger under low wind speed, which are similar to the distribution law of attack angle and wind speed. Therefore, these phenomena can be explained as follows: on one hand, the variability and randomness of wind speed and wind direction are much higher at low wind speed; on the other hand, the lower wind speed samples account for the majority of the total samples, which also aggravates the phenomena. Generally, with the increase in wind speed, the gust factor gradually decreases and tends to be stable. The distribution regularities of gust factors at v and w components are not given in this article for the similar regularity in u component.

Figure 9.

Relationship between gust factor (u component, longitudinal direction) and wind speed at: (a) 10-m level, (b) 30-m level, and (c) 50-m level.

Turbulence intensity and integral length scale

Turbulence intensity is the ratio of the SD of wind speed fluctuations over a specified period and the mean value of wind speed over the same time period. The turbulence intensity calculation formula can be expressed as follows

I_{i} = \frac{σ_{i}}{U} (i = u, v, w)

(4)

where $i = u, v, w$ , which represents longitudinal, lateral, and vertical turbulence components, respectively. In this article, the specified period is set as 10 min, and the data used in turbulence analysis are based on the ultrasonic anemometers with a threshold wind speed of 3 m/s. Figure 10 shows the polar plots of longitudinal, lateral, and vertical turbulence intensities at the 50-m level. From the results shown in Figure 10, the turbulence intensities at the 50-m level of longitudinal, lateral, and vertical components decrease in turn, and the mean values in total are 0.182, 0.162, and 0.119, respectively. The SD values at three components have the same change law as mean values and are 0.081, 0.073, and 0.047, respectively. Consistent with previous analysis, there is also a strong correlation between turbulence intensity and wind speed. In the case of low wind speed, the value and the spatial distribution of turbulence are very discrete. When the wind speed increases, the dispersion gradually decreases, the wind direction gradually concentrates to the north–south wind direction, and the value also decreases rapidly. The other two locations (10- and 30-m levels) have the same law of change. The statistical results of 10 min turbulence intensities of the winds measured by ultrasonic anemometer at different levels are given in Table 1.

Figure 10.

Polar diagrams at the 50-m level of wind components (a) u, (b) v, and (c) w.

Table 1.

Statistics of 10-min turbulence intensities of the winds measured by ultrasonic anemometer at each location.

	$I_{u}$	$I_{v}$	$I_{w}$	$I_{v} / I_{u}$	$I_{w} / I_{u}$
Mean value at the 10-m level	0.243	0.199	0.099	0.82	0.41
Mean value at the 30-m level	0.198	0.167	0.113	0.84	0.57
Mean value at the 50-m level	0.182	0.162	0.119	0.89	0.65

Figure 11 plots the variations in I_u with wind speed at 10-, 30-, and 50-m levels, respectively. In order to reflect the trend of turbulent intensity with wind speed to some extent, the power law function is adopted to fit the data (Cheung et al., 2016; Peng et al., 2018). From the figures, when the wind speed is low, the greater the turbulence intensity and the degree of dispersion, also see Figure 10. The mean values and SD values of u component at the 10-, 30-, and 50-m levels decrease in turn. The changing trend of SD values indicates that dispersion degree decreases gradually with the height of measured point increases. According to the trend of the fitting curve, it can also be shown that the turbulence intensity decreases with the increase in wind speed. For the similar change law, the related figures are not given, the other two I_v and I_w results are shown in Table 1. But I_w is an exception, the mean values and SD values increase in turn from the 10-m level to the 50-m level. This may be related to the gradual decrease in the attack angle of wind. As for the relationship of the three turbulence intensities, the recommended values in China Codes are as follows: I_v = 0.88I_u and I_w = 0.50I_u. The values of I_v/I_u and I_w/I_u at different levels are given in Table 1. From the table, the values are different from the recommended values in the Codes.

Figure 11.

Variation in I_u with wind mean speed at the (a) 10-m level, (b) 30-m level, and (c) 50-m level.

Turbulence integral length scale is a parameter to describe the average eddy size of turbulence. The turbulence scale is affected by the atmospheric layer greatly, and the method of calculation also influences the results significantly (Garg et al., 1997). In this study, the turbulence scale is calculated by equations (5) and (6), which are based on the von Kármán model for the better fitting results on the spectrum (Yu et al., 2019)

L_{u} = 0.146 \times \frac{U}{f_{p}}

(5)

L_{v, w} = 0.106 \times \frac{U}{f_{p}}

(6)

where f_p, named as peak frequency, is the frequency associated with the peak of the spectrum.

The rose diagrams of turbulence integral length scale of three components at the 50-m level can be obtained from Figure 12. From the results, the distribution of turbulence scale is similar to wind speed, shown in section “Wind speed, wind direction, and attack angle.” Compared with the results of three components with each other, the range of u component is the largest, while the w component is the smallest. With the increase in value, the degree of dispersion also gradually increases. The change law of three components of the other two levels has the same trend as the change of the 50-m level. Table 2 provides an overall summary of the results of three levels. The statistical results indicate that, for the same component, the turbulence scale increases with an increase in the height of the anemometer’s level, and for the same level, u component has the largest value always and w component has the smallest value. Moreover, the results of w component are not very sensitive to the increase in the height, which is different from the other two components.

Figure 12.

Turbulence integral length scale at the 50-m level: (a) u component, (b) v component, and (c) w component.

Table 2.

Turbulence integral length scale of the winds measured by ultrasonic anemometer at each location.

	$L_{u}$ (m)	$L_{v}$ (m)	$L_{w}$ (m)
10-m level	122.94	73.09	41.64
30-m level	144.23	99.45	45.23
50-m level	160.52	114.23	47.67

Power spectra of wind speeds

The formula for the longitudinal spectrum obtained by equation (7) is employed in China Codes. This method is an empirical formula which was proposed by Kaimal et al. (1972) and improved by Simiu and Scanlan (1996)

\frac{f \cdot S_{u} (f, z)}{u_{*}^{2}} = \frac{200 f_{z}}{{(1 + 50 f_{z})}^{5 / 3}}

(7)

where f is the frequency, S_u(f, z) is the longitudinal auto power spectrum at height z, $u_{*}^{2}$ is the friction speed, and f_z is the non-dimensional reduced frequency, also named as Monin similar coordinate, which is calculated as

f_{z} = \frac{f \cdot z}{U (z)}

(8)

where U(z) is the mean wind speed at height z.

For the lateral component spectrum of wind turbulence, the formula was proposed by Kaimal (1972) and lightly modified by Simiu and Scanlan (1996)

\frac{f \cdot S_{v} (f, z)}{u_{*}^{2}} = \frac{15 f_{z}}{{(1 + 9.5 f_{z})}^{5 / 3}}

(9)

where S_v(f, z) is the lateral power spectrum at height z.

For the vertical component spectrum of wind turbulence, the formula suggested by Panofsky and McCormick (1960) is also investigated in this article, and the empirical formula is as follows

\frac{f \cdot S_{w} (f, z)}{u_{*}^{2}} = \frac{6 f_{z}}{{(1 + 4 f_{z})}^{2}}

(10)

where S_w(f, z) is the lateral power spectrum at height z.

In addition to the aforementioned, the spectra models presented by von Kármán (1948) appear to fit the field measured data well according to many field measured research (Bastos et al., 2018; Cao et al., 2009; Fenerci and Øiseth, 2018; Hui et al., 2009b). The Von Kármán spectrum for longitudinal component is obtained by equation (11), and the von Kármán spectrum models for lateral and vertical components are obtained by equation (12)

\frac{f \cdot S_{u} (f, z)}{σ_{u}^{2}} = \frac{\frac{4 \times L_{u} f}{U}}{{[1 + 70.8 {(\frac{L_{u} f}{U})}^{2}]}^{5 / 6}}

(11)

\frac{f \cdot S_{v, w} (f, z)}{σ_{v, w}^{2}} = \frac{4 \times \frac{L_{v, w} \cdot f}{U} [1 + 755 {(\frac{L_{v, w} \cdot f}{U})}^{2}]}{{[1 + 283 {(\frac{L_{v, w} \cdot f}{U})}^{2}]}^{11 / 6}}

(12)

where L_u, L_v, and L_w are the integral length scale of longitudinal, crosswind, and vertical turbulence components, respectively. $σ_{u, v, w}$ are the SDs of longitudinal, lateral, and vertical turbulence components, respectively. U is the mean value of wind speed.

In this article, all the aforementioned spectrum models were investigated. The Simiu model and the von Kármán model are used to compare the measured spectrum of longitudinal and lateral components. For the vertical component, the Panofsky model and the von Kármán model are used. The results can be obtained from Figure 13. It can be seen that the fitting results of the Simiu spectrum and the Panofsky spectrum gradually improved with the increase in height. However, there are also great differences among the longitudinal Simiu spectrum, lateral Simiu spectrum, and the measured spectrum. Generally, the coincidence effect of the Simiu spectrum is not good at the longitudinal and lateral directions. With the increase in height of the anemometer, the coincidence effect of the Simiu spectrum in high-frequency range is improved to a certain extent. The coincidence effect of the Panofsky spectrum is better than that of the Simiu spectrum. Similar to the Simiu spectrum, the coincidence increases with the increase in height. Overall, the fitting results of the von Kármán spectrum and the measured spectrum are always the best among them.

Figure 13.

Wind power spectra of a sample at (a) 10-m level, (b) 30-m level, and (c) 50-m level of components (1) u, (2) v, and (3) w.

Coherence among different anemometers

Wind coherence, which describes the correlation of fluctuating wind speed in frequency domain, is a rather important parameter in the analysis of measured wind. The coherences of measured data are calculated by MATLAB function “mscohere.” The definition of coherence function in MATLAB is as follows

C_{xy} = \frac{| P_{xy} |^{2}}{P_{xx} \cdot P_{yy}}

(13)

where C_xy represents the coherence of x and y using Welch’s overlapped averaged periodogram method. P_xy is cross power spectral density of x and y, and P_xx and P_yy are power spectral densities of x and y, respectively.

One of the first empirical coherence formulas was proposed by Davenport (1961) and improved by Mann et al. (1991) in early 1990s for the better fitting results of data, and the improved expression is as follows

coh (f) = \sqrt{(1 - B \cdot \frac{Δ}{z})} \cdot \exp (- C \cdot \frac{f \cdot Δ}{U})

(14)

where C is the decay coefficient to be fitted, $f \cdot Δ / U$ is the reduced frequency, B is a constant to be fitted, $Δ$ is the separation between anemometers, z is the height of anemometers, and f is the frequency. But based on the research of Hui et al. (2009b), the coherence is not equal to unity when the reduced frequency approaches zero, so equation (14) was modified as follows

coh (f) = K \cdot \exp (- C \cdot \frac{f \cdot Δ}{U})

(15)

where K is the parameter introduced.

Figure 14 shows the plots of coherence for some typical samples against the reduced frequency, and the trend of variation in each sample is not very different. Some basic parameters, such as R², are expressed in plots. The K values of all plots in this article are equal to or very close to 1. The vertical component has a lower coherence of each case. The coherence decays rapidly when the reduced frequency is below 0.1 Hz, especially for lateral and vertical components. It can be observed that the decay coefficients of the 10- and 30-m levels have different laws of change from the other two, these differences may be due to the hillside surface, such as vegetation covers, which cause the wind direction and wind speed to be more uncertain. Therefore, the results associated with the 50-m level will be analyzed (Figure 14(b) and (c)). Aiming at three components, the coherence of the longitudinal component is stronger. Generally, the decay coefficient increases as the distance between the two measurement points increases. Furthermore, an increase in the distance between the two points results in a decrease in the R² value.

Figure 14.

Wind coherence between (a) 10- and 30-m levels, (b) 30- and 50-m levels, and (c) 10- and 50-m levels of (1) u component, (2) v component, and (3) w component.

Summary and conclusion

In this study, a meteorological mast with three sets of anemometers, including ultrasonic anemometers and propeller anemometers, was erected on the bridge site, which is defined as a U-shaped canyon. Wind characteristics, including mean characteristics and turbulent characteristics, based on 14 months of long-term observations were investigated and compared. The following major concluding remarks are drawn:

Affected by topography, the wind characteristics of mean characteristics and turbulent characteristics in mountainous areas are quite different from those in the plain area. Wind characteristics in plain areas cannot be directly applied to the design and construction of bridges in mountainous areas.

For the mean wind characteristics, the main wind direction, especially the wind direction corresponding to the maximum wind speed, is generally consistent with the flow direction of the canyon. The probability distribution of attack angle fits the Gaussian distribution. The lower the wind speed is, the greater the degree of dispersion of the attack angle is. The attack angle is getting concentrated with the increase in height of anemometer.

For the turbulent wind characteristics, the turbulence intensity has the similar change law to the attack angle. For the turbulence scale, the u component has the largest range, while the w component has the smallest at the same level, and the turbulence scale increases with an increase in the height of the anemometer for the same component. Also, the measured wind power spectrum for longitudinal, lateral, and vertical wind in deep-cut canyon fits the von Kármán model better, which agrees with the literature.

The coherence between any two anemometers at different levels is relatively strong, although the decay coefficient decreases as the distance between the two anemometers increases. The coherence of the longitudinal component is stronger. In this article, the coherence based on several typical samples are analyzed briefly, this is far from enough to understand the wind characteristics in mountainous areas. In the future study, based on the accumulated field data, representative coherence function and the effects of different parameters for mountainous areas by statistical method will be investigated.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was financially supported by the National Key Research and Development Program of China (Grant no. 2018YFC1507802), the National Natural Science Foundation of China (Grant nos 51525804 and 51708464), the Construction Technology Project of China Transport Ministry (Grant no. 2014318800240), the Sichuan Province Youth Science and Technology Innovation Team (Grant no. 2015TD0004), and Doctoral Innovation Fund Program of Southwest Jiaotong University.

ORCID iD

Jingyu Zhang

Mingjin Zhang

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