Turbulence characteristics in the wake of a heliostat in an atmospheric boundary layer

The mean and spectral characteristics of turbulence in the wake flow of a flat plate model resembling a heliostat in the atmospheric boundary layer flow are investigated in a wind tunnel experiment. Mean velocity and turbulence kinetic energy were characterised in the wake of a heliostat model at three elevation angles up to a distance of eight times the characteristic dimension of the heliostat panel. An increase in turbulence intensity and kinetic energy was found in the wake flow, reaching a peak at a distance equal to approximately twice the characteristic dimension of the heliostat panel. Furthermore, spectral and wavelet analysis of velocity fluctuations in the wake showed that the dominant mechanism in the immediate downstream of the plate was breakdown of large inflow turbulence structures to smaller scales. In the end, the wake-induced turbulence patterns and wind loads in a heliostat field were discussed. It was found that compared to a heliostat at the front row, the heliostats positioned in high-density regions of a field were subjected to a higher turbulence intensity, and consequently larger dynamic wind loading. The results show that it is necessary to consider the increased unsteady wind loads for the design of heliostat in high-density regions of a field, where the gap between the rows is less than three-times the characteristic length of the heliostat panel.

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Introduction
Understanding the flow characteristics in the wake of a heliostat is a fundamental step for analysis of the flow turbulence within a heliostat field which has several complexities including its dependence on the field arrangement and density. This knowledge accompanied with measurements of in-field wind loads on full-scale structures can be used to predict the wind loads in a heliostat field, which is important for the field design. As an example, heliostats placed in regions of increased turbulence intensity need to be designed to withstand larger unsteady and dynamic forces requiring higher mechanical impedance of the support structure.
Furthermore, by determination of the regions of the field where the mean and unsteady wind loads are lower, the structural stiffness and foundation depth can be decreased. As the heliostat field constitutes between 40% to 50% of the total capital cost of a solar plant (Kolb, 2011), modification of the design of heliostats can help to reduce the capital cost. This study focuses on the wake of a heliostat in an atmospheric boundary layer and aims to develop an understanding of how the statistical and spectral characteristics of turbulence change in the wake of the heliostat. The findings are however not limited to heliostats and provide an insight into the turbulence in the wake of other flat-plate-like structures in the atmospheric boundary layer including solar photovoltaic panels, billboards and wind barriers.
Heliostats in a solar field are arranged in rows surrounding a receiver in a central or a polar design, with a gap between the subsequent rows which typically varies from a value equal to the characteristic length of the mirror panel to about 8-times the characteristic length as the heliostats are installed further away from the central tower (Hui, 2011). Heliostats within the field are exposed to the turbulence in the wake of other heliostats or the solar tower which alters the approaching turbulence in the atmospheric boundary layer. Based on the field arrangement and the gap between the heliostat rows, both the mean flow and turbulence characteristics inside the field can be very different from the incoming conditions. For instance, wind velocity measurements by ultrasonic anemometers in a five-row array of heliostats in a field found an increase in turbulence intensity from 10% in the approaching flow to 50% in the second row of heliostats (Sment and Ho, 2014). Available field measurements are however very limited due to the complexity of field measurements and the variations of velocity and intensity and length scales of turbulence in a heliostat field are not well known. The increased turbulence in the field is related to the vortex shedding in the wake of heliostats. A large eddy simulation of the flow field around a heliostat, at an elevation angle =25°, in a uniform inflow showed formation of coherent turbulence structures and counter rotating vortices in the This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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wake (Boddupalli et al., 2018), which subject the downstream structures to dynamic loading.
Experimental investigations of the wind loads on multiple heliostats also show the changes in the wind loads from a single heliostat. For instance, measurements of surface pressure distribution on a second heliostat placed in tandem of another one in an atmospheric boundary layer flow showed significant changes in the pressure distribution on the second heliostat, which varied with the gap between the two heliostats (Jafari et al., 2019c). Furthermore, Peterka et al. (1987b) measured the wind loads in a four-row arrangement of heliostat models in a wind tunnel experiment and found that while the mean drag force coefficient on a heliostat in the fourth row was lower than that for a heliostat in the first row, the peak drag force coefficient was larger. The increase in the peak drag force suggests an increase in the turbulence intensity in the wake of the upstream heliostats. Hence, understanding how the flow turbulence changes inside the field can help to provide an estimate of the changes in the unsteady wind loads on in-field heliostats.
The flow past a heliostat, if excluding the support structure and the pylon, is similar to the flow past a flat plate at different angles of attack. The wake of a flat plate in a uniform flow, which is a widely studied subject, is characterised by flow separation and vortex shedding. The blockage of the flow by the bluff body creates a velocity deficit in the wake accompanied with periodic velocity fluctuations due to vortex shedding. Three-dimensional and large coherent turbulence structures are formed in the wake. Turbulence intensity in the wake of a square flat plate normal to a uniform flow can increase by up to 16% in the near wake (Nedić et al., 2013).
The angle of attack, which resembles the elevation angle of a heliostat panel during its operation, affects the symmetry of the wake. While the wake of a flat plate normal to a uniform flow is symmetric, when inclined at different angles to the flow, the wake becomes asymmetric due to the unequal strength of vortices shed from the leading and trailing edges, resulting in an asymmetric velocity deficit in the wake (Lam and Leung, 2005;Yang et al., 2012).
Inflow turbulence impacts the wake dynamics including structure of turbulence and vortex shedding. Experimental investigation of the wake of flat disks normal to a gridgenerated turbulent flow showed the effect of turbulence length scale and kinetic energy in the incoming flow on the flow around the disk (Humphries and Vincent, 1976). Increase of incoming turbulence enhanced mixing in the shear layer and increased entrainment of fluid into the wake, and consequently, decreased the wake recovery length over which the flow properties returned to the undisturbed condition. A large eddy simulation of the wake behind a sphere developed in a turbulent pipe flow also showed that the incoming turbulence resulted in a wider This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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radial expansion of the wake and a faster recovery of velocity deficit along the wake centreline (Legendre et al., 2006). Hearst et al. (2016) studied the wake of a wall-mounted cube in four turbulent boundary layers with grid-generated turbulence intensities between 5.4% and 9%. At constant inflow shear level, the wake recovered faster for larger inflow turbulence intensities.
In contrast, shear at the cube height was found to have a stronger impact on the flow recovery when comparing wakes with different values of inflow velocity gradient. On the other hand, inflow turbulence is found to have a stronger effect than mean shear at large inflow turbulence intensities (Amoura et al., 2010). An experimental investigation of the effect of inflow turbulence on the wake of a sphere, with inflow turbulence intensities between 15% and 26% and length scales of 3-4 times larger than the sphere diameter, showed that turbulence and velocity deficit in the far wake scaled with the intensity of incoming turbulence (Amoura et al., 2010). It was found that existence of the incoming turbulence altered the wake flow characteristics as the wake instabilities were mainly resulted from the distortion of the incident turbulence, and not the mean velocity, by the sphere. Furthermore, an experimental study of the effect of grid-generated turbulence, with turbulence intensities between 0.8% and 4.3%, on the wake of a disk normal to the flow found that the inflow turbulence weakened vortex shedding in the near wake and reduced its strength (Rind and Castro, 2012). The turbulence decay rate in the far wake was significantly varied by the inflow turbulence such that the wake turbulence evolved towards the inflow characteristics eventually. The observed effects were found to be stronger when the freestream turbulence intensity was larger than 3%. These findings suggest that the inflow turbulence significantly influences the dynamics of wake instabilities and turbulence within the wake flow. Heliostats are placed in the lower the 10 m of the turbulent atmospheric boundary layer and are subjected to large velocity gradients and large-scale turbulence structures. Hence, the inflow turbulent boundary layer alters the wake of a heliostat from a flat plate developed in a uniform flow.
Another parameter, in addition to the inflow turbulence, which affects the wake of a heliostat is the ground effect. The mirror panel of a heliostat is hinged on a pylon such that there is typically a gap between the bottom edge of the panel and the ground which varies with the elevation angle of the panel. The studies on bluff body wakes in a uniform flow show that decreasing the gap from the ground beyond a certain threshold can suppress vortex shedding (Bearman and Zdravkovich, 1978;Bosch et al., 1996). Furthermore, investigation of the effect of the gap flow on the wake of a sharp-edged flat plate suspended in a water channel showed formation of a wall jet which influenced the near wake significantly (Krampa-Morlu and This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. PLEASE CITE THIS ARTICLE AS DOI:10.1063/5.0005594 Balachandar, 2007;Shinneeb and Balachandar, 2016a). It was found that when the gap increased, the reverse flow in the wake was eliminated and the streamwise velocity fluctuations were decreased (Shinneeb and Balachandar, 2016b).
The present study aims to develop an understanding of the turbulence characteristics in the wake of a heliostat in an atmospheric boundary layer flow. Extensive velocity measurements were conducted in the wake of a flat plate model representing a heliostat in two simulated neutral atmospheric boundary layer flows in the University of Adelaide large-scale wind tunnel to characterise turbulence in the wake flow. The remainder of this paper is organised as follows. A description of the experimental method is presented in Section 2. In Section 3, the wake flow and turbulence were characterised by statistical and spectral analysis of the velocity measurements. The findings are then used as a basis for prediction of how wind loads in a heliostat field change in Section 4. Finally, conclusions are given in Section 5.

Methodology
Experimental measurements were performed in the University of Adelaide large-scale wind tunnel. The working section of the boundary layer wind tunnel is 3 m × 3 m × 17 m, and the turbulence intensity in the empty tunnel is between 1% and 3%. Spires and floor roughness elements were used to simulate the atmospheric boundary layer in the wind tunnel. Five spires with identical dimensions were placed at the inlet of the test section with a centre-line distance of 0.5 m in the lateral ( ) direction. The spires were followed by a 7.2 m streamwise fetch of wooden roughness elements covering approximately 24% of the floor area over the fetch length. The sizing and spacing of the roughness elements were similar to previous experiment by the authors (Jafari et al., 2019c). In order to minimise the parameters affecting the wake flow, it was attempted to create two boundary layers of a similar height so that the relative position of the models in the boundary layers, / , does not change. Therefore, the spires for the two boundary layers, boundary layer A and B, were designed with an identical height (1.3 m). Figure 1(a- insignificant and hence blockage does not affect the measurements as the maximum allowable blockage ratio is 10% (Barlow et al., 1999). The inflow conditions and the wake behind the heliostat model were measured using a Turbulent Flow Instrumentation (TFI) multi-hole pressure probe (Cobra probe), which is capable of measuring the three unsteady velocity components and the local static pressure. The accuracy of the measured velocity by the multi-hole pressure probe is within ±0.5 m/s and ±1° in pitch and yaw angles for turbulence intensities of up to 30% according to the manufacturer datasheet. The turbulence intensities in this study are generally below this limit except at immediate near-wake regions. Furthermore, the measurement error of mean velocity calculated This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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as the standard deviation of five identical measurements was found to be 1.1%. Cobra probes have been found to provide reasonable accuracy for measurement of complex turbulent flows in the literature. Cobra probes have been used in the literature (Vino et al., 2003;Bell et al., 2014;Peng et al., 2016;Gilhome, 2017;Lam and Peng, 2017;Aliferis et al., 2019) for study of both time-averaged and time-resolved velocity and turbulence characteristics in the wake flow. Furthermore, a comparison of the velocity measurements obtained by a Cobra probe with those from laser Doppler anemometry and hot wire anemometry in a turbulent pipe flow and in the wake of a wind turbine showed that the maximum error in the mean velocity and turbulence intensity measured by the Cobra probe were 2% and 1%, respectively (Draskovic, 2017).

Incoming Flow Conditions
The comparison for all cases. The non-dimensional shear = ( / )( / )| is also given in Table 1. This non-dimensional form of shear is selected as recommended by Hearst et al.
(2016) as free-stream measurements in the atmospheric surface layer are not usually available.
Hence, is normalised with the time scale of the flow at the hinge height of the model. This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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Furthermore, to achieve similarity in the wind tunnel experiments, ideally, both the boundary layer and the heliostat model must be scaled down by an identical length scale factor.
However, this similarity cannot be achieved for small-scale structures such as heliostats and solar panels as it requires the model dimensions to be very small. The inevitable consequence of the mismatch of length scale factors is a change in / and a different / and / between the wind tunnel and the full-scale conditions. This scaling issue has been extensively discussed in the literature (Tieleman, 2003;Richards et al., 2007;Jafari et al., 2019c) and its discussion is out of the scope of the current study. However, with consideration of the differences, the results are interpreted with respect to the inflow conditions for characterisation of the wake flow.

Wake Measurements
The velocity in the wake of the heliostat model at elevation angles of =30°, 60°, and 90° were measured within the two boundary layers. These elevation angles are considered to represent a range of operational angles for heliostats. Velocity measurements were performed over streamwise wall normal planes downstream of the heliostat model at =0 mm. Figure 3 shows the measurement grid which was determined based on initial measurements and evaluation of the resolution of the results. The measurement grid ranges from =10 mm to =500 mm in the vertical direction, with a grid spacing ∆ =20 mm. In the streamwise direction, the measurements were taken at positions ranging from =150 mm to =1600 mm downstream of the model, with ∆ increasing from 50 mm in the near wake to a maximum of 200 mm at =1000-1600 mm. Velocity measurements were acquired for a duration of 30 seconds at each point with a sampling frequency of 2 kHz. The measurements for spectral analysis were taken over a duration of 120 seconds. A low-pass filter was applied to all the measured velocity signals filtering them at 900 Hz to avoid aliasing. This frequency response is deemed sufficient for the current measurements as the entire energy containing frequencies are resolved.
Furthermore, estimation of the spatial resolution of the Cobra probe shows that the velocity measurements are of acceptable accuracy. Based on Taylor's frozen turbulence theory, for a frequency response of 900 Hz, and the maximum mean velocity at measurement locations equal to 6.77 m/s (corresponding to the mean inflow velocity at the heliostat hinge height in Boundary Layer B), the minimum spatial resolution of the probe is approximately 1.19 mm.
This minimum resolvable length scale is two orders of magnitude smaller than the plate chord length (200 mm) and the integral length scale of the two inflow boundary layers (402 mm and 480 mm), and three orders of magnitude smaller than the depth of the boundary layer This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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(approximately 1 m). It must be noted that larger errors may exist in the immediate proximity of the plate in the wake, at / ≤1 where turbulence intensity is very large. Comparison of the flow for the two incoming conditions in Figure 4 shows a slightly faster recovery of the wake for the incoming flow with the larger turbulence intensity, which is due to the increased entrainment of fluid into the wake.
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.
PLEASE CITE THIS ARTICLE AS DOI:10.1063/5.0005594 This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.  Figure 6 shows the normalised turbulence kinetic energy calculated from the variance of all three velocity components in the wake at different elevation angles and inflow conditions.

Wake Turbulence
As shown in Figure 6, there is a significant increase in turbulence kinetic energy in the near wake region, / <4, which is caused by separation of flow at the edge of the plate. The increased turbulence kinetic energy region is mainly concentrated at the top edge of the plate and much less effect is seen at the bottom edge of the plate. This asymmetry is due to velocity gradient of the incoming boundary layer flow and the ground proximity where shear is smaller at lower heights.
Comparison of the turbulence kinetic energy for the plates at the three elevation angles shows that the increase in turbulence energy is larger for the plate at =90° compared to =60° and 30°. Furthermore, the regions of increased turbulence kinetic energy are extended further downstream for lower elevation angles which is due to the increased gap between the plate and the ground, forming a stronger wall jet in the gap region as discussed in (Krampa-Morlu and Balachandar, 2007;Shinneeb and Balachandar, 2016a).
The inflow condition has a slight impact on the turbulence kinetic energy distributions as shown in Figure 6. For instance, comparison of the turbulence kinetic energy at =90° for the two inflow conditions, Figure 6(a) and Figure 6(b), shows a slightly larger peak of turbulence kinetic energy in the wake of the plate in boundary layer A. This can be attributed to the inflow conditions. The difference between the inflow turbulence intensities is not significant, ( =13% and 15% in A and B, respectively). Hence, the larger shear, , in This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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boundary layer A, which is twice that in boundary layer B, may be the source of the larger peak turbulence kinetic energy in the wake.  Comparison of the shear stress distributions for the two inflow conditions shows that the regions of large Reynolds stress extend further downstream in boundary layer A. A similar effect is observed for the turbulence kinetic energy in Figure 6. The increased spatial extent of This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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regions of large turbulence kinetic energy and Reynolds stress in boundary layer A is due to the larger mean shear and the lower turbulence intensity in boundary layer A (Table 1).

Spectral Characteristics of Velocity Fluctuations
The power spectral density of the streamwise velocity fluctuations in the wake of the plate at =90° is shown in Figure 8. The power spectral density pre-multiplied by frequency and normalised with the velocity variance, / 2 , is presented. This non-dimensional form is chosen as it displays the frequencies which are the major carriers of energy in the flow. As similar trends were found for the streamwise and vertical velocity spectra, only the results for the streamwise velocity are presented here. Figure 8(a) shows the normalised spectra in the near wake region, / =1, at different vertical heights inside and outside the wake flow. A clear distinction between the spectral distributions in the wake, / =0.5-1, and outside the wake, / =2-2.5, is found. Outside the wake flow, at / =2-2.5, the peak of the spectrum is at / ∞ =0.03, which is the dominant peak of the turbulent boundary layer flow corresponding to the integral length scale. There is an increase in the energy of non-dimensional frequencies / ∞ >0.1 at / =1.5, which is the location of increased turbulent kinetic energy ( Figure   6(a)). When descending further into the wake flow, / =0.5-1, the spectral distribution changes drastically showing transfer of energy to high frequencies such that the inflow peak This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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diminishes. The transfer of energy from the large-scale turbulence structures to the small scales shows the breakdown of large inflow turbulence structures by the plate. downstream, in the far wake region, / =4 to 8, the spectral distribution is more similar to the inflow although containing higher energy at the mid-to high frequencies, / ∞ >0.1, compared to the inflow. Furthermore, comparison of the spectrum at / =8 with the inflow spectrum shows that the wake flow has not fully recovered up to / =8 (as also shown in mean velocity contours in Figure 4).
The results in Figure 8 show no dominant shedding peak in the turbulence spectrum making it difficult to determine a unique Strouhal number for vortex shedding. Instead, an increase in the energy of a range of turbulence scales is identified. Lack of a distinguished shedding frequency in the wake was also found by Hearst et al. (2016) in the wake of a cube exposed to free-stream turbulence, where an increase in the energy over a range of frequencies was observed instead of a prominent shedding frequency. Rind and Castro (2012) also found that inflow turbulence damped vortex shedding and reduced its energy, such that at high inflow turbulence intensities the trace of vortex shedding in the turbulence spectrum was hardly visible. This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. Figure 9 shows the normalised spectral density of streamwise velocity fluctuations at / =0.65 at several downstream distances for the plate at =60° and =30°. For both elevation angles, increase of higher-frequency turbulent scales is evident in both the near and far wake regions showing that the plate at both elevation angles breaks down the large inflow turbulence structures. To identify the effect of the elevation angle, the near wake spectra at the hinge height for the three elevation angles are compared in Figure 9(c-d), which show the energy transfer is more significant at =90°.

Orthogonal Wavelet Decomposition of Velocity Fluctuations
To determine the most energetic scales in the wake flow, the orthogonal wavelet method is employed in this study to decompose velocity according to the scales of turbulence structures. Using the wavelet multi-resolution technique, the velocity signal is broken down into frequency bands which directly represent the scales of turbulent structures (Razali et al., 2010). The decomposed velocity signals corresponding to each level can then be analysed individually in time or frequency domain providing detailed information about each specific This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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turbulence scale. Using this method, a better understanding of the various scales in the wake flow can be achieved. This method has been used in the literature for analysis of turbulent structures in wake flows (Rinoshika and Zhou, 2005;Zhou et al., 2006;Rinoshika and Zhou, 2007;Razali et al., 2010;Rinoshika and Omori, 2011;Ali et al., 2016). Further details of the orthogonal wavelet method are given in (Rinoshika and Zhou, 2005;Razali et al., 2010).
The wavelet basis function used in this study is the Daubechies wavelet with an order of 20, as according to Rinoshika and Zhou (2007) the Daubechies is a suitable filter for turbulence analysis due to its smoothness and frequency localisation. Using the orthogonal discrete wavelet transform, the streamwise and vertical velocity signals are decomposed into 10 levels.  velocity variances in the wake increase to reach a peak at / =2.5 and 3, respectively, which is then followed by a decrease in the variance (the same trend as turbulent kinetic energy in Figure 6). The normalised variance of the wavelet levels of the streamwise and vertical velocity components in the wake is shown in Figure 11(b) and 11(d), respectively. According to Figure   11(b), the variances of wavelet Levels 1-3, which represent the small turbulence structures, remain almost constant along the streamwise direction. In contrast, the variances of large scales, wavelet Levels 8-10, increase significantly reaching a peak at / =2.5. According to Figure 11(b) and Figure 11(d), in the near wake region at / =1, the variances of all 10 levels are almost in the same order due to the breakdown of large scales to smaller scales which leads to reduction of energy of large scales, which agrees with the spectral analysis in Figure 8.
Further downstream as the large scales grow, their energy increases and the variances of Levels 8-10 increase by four to five times between / =2 and / =8. A similar trend is observed in These results along with the spectral analysis show that the dominant mechanism in close proximity of the plate in the near wake is breakdown of large-scale turbulence structures of the inflow boundary layer and transfer of energy to small scales. When moving further downstream, the flow starts to recover, and turbulence scales develop towards the inflow distribution. Evolution of turbulence structures towards the external turbulence was also found in the in the far wake of a sphere exposed to inflow turbulence by Rind and Castro (2012).
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(a) (b) (c) (d) Figure 11: Normalised velocity variance in the wake in streamwise direction for =90° at / = 0.65: (a-b) variance of streamwise velocity and its wavelet levels, (c-d) variance of vertical velocity and its wavelet levels. Figure 12 shows the normalised variance of the wavelet levels of the streamwise velocity component in the wake at / =0.65 for =60° and =30°. The streamwise distribution of the different wavelet levels in Figure 12(a) for =60° is similar to that in Figure 11(b) for =90° with a slightly larger magnitude of the variance of the large scales in the proximity of the plate. For =30°, Figure 12(b), no significant change in the streamwise distribution of the variances of the different levels is observed indicating that there is much less breakdown of large scales by the plate compared to the other two elevation angles. This agrees with the results found from the spectral distributions in Figure 9(b).
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. Since the length scales of turbulence and their corresponding intensity can directly impact the wind loads on structures placed in the wake flow, these results can have important implications for the dynamic wind loads in an array of heliostats, which are discussed in Section 4.

Wake-induced wind loads in a heliostat field
The results in Section 3 provide an insight into the velocity and turbulence characteristics in the wake of a model heliostat in a simulated atmospheric boundary layer flow. In a heliostat field, the heliostats which are placed inside the field are exposed to the wake flow of the upstream heliostats. Although the presence of the other heliostats in the wake affects the flow, the wake characteristics can be used as a basis for prediction of the flow characteristics in the field. As the flow turbulence characteristics are directly related to the wind loads on heliostats, the findings in Section 3 can have several implications for the design of heliostat fields which are discussed in this section.
A summary of changes in mean velocity and velocity variances in the wake flow compared to the inflow boundary layer is presented in Figure 13. To highlight how the flow in the wake changes from the inflow atmospheric boundary layer, the mean velocity, streamwise and vertical velocity variances, and the streamwise and vertical turbulence intensities in the wake are normalised with their inflow values and are given for the plates at the three elevation angles. According to Figure 13, despite the decrease in mean wake velocity, the velocity This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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variance is larger than the inflow condition. Except at / <1.5 for =90°, both the streamwise and vertical velocity variances are larger in the wake for all other cases. The increase of velocity variance accompanied with the reduction of mean velocity leads to an increased turbulence intensity, such that both the streamwise and vertical turbulence intensities are larger than the inflow at / <5 for all the three elevation angles. The maximum velocity variances in the wake flow for all three elevation angles occur at approximately / =2, where the velocity variance is more than double the inflow value. The maximum turbulence intensity at the heliostat hinge height occurs at / =1.5 with more than 12-times increase in turbulence intensity for =90° and 60°, Figure 12(a-b).  Figure 13 shows that velocity variance and turbulence intensity in the wake are in general larger than the inflow boundary layer. Hence, the heliostats positioned inside the field are exposed to an increased turbulence intensity compared to the heliostats in the first row, which This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

Operating wind loads
is in agreement with the field measurements by Sment and Ho (2014). Since the increased turbulence intensity is directly correlated with an increase in unsteady forces (Bearman, 1971;Peterka et al., 1989;Jafari et al., 2018;Pfahl, 2018), the unsteady wind loads on the in-field heliostats are expected to be larger than the wind loads on the heliostats in the first row. For instance, according to Figure 13(a), in the wake of a heliostat at =90° at / =2 increases to a value 7-times larger than the inflow turbulence intensity. If a second heliostat is placed at this location, it will be exposed to = 7.6 , . Such increase in turbulence intensity will lead to more than 80% increase in the unsteady drag force coefficient on the second heliostat according to the relationship given in Jafari et al. (2018). Hence, a significant increase in the unsteady loads on the downstream heliostats in a field is expected due to the increase of turbulence intensity.
The changes in wind loads predicted from the wake turbulence is confirmed by experimental measurements of wind loads on tandem heliostats. Measurements of pressure distribution on two heliostat models placed in tandem show that the pressure distribution on the heliostat panel varies significantly as the gap between the two heliostats changes leading to variations in the position of the centre of pressure (Jafari et al., 2019a), which can be attributed to the turbulence in the wake of the upstream heliostat. The standard deviation of the position of centre of pressure, representing the unsteady variations of the pressure distribution on the downstream heliostat panel, was found to be larger than the single heliostat when the gap between the two heliostats, / , varied between 1 and 7 reaching a peak at / =2 (Jafari et al., 2019a). Furthermore, the standard deviation of the position of centre of pressure was the largest when both plates were elevated at 90° which shows the effect of the dramatically increased turbulence intensity in the wake of the heliostat at =90°.
As the magnitude of the forces on the panel and the position of the centre of pressure vary, the induced moments at the heliostat hinge and pylon base change, which is important for the design of elevation drives and foundation. Figure 14 shows the hinge moment coefficient, , on the second tandem heliostat compared to the single heliostat based on the experimental measurements by (Jafari et al., 2019a). The mean and peak coefficients and the root mean square (RMS) of the fluctuating coefficient normalised with those on a single heliostat are shown. It is observed that the peak and RMS coefficients are larger than those for the single heliostat for all the gap ratios for =90° and 60°, and at / ≥2 for =30°. The increase in the peak and RMS coefficients is larger for =90° and 60° compared to =30° which shows the effect of the larger increase in turbulence intensity in the wake of the heliostat This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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at the two larger elevation angles. Moreover, the results of Figure 14 show an increase in the mean hinge moment coefficient at / ≥2 for =30° and 60° and / =3-4 for =90°. The increase of mean hinge moment is despite the reduction of mean lift and drag force coefficients reported by Peterka et al. (1987a) for the heliostats in five downstream rows, which is due to the reduction of mean velocity in the wake of the upstream heliostat. Larger mean hinge moment coefficient, in spite of lower mean lift and drag force coefficients, is attributed to the unsteady variations of the position of the centre of pressure as reported by Jafari et al. (2019a), and is a consequence of the increase of turbulence intensity and variation of the length scales of turbulence in the wake of the upstream heliostat. Hence, the increase in turbulence intensity in the wake of a heliostat not only leads to an increase in the fluctuating lift and drag forces on the downstream heliostat, but may also lead to an increase of the mean hinge moment coefficient. This highlights the importance of modification of heliostat design for the heliostats positioned inside the field compared to those at the front rows.

Effect of field density on operating wind loads
Since the wake flow characteristics are found to vary at different streamwise distances, the distance between the rows in a heliostat field, which is indicated by field density, is an important parameter affecting the flow and the wind loads. According to Figure 13, the maximum turbulence intensity in the wake flow for all three elevation angles occurs at approximately / =1.5, and both streamwise and vertical turbulence intensities are significantly larger at / ≤3 being more than 4-times larger than the inflow for =90° and 60° and double the inflow for =30° ( Figure 13). Hence, in high density areas of a heliostat field, where the gap between the heliostat rows is between 1-3 times the characteristic length, the unsteady wind loads are expected to be larger than other regions of the field indicating a This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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critical design case. The increase in the unsteady wind loads on the inner field heliostats is expected to be less in regions of the field with a very low density, / >6, as the increase in the turbulence intensity is less than 20%, where the 20% increase is for =90°. Hence, the wind loads on heliostats in the low-density regions near the perimeter of the field are likely to show a smaller variation with distance into the field than those in high-density regions close to the tower. The predicted effects are in agreement with the pressure measurements on tandem heliostats which show the largest variations of the position of the centre of pressure at / =1-3 (Jafari et al., 2019a) and the maximum hinge moment coefficients at / =3 for =90° and 60° ( Figure 14).
Field density can also affect the dominant frequencies and scales of turbulence in the flow. Based on the spectral analysis of wake turbulence, it was found that the spectral distribution of turbulence in the immediate wake at / =1 differs significantly from the atmospheric boundary layer spectrum showing an increase of small scale turbulence structures and breakdown of the larger inflow turbulence structures ( Figure 8). The wavelet analysis also showed that the different frequency bands of turbulence spectrum have a similar variance, without a prominent peak at the heliostat hinge height at / =1 ( Figure 11). In contrast for / > 2, the frequencies with the peak variance and energy are the same as the peak frequencies of the inflow boundary layer. The peak frequencies in the wake flow at / > 2 are therefore dominated by the incoming flow. As the minimum gap ratio in a heliostat field is typically larger than / = 1 (Hui, 2011), for gaps between the rows in a dense region of a field where / ≤ 2, the spectral content of the flow will differ significantly from the inflow boundary layer. In contrast, peak frequencies of the velocity fluctuations in the field in regions where / > 2 will be similar to the atmospheric boundary layer flow. As the unsteady wind loads and the length scales of turbulence in the flow are strongly correlated (Jafari et al., 2019c), these changes will affect the unsteady wind loads on heliostats in very dense regions. This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.
PLEASE CITE THIS ARTICLE AS DOI:10.1063/5.0005594

Stow wind loads
During periods of high wind speeds, heliostats are usually stowed by aligning the mirror panel horizontally to reduce the mean wind loads. The unsteady forces on the stowed heliostats in the turbulent atmospheric flow however can be large due to the large vertical velocity variance which is correlated with the unsteady lift force on stowed heliostats (Jafari et al., 2019b). The peak turbulence-induced forces are critical for survivability of the heliostat structure since heliostats need to withstand the largest wind speeds at stow position. Partial stowing of a heliostat field has been suggested to increase the field operation hours over a larger range of wind speeds such that heliostats in regions of predicted larger wind load coefficients are stowed at lower mean wind speeds, with other regions of the field still in operation (Pfahl et al., 2017). Such stowing strategies require a reliable estimation of the wind loads in different regions of the field in order to determine the regions which need to go to stow. Based on the wind direction, the stowed heliostats may be positioned in the wake of the heliostats which are still in operation. As according to Figure 13, the vertical velocity variance and turbulence intensity in the wake of the operating heliostats for all three elevation angles are always larger than the inflow, the stowed heliostats will be exposed to increased vertical turbulence intensity.
For instance, vertical turbulence intensity in the wake of a heliostat at =30° at / =2 is approximately double its inflow level according to Figure 13(c). If a stowed heliostat is placed in the wake of the mentioned heliostat at / =2, the doubled vertical velocity will subject it to 40% increase in the peak lift force coefficient according to Jafari et al. (2019b). Hence, the results of this study show that in addition to mean wind speed as the criteria for partial stowing, vertical turbulence intensity in the field must also be considered.

Conclusions
The mean and spectral turbulence characteristics in the wake of a flat plate placed in turbulent atmospheric boundary layers were investigated. The results showed a significant increase in turbulence kinetic energy in the near wake region, / <4 at the top edge of the plate. The increase in turbulence kinetic energy was the largest for =90° and the lowest for =30°. Spectral analysis of velocity fluctuations in the wake showed two distinct regions.
There was an increase in high frequencies and smaller scales of turbulence structures at / ≤ 2, while in the far wake region, / =4-8, the spectral distribution was a closer match to the incoming turbulent boundary layer. Furthermore, the variances of the streamwise and vertical velocity components were compared to the variances of their wavelet levels. It was found that in the immediate wake region, / =1, breakdown of large inflow turbulence structures to This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.
smaller scales was the dominant effect. When moving further downstream turbulence within the wake evolved towards the external turbulence structure.
The results of this study were applied to predict the wake-induced turbulence in a heliostat field. It is acknowledged that the presence of the downstream heliostats in the wake affects the flow pattern and the flow around multiple heliostats is more complex compared to a single heliostat. The results of the wake of a single heliostat could however be used as a basis for estimation of the turbulence changes in a heliostat field and consequently the wind loads.
Based on this analysis, it was proposed that due to the increased turbulence intensity in the wake flow, the unsteady wind loads on the in-field heliostats increased compared to the front row, with a peak at high density areas of a field where the gap between the heliostat rows is between one to three times the characteristic length of the heliostat panel. Depending on the wind direction, the high-density regions of a field, which are typically positioned close to the tower, may be positioned in the wake of their upstream heliostats. Although the mean wind speed is lower in the wake, they are subjected to higher turbulence intensities in the wake of the upstream heliostats, which highlights the importance of dynamic wind loading for design of heliostats in regions of high density. Further studies in future are required to investigate the dynamic wind loading in different regions of a field, and to determine the effect of the field layout and wind direction on the wake flow.