3.1 Near-wake velocity field

The turbulent flow field in the near wake of the turbine is examined using the Feb 2016b dataset which has a FOV of 115 m (vertical) $\times$ 66 m (streamwise) centred at 0.41 $D$ downstream of the turbine tower and 0.19 $D$ offset from the central tower plane. Figure 4 presents the time-averaged velocity field and the streamwise velocity profile in the near wake obtained from a recording of 30 min duration. In this dataset, the turbine blade intersects with the light sheet plane at $z=33~\text{m}$ and $z=127~\text{m}$ , as indicated by the dashed horizontal lines in figure 4(b). The contours of the velocity magnitude exhibit a region of low velocity spanning from 7 to $8~\text{m}~\text{s}^{-1}$ in the centre portion of the wake, and the velocity increases substantially as it approaches the region near the edge of the wake, showing a clear velocity deficit.

Figure 4. (a) Time-averaged velocity vector field ( $1:2$ skip applied in both horizontal and vertical directions for clarity) superimposed with the velocity magnitude contours, showing the near wake of the EOLOS turbine for the Feb 2016b dataset. (b) Time-averaged streamwise velocity profile at $x=0.5D,y=0.19D$ in comparison to the time-averaged velocity profile obtained from the cup-and-vane anemometers from the met tower located at $x=1.71D,y=0.46D$ . The dot-dashed line in the figure is a logarithmic fit of the data points at $z=27$ and 126 m, i.e. $U/U^{\ast }=\unicode[STIX]{x1D705}^{-1}\ln (z/z_{0})$ , where the friction velocity $U^{\ast }=0.95~\text{m}~\text{s}^{-1}$ , the roughness length $z_{0}=0.53~\text{m}$ and the von Kármán constant $\unicode[STIX]{x1D705}=0.41$ . (c) Time-averaged streamwise velocity deficit profile at $x=0.5D$ , $y=0.19D$ in comparison to the profile measured by wind tunnel PIV of Hancock & Pascheke (Reference Hancock and Pascheke2014) at $x=0.5D,y=0$ and the profile measured with lidar of the 2 MW Enercon E-70 wind turbine (Iungo et al. Reference Iungo, Wu and Porté-Agel2012) at $x=0.5D,y=0$ .

To further examine the velocity distribution quantitatively, figure 4(b) presents the averaged streamwise velocity profile at $x=0.5D$ extracted from the velocity vector field shown in figure 4(a), in comparison with the incoming flow velocity profile obtained from the anemometer data from the met tower. According to the average wind direction in the Feb 2016b dataset, the met tower is located at $1.71D$ downstream of the turbine tower with a $0.46D$ offset from the central tower plane (i.e. $x=1.71D,y=0.46D$ ). Under this circumstance, all of the sonic anemometers installed on the met tower are adversely affected by the wake produced by the met tower itself. In addition, considering $5^{\circ }$ wake expansion and no presence of wake meandering at $x=1.71D$ , the cup-and-vane anemometers at $z=102$ , 77 and 52 m are influenced by the EOLOS turbine wake. Therefore, the time-averaged incoming flow profile $U_{\infty }(z)$ during the deployment is obtained using a logarithmic fit of the velocity measured with the two cup-and-vane anemometers, located at $z=126$ and 27 m, which are free from the influence of both the wakes of the met tower and the turbine. Note that the anemometer located at $z=7~\text{m}$ is also excluded in the fitting of incoming flow profile due to the non-negligible influence of ground roughness on the velocity profile at this elevation. All the velocity profiles are normalized with $\overline{U}_{\infty }=11.6~\text{m}~\text{s}^{-1}$ which is the mean incoming velocity obtained by spatially averaging the incoming velocity profile between the top and bottom tip elevations. The figure shows a clear deficit of the cup-and-vane measurements at $z=102$ , 77 and 52 m in comparison to the logarithmic fit, confirming the influence of the turbine wake on the measurements at these elevations. More importantly, the comparison highlights the significant deficit in the near-wake velocity distribution.

To facilitate comparison between the near-wake profile obtained using SLPIV with those from the literature, the profile of the wake deficit at $x=0.5D$ , i.e. $\unicode[STIX]{x1D6E5}U(z)/U_{\infty }(z)=1-U(z)/U_{\infty }(z)$ is presented in figure 4(c). For comparison, the wake deficit obtained from a wind tunnel PIV measurement of Hancock & Pascheke (Reference Hancock and Pascheke2014) at $x=0.5D,y=0$ , and that from a recent lidar measurement of Iungo et al. (Reference Iungo, Wu and Porté-Agel2012) at $x=0.5D,y=0$ , are also provided in the figure. In particular, the wind tunnel measurement was performed on a model turbine with the scale ratio of $1:300$ to represent a 5 MW turbine with a hub height of 90 m and a rotor diameter of 120 m. The incoming and wake flow were both measured using a Dantec FibreFlow Laser Doppler Velocimetry system, and the incoming flow yields $z_{0}$ of 0.0002 m and $U^{\ast }$ of $0.137~\text{m}~\text{s}^{-1}$ . The lidar measurement was performed around a 2-MW Enercon E-70 wind turbine with a spatial resolution of 18 m. This lidar dataset is selected for comparison as it is the only published field measurement around utility-scale turbines that provides the near-wake velocity distribution at a downstream location close to that of our SLPIV measurements. Since Iungo et al. (Reference Iungo, Wu and Porté-Agel2012) does not provide lidar data for the incoming flow, to obtain its wake deficit profile, the incoming flow is estimated through a logarithmic fit of the lidar measurements of the velocity profile outside the turbine wake at $x=6D$ , similar to that shown in figure 4(b). The corresponding logarithmic curve yields $z_{0}$ of 0.057 m and $U^{\ast }$ of $0.72~\text{m}~\text{s}^{-1}$ . To compare the measurements of different turbines, in figure 4(c), the elevation is normalized using the rotor diameter $D$ and hub height $H$ of the corresponding turbine.

As the figure shows, SLPIV and lidar measurements display similar variation in velocity deficit across the elevation span, while the wind tunnel result exhibits a much lower deficit in the region around the turbine hub. Moreover, the lidar-measured profile shows a substantially larger velocity deficit compared to other profiles even though it was collected at the same downstream location with respect to the turbine tower (i.e. $x=0.5D$ ). To provide a more quantitative and robust comparison of the wake deficit across these profiles, we calculated the spatially averaged wake deficit $\unicode[STIX]{x1D711}=\overline{\unicode[STIX]{x0394}U(z)/U_{\infty }(z)}$ by averaging the wake deficit within the blade span (i.e. the elevations between the top tip and the bottom tip indicated by the two dashed horizontal lines in figure 4 b). The results show that $\unicode[STIX]{x1D711}=0.29$ for SLPIV, 0.31 for the wind tunnel and 0.52 for the lidar measurements. In addition, based on the parameters (e.g. thrust coefficient $C_{T}=0.7$ ) from our SLPIV, we calculate $\unicode[STIX]{x1D711}$ using a number of wake models to assess their performance in capturing the velocity deficit of the near wake of utility-scale wind turbines. For models with range extended to the near wake, such as the Risø WAsP model of Katic et al. (Reference Katic, Højstrup and Jensen1986) and the Risø analytical model of Frandsen et al. (Reference Frandsen, Barthelmie, Pryor, Rathmann, Larsen and Højstrup2006), the calculations show that $\unicode[STIX]{x1D711}=0.29$ for Risø WAsP and 0.34 for Risø analytical, both in a close range compared to the SLPIV result. Other models, including the UO FLaP model of Ainslie (Reference Ainslie1988), ECN Wakefarm model of Crespo et al. (Reference Crespo, Hernandez, Fraga and Andreu1988) and the one from Bastankhah & Porté-Agel (Reference Bastankhah and Porté-Agel2014), are intended to be used downstream of $x=2D$ , where the $\unicode[STIX]{x1D711}$ is calculated to be 0.52 for UO FLaP, 0.54 for ECN Wakefarm and 0.30 for Bastankhah’s model, respectively.

In addition, both the velocity and wake deficit profiles from our SLPIV measurements exhibit two ‘bumps’ (i.e. local velocity minima) at $z=60~\text{m}$ and 110 m, respectively, which are a result of a slight upsurge of streamwise velocity at elevations around the hub height. Similar features of this kind in the near-wake profile have also been reported in Magnusson (Reference Magnusson1999), Whale et al. (Reference Whale, Papadopoulos, Anderson, Helmis and Skyner1996) and Schulz et al. (Reference Schulz, Letzgus, Lutz and Krämer2017). In particular, Magnusson (Reference Magnusson1999) attributed the cause of such features to the local blade geometry and lift generation. Specifically, the flow blockage can reduce substantially around the blade root according to the specific blade design, leading to a decrease of velocity deficit. Comparatively, a considerable increase of deficit occurs in the mid-section of the blades where the optimum lift is produced. Moreover, due to a reduction of lift generation associated with the presence of tip vortices, the velocity profile tends to recover to the undisturbed state at the elevations closer to the blade tip. A combination of the above-mentioned variation in velocity profiles results in the two-bump feature in the near-wake velocity deficit profile. Compared with the SLPIV result, the deficit profile from the wind tunnel experiment shows a significantly steeper reduction around the hub height, which makes the bumps in the profile more prominent and they shift towards the elevations corresponding to the blade tips. Such difference between SLPIV and wind tunnel measurements may be a result of the following two reasons: (i) the results from the two measurements are not at the same spanwise location, with SLPIV recorded at $y=0.19D$ and the wind tunnel data on the tower plane; (ii) the turbine model employed in the wind tunnel experiment has a larger spacing between the blade roots and the hub, and yields less blockage. The profile of lidar does not display similar features, which may be primarily caused by its relatively low spatial resolution (i.e. 18 m) compared to PIV measurements.

Figure 5. (a) Time-averaged in-plane TKE ( $k_{xz}$ ) contour showing the near wake of the EOLOS turbine for the Feb 2016b dataset. (b) The in-plane TKE profile of SLPIV at $x=0.5D,y=0.19D$ in comparison to the profile measured by wind tunnel PIV of Hancock & Pascheke (Reference Hancock and Pascheke2014) at $x=0.5D,y=0$ .

To examine the turbulent characteristics of the near wake, the in-plane turbulent kinetic energy (TKE, i.e.  $k_{xz}=(\langle u^{\prime 2}\rangle +\langle w^{\prime 2}\rangle )/2$ , where $u^{\prime }$ and $w^{\prime }$ are the velocity fluctuations in $x$ and $z$ directions, respectively) is calculated using the instantaneous velocity fields and is presented in figure 5. The contour of $k_{xz}$ (figure 5 a) shows a region of relatively low $k_{xz}$ around the hub height, and local maxima of $k_{xz}$ in the region between the hub height and the elevations corresponding to the turbine blade tips. Quantitatively, a more than 80 % increase in $k_{xz}$ is observed in the region of local maxima with respect to the values in the region around the hub height. Accordingly, figure 5(b) presents the in-plane TKE profile extracted from the contour plot, in comparison to that from the wind tunnel experiment of Hancock & Pascheke (Reference Hancock and Pascheke2014). For better comparison, both profiles are scaled by $\overline{U}_{\infty }^{2}$ . Note that the lidar result of Iungo et al. (Reference Iungo, Wu and Porté-Agel2012) shown in figure 4 is not provided for TKE comparison here, since the paper only shows the TKE profiles along fixed elevation angles rather than at fixed streamwise locations, which makes the comparison difficult. As the figure shows, the $k_{xz}$ profile of SLPIV highlights a local minimum around the hub height. In contrast, the $k_{xz}$ profile from the wind tunnel measurement exhibits a strong upsurge, near the same region, around the blade root elevations. Such a difference is attributed to the spanwise offset of the two measurements. At the tower plane (i.e. in the case of the wind tunnel measurement), the turbulence associated with the nacelle wake can significantly enhance the near-wake TKE in this region. With a spanwise offset (i.e. in the case of the SLPIV measurement), the influence of nacelle wake on the local TKE decreases in the region around the hub height. In addition, the SLPIV result exhibits two local maximum values around $z=55~\text{m}$ and 112 m, respectively. The locations of the maxima correspond to $(z-H)/D\approx \pm 0.3$ , in the vicinity of the locations where ‘bumps’ in the velocity profiles are identified in figure 4(b), suggesting the $k_{xz}$ peaks may be connected to the high local mean velocity gradient. Such bumps are shifted to the region slightly outside of the blade tip at $(z-H)/D\approx \pm 0.55$ for the wind tunnel profile. Simple geometrical considerations reveal that the spanwise offset between measurement planes is insufficient to account for the difference observed in the figure. In other words, considering the TKE peaks above the hub height, peak in our measurement is below the corresponding elevation where the blade tip intersects the measurement plane, while in the wind tunnel measurement the TKE peak occurs above the blade tip elevation. Notably, a recent numerical study using LES on a model-scale turbine (Santoni et al. Reference Santoni, Carrasquillo, Arenas-Navarro and Leonardi2017) revealed that a considerable (and asymmetrical) flux of TKE occurs in the spanwise directions. In addition, another LES study (Foti et al. Reference Foti, Yang, Campagnolo, Maniaci and Sotiropoulos2018) showed that the operation region of the turbine also induces a shift of the TKE peaks (streamwise turbulence intensity in the paper, which is similar to TKE) to the inside of the blade tip elevations, specifically for region 3 of turbine operation. Therefore, we believe this shift of TKE peaks could be an effect of spanwise transport of TKE and/or variations in the region of operation of the turbine, which needs to be further investigated in future studies.

Before closing this section, it is worth pointing out that SLPIV can only resolve a certain percentage of the in-plane TKE due to the filtering effect associated with two-point cross-correlation with a finite interrogation window size. Correspondingly, the turbulence associated with flow structures smaller than our interrogation window, e.g. the velocity fluctuations induced within the snow voids formed by tip vortices, cannot be captured from our measurements. Hence, for the completeness of our analysis, a rough assessment of the filtering effect is provided here using sonic anemometer measurements which were shown to effectively capture wake turbulence, including that induced by the tip vortices at the EOLOS site (Toloui, Chamorro & Hong Reference Toloui, Chamorro and Hong2015). The assessment is conducted using the hub height sonic anemometer at the met tower for a time period of 14 min, different from that of the SLPIV experiment. The period is carefully selected using the following criteria: (i) mean wind direction of $-7^{\circ }$ from the north to ensure that the sonic anemometer is located inside the turbine wake but outside the influence zone of the wake of the met tower structure; (ii) mean wind speed of ${\sim}10~\text{m}~\text{s}^{-1}$ and a turbulence intensity of ${\sim}$ 18 %, matching those of the SLPIV measurement. The in-plane TKE is calculated using both the filtered and unfiltered velocity components from the sonic anemometer data. Based on the Taylor frozen eddy hypothesis, the scale of the temporal filter is chosen to match the interrogation window size of the SLPIV measurements. Accordingly, the ratio of filtered to unfiltered in-plane TKEs is regarded as the percentage of the in-plane TKE captured by SLPIV. The result shows that SLPIV is capable of capturing 95 % of the total in-plane TKE. This estimate involves uncertainties due to the following reasons: (i) the sonic measurement provides only single-point estimates rather than those of the entire two-dimensional plane; (ii) the sonic and SLPIV measurements do not occur at the same period; (iii) the measurement location of SLPIV (centred around $x=0.41D$ ) differs from that of the sonic anemometer ( $x=1.71D$ ). Note that the above analysis assumes the 20 Hz sonic anemometer captures all the TKE within the turbine wake. This assumption is reasonable since the energy-containing scale in the turbine wake has been shown to be close to (at least of the order of) that of atmospheric flows according to the literature (Vermeer et al. Reference Vermeer, Sorensen and Crespo2003; Frandsen Reference Frandsen2007). According to Kunkel & Marusic (Reference Kunkel and Marusic2006), who compared the performance of hotwire and sonic anemometers for measuring atmospheric turbulence, we estimate the sonic anemometer captures ${>}97\,\%$ of TKE measured from the hot-wire under the field conditions of our SLPIV experiment.

To further investigate the characteristics of the near wake, the instantaneous velocity vector fields are examined individually in conjunction with the turbine operational conditions. In particular, figure 6 presents two samples of the instantaneous velocity field at different instances in time where the near wake depicts distinct behaviours, referred to as the wake expansion state and wake contraction state hereafter. Figures 6(a) and 6(b) show a sample of the instantaneous flow field and the corresponding streamwise velocity profile at $x=0.5D$ , respectively, illustrating a typical wake expansion state. The wake expansion, characterized by a significant velocity deficit in the central portion of the wake, is the dominant wake state as the turbine is operated to extract kinetic energy from the incoming wind. Nevertheless, it is observed that the near wake also exhibits contracting behaviour occasionally. As shown in figure 6(c,d), the wake contraction state exhibits a pronounced upsurge of the velocity in the central portion of the wake. In this region, the velocity magnitude rises above the average velocity (over the entire elevation span) of the wake, and occasionally exceeds the free stream velocity measured above the blade-top tip height in the field of view of the SLPIV.

Figure 6. Samples of instantaneous velocity field ( $1:2$ skip applied in both horizontal and vertical directions for clarity) in the near wake of the EOLOS turbine showing two distinct wake behaviours. A sample of the wake expansion state including (a) the instantaneous velocity vector field superimposed with velocity magnitude contours and (b) the corresponding streamwise velocity profile at $x=0.5D$ . A sample of the wake contraction state including (c) the instantaneous velocity vector field superimposed with velocity magnitude contours and (d) the corresponding streamwise velocity profile at $x=0.5D$ .

Figure 7. A schematic illustrating inner and outer wake zones for the definition of wake velocity ratio $R_{w}$ .

To obtain a quantitative characterization of the two distinct wake states mentioned above, we introduce the wake velocity ratio $R_{w}$ based on the instantaneous near-wake velocity field obtained from SLPIV. Specifically, as shown in figure 7, the cross-section of the entire wake is divided into an inner disk (referred to as the inner wake hereafter) and an outer annulus (referred to as the outer wake hereafter) of equal area. Then $R_{w}$ is defined as the ratio of the spatially averaged velocity of the inner wake ( $\bar{u}_{in}$ ) to that of the outer wake ( $\bar{u}_{out}$ ), i.e. $R_{w}=\bar{u}_{in}/\bar{u}_{out}$ . At the sampling plane of the SLPIV (i.e. $y=0.19D$ ), the inner wake corresponds to an elevation span from $z=46$ to 114 m, and the outer wake includes the region between $z=33$ and 46 m as well as that between $z=114$ and $z=127~\text{m}$ . For each instantaneous sample, we can calculate $\bar{u}_{in}$ and $\bar{u}_{out}$ by spatially averaging the streamwise velocity over the corresponding elevation spans within the field of view of the SLPIV, and subsequently obtain the $R_{w}$ . Note that the streamwise velocity of the entire region rather than that at a specific streamwise location is used for spatial averaging to ensure a more robust characterization of the inner wake flow speed in comparison to that of the outer wake. According to the definition of $R_{w}$ , $R_{w}>1$ indicates the averaged streamwise velocity in the inner wake is higher than that in the outer wake, representing the characteristic of a wake contraction, while $R_{w}<1$ suggests a lower velocity in the inner wake and matches the trait of wake expansion. In the following analysis, the $R_{w}$ will be employed to quantify the different wake states. Nevertheless, it is important to point out that the contraction state defined using $R_{w}>1$ does not necessarily correspond to a propeller state of a wind turbine which would require a comparison between the incoming and the wake flows. Instead, the $R_{w}$ criterion provides a demarcation of when the turbine operates at the desired conditions and when it is underperforming, which leads to a reduced velocity deficit in the inner wake.

Figure 8. (a) Time series of wake ratio $R_{w}$ . (b) Probability histogram of $R_{w}$ .

Figure 8(a) shows the variation of $R_{w}$ over the time duration of the SLPIV measurements. In this period, the turbine was operated mostly in the region ${>}$ 2 (i.e. 94.6 % of the time) and the averaged yaw error was $5.42^{\circ }$ . The mean value of $R_{w}$ was $\langle R_{w}\rangle =0.947$ , indicating a predominately wake expansion state according to our $R_{w}$ -criterion described above. However, the $R_{w}$ also fluctuates substantially over the period and has a standard deviation, $\unicode[STIX]{x1D70E}_{R_{w}}=0.089$ . Particularly, approximately 25 % of the time duration can be classified as a wake contraction state with $R_{w}>1$ . Moreover, figure 8(b) indicates approximately 16 % of the time duration yields a value of $R_{w}$ that is more than one $\unicode[STIX]{x1D70E}_{R_{w}}$ above $\langle R_{w}\rangle$ , representing a strong wake contraction state, while approximately 10 % of the cases have $R_{w}$ more than one $\unicode[STIX]{x1D70E}_{R_{w}}$ below $\langle R_{w}\rangle$ which is classified as a strong expansion for the following analysis.

Figure 9. Schematics illustrating the blade element velocities and the corresponding angles associated with blade element velocity triangle.

Although not discussed extensively in the literature, the variation of wake states observed here is reminiscent of the wind turbine wake transition to a propeller state reported in a number of prior analytical and numerical studies (Eggleston & Stoddard Reference Eggleston and Stoddard1987; Sørensen, Shen & Munduate Reference Sørensen, Shen and Munduate1998; Sebastian & Lackner Reference Sebastian and Lackner2011, Reference Sebastian and Lackner2012). These studies suggest that wind turbine wakes can show a contraction-like behaviour under specific conditions of operation. Specifically, the theoretical analysis presented in Eggleston & Stoddard (Reference Eggleston and Stoddard1987) pointed out that wake contraction phenomena can appear in the operation of a variable-pitch turbine with an axial induction factor ( $a$ ) greater than 0.5. They referred to the operating state of the turbine under such conditions as the propeller transition state, including turbulent wake state (TWS) occurring for $0.5<a<1.0$ and the vortex ring state (VRS) occurring for thrust coefficient, $C_{T}>1.0$ and $a>1.0$ (figure 2.7 on page 32 of Eggleston & Stoddard (Reference Eggleston and Stoddard1987)). They further showed that the specific values of $C_{T}$ and $a$ causing different turbine operational states depend on the relative values of blade pitch ( $\unicode[STIX]{x1D6FD}$ ) and relative velocity angle ( $\unicode[STIX]{x1D6F7}$ ) formed at the wind turbine blade leading edge, as illustrated in figure 9. During regular operation, the turbine is continuously subjected to highly fluctuating incoming velocities $U_{\infty }$ , due to atmospheric turbulence, and rapid $\unicode[STIX]{x1D6FD}$ changes associated with the turbine control mechanism. The net effect of such rapid changes is a change in the angle of attack $\unicode[STIX]{x1D6FC}$ shown in figure 9(c). The results from this theoretical work were supported by a follow-up study from Sørensen et al. (Reference Sørensen, Shen and Munduate1998) using a numerical method that combines the actuator disc principle with the Navier–Stokes equations, which provided additional refinement of the transition conditions of different turbine wake states. The specific role of unsteady effects was further explored by Sebastian & Lackner (Reference Sebastian and Lackner2011, Reference Sebastian and Lackner2012) who studied the appearance of propeller transition states for the case of offshore turbines subjected to highly unsteady conditions (e.g. turbines undergoing rocking motion due to turbine tower/platform pitching). Specifically, these transition states, which essentially cause the wake to contract, representing a momentary loss of lift of the turbine, were correlated to the time derivative of the pitch of the turbine tower. Exclusively during leeward motion, the turbine blade bound circulation was found to change from a positive to a negative value indicating a clear transition to propeller states. As the turbine tower moves in the leeward direction, the relative velocity of the incoming wind approaching the blade decreases (i.e. decrease of the angle of attack) which causes a loss of lift. Alternatively, as $U_{\infty }$ drops suddenly (resulting in a much lower $\unicode[STIX]{x1D6FC}$ ) due to any other unsteadiness, the wind turbine may not extract any energy at that moment and instead acts like a propeller as the rotor cannot slow down rapidly due to inertia. In addition, the turbine tower in leeward motion can cause the rotor to interact with its own wake which also contributes to the contraction of the turbine wake (Sebastian & Lackner Reference Sebastian and Lackner2011). It is noteworthy that, using numerical simulation, Sebastian & Lackner (Reference Sebastian and Lackner2011) also showed that propeller transition states occur a staggering 30 %–50 % of the time for offshore (floating and monopile) turbines. Specifically, the monopile type of offshore turbines, which are similar to on-land turbines in the way they are mounted, do undergo wake transitions approximately 30 % of the time, which is close to the observations in the current SLPIV study.

Following guidance from the above-mentioned literature, we examined blade pitch ( $\unicode[STIX]{x1D6FD}$ ), incoming velocity ( $U_{\infty }$ ), the effective angle of attack ( $\unicode[STIX]{x1D6FC}_{E}$ ), revolutions per minute (r.p.m.) of the rotor ( $\unicode[STIX]{x1D6FA}$ ), $\unicode[STIX]{x1D6F7}$ and the gradient of blade pitch ( $\text{d}\unicode[STIX]{x1D6FD}/\text{d}t$ ) to study the wake expansion and contraction states (defined using $R_{w}$ -criterion). Two key turbine operational parameters that represent the relative positioning of the turbine blades and the wind are the effective angle of attack $\unicode[STIX]{x1D6FC}_{E}$ and the blade pitch $\unicode[STIX]{x1D6FD}$ . Both parameters are readily available from the sensor readings of the EOLOS turbine. The former is derived using $\unicode[STIX]{x1D6FC}_{E}=a\tan (2U_{\infty }(1-a)/\unicode[STIX]{x1D6FA}D(1+a))-\unicode[STIX]{x1D6FD}-\unicode[STIX]{x1D6FD}_{0}$ , where $U_{\infty }$ is measured from the sonic anemometer on the nacelle, $\unicode[STIX]{x1D6FA}$ is the turbine rotational speed, $D$ is the rotor diameter, $\unicode[STIX]{x1D6FD}$ is the blade pitch angle controlled by the control mechanism and $\unicode[STIX]{x1D6FD}_{0}$ is the blade pre-twist of $2.1^{\circ }$ , and the axial induction factor $a$ is neglected in the calculation of $\unicode[STIX]{x1D6FC}_{E}$ due to the relatively large uncertainty involved in its estimate. Here $U_{\infty }$ is estimated at the hub height which does not capture the variation of local wind speed approaching the turbine blades across the entire rotor span. Therefore, the latter ( $\unicode[STIX]{x1D6FD}$ ) is introduced potentially as a more effective indicator of change of blade position relative to the wind since it is controlled by the pitch control unit at nacelle and is not affected by the variation of incoming wind speed across the rotor span.

Figure 10 presents histograms of wake states over the effective angle of attack (i.e. $\unicode[STIX]{x1D6FC}_{E}$ ) and the rate of change of blade pitch (i.e. $\text{d}\unicode[STIX]{x1D6FD}/\text{d}t$ ). To reduce the adverse impact of a number of uncertainties on the correlation among wake states and these turbine operational parameters, the following pre-processing steps have been applied to the data before they are presented in figure 10. First, a 10 s low-pass filter is applied to $\unicode[STIX]{x1D6FC}_{E}$ to eliminate the jitter in the signal. The 10 s span is determined considering that $\unicode[STIX]{x1D6FC}_{E}$ is employed to represent the relative positioning of the turbine blades and the wind across the entire rotor span in an average sense. With a rotor diameter of 96 m and the averaged incoming wind velocity measured at the hub height of ${\sim}10~\text{m}~\text{s}^{-1}$ , the turbulent flow time scale corresponding to the spatial scale of the rotor span is approximately 10 s based on the Taylor frozen eddy hypothesis. In general, this low-pass filter reduces the impact of the uncertainties associated with the variation of flow speed across the rotor span in our analysis. For consistency, the blade pitch and the $R_{w}$ are also smoothed with the low-pass filter of the same size. In addition, for better correlation between wake flows and turbine operation, a 4 s shift (backward in time) is applied to the data of $R_{w}$ considering the difference of locations between the rotor plane and the centre of the SLPIV measurement region as well as the average wind speed at the hub height. Moreover, conditional sampling is employed on the turbine operation region (i.e. region ${>}$ 2 to rule out time periods with a constant blade pitch of $1^{\circ }$ ). This condition ensures only time periods with varying $\unicode[STIX]{x1D6FD}$ are considered to calculate $\text{d}\unicode[STIX]{x1D6FD}/\text{d}t$ . As a last step, conditional sampling on nacelle misalignment (i.e. the misalignment angle between the rotor axis and the light sheet orientation) is also applied to avoid the influence of the nacelle flow structures on the FOV. Both conditional sampling steps in total eliminated ${\sim}$ 23 % of the data samples over the SLPIV measurement duration of 1790 s ( ${\sim}$ 30 min).

Figure 10. Probability histograms of $\unicode[STIX]{x1D6FC}_{E}$ and $\text{d}\unicode[STIX]{x1D6FD}/\text{d}t$ under different $R_{w}$ ranges.

As shown in figure 10(a), the histograms of the wake expansion and contraction states do not show any appreciable separation over $\unicode[STIX]{x1D6FC}_{E}$ when all expansion and contraction events are considered (i.e. $R_{w}<1$ for expansion and $R_{w}>1$ for contraction). Nevertheless, a remarkable shift of the histogram for the contraction state towards negative $\unicode[STIX]{x1D6FC}_{E}$ can be observed when only strong expansion and contraction events (i.e. $R_{w}\leqslant \langle R_{w}\rangle -\unicode[STIX]{x1D70E}_{R_{w}}$ for expansion and $R_{w}>\langle R_{w}\rangle +\unicode[STIX]{x1D70E}_{R_{w}}$ for contraction) are included (figure 10 b). Compared to the trend for $\unicode[STIX]{x1D6FC}_{E}$ , the expansion and contraction histograms exhibit a significantly clearer separation over $\text{d}\unicode[STIX]{x1D6FD}/\text{d}t$ (figure 10 c,d). In particular, the mean value of $\text{d}\unicode[STIX]{x1D6FD}/\text{d}t$ for expansion and contraction is $0.21~\text{deg}~\text{s}^{-1}$ and $-0.11~\text{deg}~\text{s}^{-1}$ (figure 10 c), respectively. When only strong expansion and contraction events are sampled (figure 10 d), 98 % of strong expansion events occur at positive $\text{d}\unicode[STIX]{x1D6FD}/\text{d}t$ and 67 % of strong contraction is concentrated in the region of negative $\text{d}\unicode[STIX]{x1D6FD}/\text{d}t$ . Overall, figure 10 clearly shows a strong connection between the wake states and turbine operational parameters. Compared to $\unicode[STIX]{x1D6FC}_{E}$ , $\text{d}\unicode[STIX]{x1D6FD}/\text{d}t$ is evidently the more effective parameter to correlate with the transition of wake states owing to the uncertainties involved in the estimation of $\unicode[STIX]{x1D6FC}_{E}$ using the available sensor information from the turbine.

To further substantiate the direct connection between the pitch control and the wake transition, two sample time sequences of $R_{w}$ are extracted from SLPIV. Each sequence has a time duration of 60 s, covering at least one incident of the wake transition between wake expansion and contraction states. The sequences of $R_{w}$ , corresponding $\unicode[STIX]{x1D6FD}$ and $\text{d}\unicode[STIX]{x1D6FD}/\text{d}t$ (with low-pass filter applied as mentioned in the last paragraph) are presented in figure 11. The SLPIV velocity fields corresponding to these two time sequences are provided as supplementary movies 1 and 2 available at https://doi.org/10.1017/jfm.2018.779. Figure 11(a) shows a sequence that consists of a strong wake contraction event, in which $R_{w}$ becomes significantly larger than 1 for ${\sim}$ 40 % (23 s out of 60 s) of the entire time duration. The figure shows a clear one-to-one correspondence between $R_{w}$ and $\text{d}\unicode[STIX]{x1D6FD}/\text{d}t$ . Specifically, as $\unicode[STIX]{x1D6FD}$ increases during the time stamps of 1015–1035 s, $\text{d}\unicode[STIX]{x1D6FD}/\text{d}t$ is positive and the corresponding $R_{w}<1$ . Accordingly, in this period, the wake flow stays predominantly in the expansion state (evidenced by the two inset figures at 1027 and 1033 s; please see the supplementary movie 1 for more information). As soon as $\unicode[STIX]{x1D6FD}$ starts decreasing at approximately 1035 s, $\text{d}\unicode[STIX]{x1D6FD}/\text{d}t$ becomes negative and $R_{w}$ rises above 1 within $\pm 1~\text{s}$ (i.e. within the uncertainty involved in the time shift between the rotor plane and the centre of the SLPIV measurements). The corresponding wake flow switches to the contraction state and shows consistent contraction until approximately 1060 s when $\text{d}\unicode[STIX]{x1D6FD}/\text{d}t$ goes back to approximately 0 and $R_{w}$ drops to values very close to 1 (evidenced by the two inset figures at 1042 and 1048 s; and check the supplementary movie 1 for viewing the dynamic process of wake transition). For comparison, as shown in figure 11(b), the second time sequence is selected to show the wake transition that involves a weak contraction/expansion event (i.e. with $R_{w}$ in the close vicinity of 1). Similar to figure 11(a), the correspondence between $\text{d}\unicode[STIX]{x1D6FD}/\text{d}t$ and $R_{w}$ is still appreciable. Specifically, $\text{d}\unicode[STIX]{x1D6FD}/\text{d}t$ starts with a positive value, then drops below 0 and rises above 0, while accordingly, $R_{w}$ increases from significantly below 1 to slightly above 1 and drops down. However, as shown in the corresponding inset figures of the wake velocity fields and the supplementary movie 2, the absolute value of $R_{w}$ is not a clear indicator of a contraction/expansion wake state. This situation corresponds to the distributions in the vicinity of $\text{d}\unicode[STIX]{x1D6FD}/\text{d}t=0$ in figure 10(d), where there is no substantial separation between the wake expansion and contraction states over $\text{d}\unicode[STIX]{x1D6FD}/\text{d}t$ . Such a situation occurs when the flow surge in the inner wake introduced by negative $\text{d}\unicode[STIX]{x1D6FD}/\text{d}t$ is not strong enough compared to the outer wake velocity, and the turbine performance is less affected.

Figure 11. Sample time sequences of the blade pitch $\unicode[STIX]{x1D6FD}$ , the corresponding rate of change of pitch $\text{d}\unicode[STIX]{x1D6FD}/\text{d}t$ and $R_{w}$ showing the wake transition involving (a) a strong contraction state and (b) a weak contraction state. Inset figures are the instantaneous velocity vector fields ( $1:3$ skip applied in both horizontal and vertical directions for clarity) superimposed with the velocity magnitude contours obtained from SLPIV measurements.

To summarize, the above analysis indicates that the temporal variation in $\unicode[STIX]{x1D6FD}$ (i.e. $\text{d}\unicode[STIX]{x1D6FD}/\text{d}t$ ) is best correlated with the contraction phenomena identified through $R_{w}$ . Furthermore, to establish a physical link between $\text{d}\unicode[STIX]{x1D6FD}/\text{d}t$ and turbine (both tower and blade) deflection as suggested in the literature (e.g. Sebastian & Lackner (Reference Sebastian and Lackner2011)), we analyse the signals of tower strain and blade strain gauges installed on the EOLOS turbine during our flow measurements. Figure 12 presents the signals of these strain gauges together with the blade pitch change, illustrating the strong connections between the $\unicode[STIX]{x1D6FD}$ variations and the thrust on the turbine tower and blades. Specifically, figure 12(a) shows a strong negative correlation with a correlation coefficient of $-$ 0.90 between the blade pitch and the tower foundation strain measured on the downstream side of the turbine (a measure of leeward motion of the turbine). Similarly, a strong correlation (correlation coefficient of $-$ 0.92) is found between the blade pitch variations and the flapwise deflections of the rotor measured by the blade strain gauges mounted at 44.4 % span of the blade (21.6 m from the blade root, i.e. the farthest point where a strain gauge is installed) on the high pressure side as shown in figure 12(b). The results suggest that as $\unicode[STIX]{x1D6FD}$ decreases, both the blades and the tower are flexed in the leeward direction (into the rotor wake), causing interaction between the rotor and the turbine wake that results in wake contraction, as identified in the above-mentioned literature and observed in our experiments.

Figure 12. Time series of (a) blade pitch $\unicode[STIX]{x1D6FD}$ (solid line) and tower strain (dashed line) representing tower deflections in the streamwise direction of the flow, and (b) blade pitch $\unicode[STIX]{x1D6FD}$ (solid line) and the blade strain (dashed line) representing flapwise deflection from high pressure side to the low pressure side. Both strains are reported in microstrain.

It is to be noted that on-land turbines may not have the intense rocking motion expected for offshore turbines, but the literature has provided support for substantial deflection of the tower and blades experienced by utility-scale on-land turbines, particularly during higher regions of operation. For the tower deflection, Bang, Kim & Lee (Reference Bang, Kim and Lee2012) performed measurements on a 1.5 MW turbine and found that the turbine tower deflects by 0.17 m at the nacelle elevation during the low wind conditions. Nasrabad (Reference Nasrabad2016) carried out FAST simulations on 1.5 MW turbine and showed that the turbine nacelle could deflect by 0.2 m under normal operation. Another recent study, by Zendehbad, Chokani & Abhari (Reference Zendehbad, Chokani and Abhari2017), conducted experiments on a 2 MW turbine using a novel ground-based optical technique and demonstrated a strong correlation between the tower tip deflection and the strain gauge measurements at the tower foundation. The study also revealed the turbine tower to deflect by a maximum of 0.8 m for high wind velocities (which are very similar to our experimental conditions). Although the experiments measured deflections of the tower in the sideways direction (perpendicular to the incoming wind direction), the study highlights the extent of the deflections that typical on-land turbines experience. Moreover, through accelerometer measurements conducted on a 3 MW offshore turbine, El-kafafy et al. (Reference El-kafafy, Devriendt, Weijtjens, Sitter and Necati2014) showed that the deflections in the predominant wind direction (fore–aft direction), which constitute a primary mode of vibration, are typically 50 % higher than that those in the sideways direction. For turbine blade deflection, using FAST simulations on NREL 5 MW (126 m diameter rotor, 90 m hub height) turbine, Jonkman et al. (Reference Jonkman, Butterfield, Musial and Scott2009) showed that the turbine blades experience a 10 times larger deflection in the fore–aft direction (4–5.5 m relative to the undeflected blade pitch axis) compared to a typical nacelle deflection of 0.5 m in the fore–aft direction when the turbine operates above region 2. Follow-up numerical simulations on utility-scale turbines based on fluid–structure interaction, by Bazilevs et al. (Reference Bazilevs, Hsu, Kiendl, Wüchner and Bletzinger2011) and Bazilevs et al. (Reference Bazilevs, Takizawa, Tezduyar, Hsu, Kostov and McIntyre2014), further found flapwise deflections of up to 5.6 m.

Figure 13. Schematic illustrating the fore–aft deflection of the turbine tower and the blade flapwise deflection due to blade pitch ( $\unicode[STIX]{x1D6FD}$ ) variation. (a) Typical wake expansion state of the turbine and (b) wake contraction state caused by the interaction of rotor and turbine wake.

Overall, based on the above-mentioned literature and the strong correlations between blade pitch and the thrust forces on the tower and blades observed in our experiments, we suggest that the interaction between rotor and turbine wake can contribute considerably to the wake contraction. This mechanism is schematically represented in figure 13. As blade pitch $\unicode[STIX]{x1D6FD}$ decreases, the turbine tower and blades flex in the streamwise direction, as shown in figure 13(b), leading to wake contraction. We also acknowledge that aeroelastic flutter of the turbine blades, during rapid changes of $\unicode[STIX]{x1D6FC}$ or rocking of the turbine, could also play a role in the appearance of wake transitions, though it is not considered in the current analysis. It is noteworthy that, to the best of our knowledge, very few laboratory and field experiments have reported and discussed such intermittent wake transition, which may be attributed to the following reasons. Regarding the laboratory experiments, the incoming flow conditions are generally idealized and the turbine models do not fully capture the control dynamics and mechanical characteristics of utility-scale turbines. For field measurements, the conventional techniques do not have sufficient temporal and spatial resolution to capture such wake behaviour. In addition, the majority of field measurements were conducted further downstream of the turbines where such intermittent wake behaviour may not persist.

3.2 Near-wake tip vortex behaviours

In this section, the behaviours of near-wake tip vortices visualized as snow voids are analysed and correlated with turbine operation/response parameters. This analysis is an extension of the work from Hong et al. (Reference Hong, Toloui, Chamorro, Guala, Howard, Riley, Tucker and Sotiropoulos2014) which, for the first time, demonstrated the inter-connection between tip vortex behaviour and turbine operation/response parameters using a 6 min video of snow voids in the near wake of a utility-scale turbine. As described in § 2, the present analysis includes 4 datasets (i.e. Apr 2014, Nov 2015, Dec 2015, Feb 2016a) with a total duration of 2 h and with a field of view confined to the region covering the tip vortices generated at the blade-bottom tip level. These datasets, obtained from multiple deployments conducted in 2014–2016, cover a wide range of turbine operational and atmospheric conditions. The turbine operation/response parameters used for the analysis include critical turbine supervisory control and data acquisition (SCADA) parameters, their derivatives as well as the strain sensor data at the base of the turbine tower. These parameters either have been employed or can be readily incorporated into the control strategy of the turbine. As discussed in § 1, the behaviour of tip vortices in the near wake can significantly influence the turbulence characteristics and the evolution of the wake far downstream. Therefore, the analysis in the section aims to establish a statistical correlation between tip vortex behaviour and readily available operational and response information from utility-scale turbines, which can benefit wind energy developers in formulating advanced control strategies to improve the total power production and load mitigation of wind farms in the future.

In the present analysis, the tip vortex behaviour is categorized primarily into a consistent state and disturbed state, according to the general temporal variation of snow void patterns shown in each image frame of the recorded videos. The disturbed state is further divided into different types, referred to as Type I, Type II and Type III hereafter, based on specific features of the disturbed snow voids in the images. Figure 14 presents sample images illustrating the consistent state of tip vortices and different types of disturbed state. As figure 14(a) shows, the consistent state of tip vortices is characterized by a sequence of snow voids with clearly defined outlines, typically resembling the shape of a disk or an ellipse with a tapered tail. The number of voids appearing in the images ranges from 3 to 5 in our datasets, depending on the incoming flow velocity and tip-speed-ratio of the turbine. In the Type I disturbed state, as shown in figure 14(b), the snow voids are utterly unrecognizable or absent within the field of view. In contrast, for both Type II (figure 14 c) and III (figure 14 d) disturbed states, snow voids are still identifiable but smeared due to disturbance. Particularly, Type III state shows disturbed voids associated with vortex interactions such as leap frogging (i.e. roll-up of adjacent tip vortex filaments around each other) and merging, while such vortex interactions are not appreciable in the Type II state. To obtain an objective classification of different tip vortex states, we use the criteria based on the temporal variation of void size, void shape and void spacing for the first void (i.e. the most upstream void which is expected to be best correlated with the turbine operation) that enters the field of view of our measurements. These criteria are summarized in table 3. Specifically, tip vortex voids are earmarked as consistent only if all of the criteria are satisfied and as Type II/III if at least one criterion is satisfied. In addition, based on these criteria, we have developed image analysis algorithms to autonomously classify different vortex states. The results from the autonomous image processing are not very sensitive to the change of the exact threshold (i.e. 50 % in the table) within the range of 50 %–80 %. Note that although we present the qualitative observation of Type II and III disturbed states as mentioned above, we do not differentiate the two states through quantitative metrics due to the challenges of determining non-ambiguous metrics for such classification. More importantly, as the classification of the void states is mutually exclusive, a robust decorrelation of the samples is ensured. The decorrelation process renders $2/3$ of the total duration of the visualization data for correlating with turbine operation/response, i.e. for example, the Feb 2016a dataset which is 1790 s long produces 1193 tip vortex behavioural events/classifications which are completely de-correlated from one another.

Figure 14. Sample images of snow voids illustrating (a) consistent state, (b) Type I disturbed state, (c) Type II disturbed state and (d) Type III disturbed state of tip vortices.

Table 3. The criteria used to classify different tip vortex states.

In the following analysis, the probabilistic distribution of turbine operation/response parameters corresponding to the categorized tip vortex states above is examined in the form of histograms. For this statistical analysis, we have conducted a thorough exploration of the information available in the EOLOS turbine database at the time duration corresponding to the tip vortex videos. Such information includes: (i) turbine SCADA parameters such as wind velocity measured from the sonic anemometer at the nacelle (used for gauging turbine tip-speed-ratio and controlling turbine operational region and yaw angle), turbine power, rotor speed and blade pitch; (ii) the strain gauge data at the turbine tower base. Several critical variables are also derived from turbine operation/response, namely, normalized turbine power $P^{\ast }$ and downwind tower strain $S^{\ast }$ , the corresponding fluctuation intensity of power $I_{P}$ , fluctuation intensity of tower strain $I_{S}$ and effective angle of attack $\unicode[STIX]{x1D6FC}_{E}$ . All these variables are used for a statistical demarcation of consistent and disturbed states of tip vortices and are presented in the analysis below. Specifically, the normalized turbine power $P^{\ast }$ is calculated as $(P-P_{min})/(P_{max}-P_{min})$ where $P$ , $P_{min}$ and $P_{max}$ are the instantaneous, minimum and maximum values of power recorded within a dataset, respectively, and the downwind tower strain $S^{\ast }$ is obtained through the same fashion of normalization as that of the power, with the data from the strain gauge closest to the direction opposite (i.e. $180^{\circ }$ ) to the mean wind direction of each dataset. The fluctuation intensity of power $I_{P}$ is calculated as the ratio of standard deviation of the power $P$ to the mean of $P$ over a sliding period of 30 s. The fluctuation intensity of strain $I_{S}$ is calculated in the same fashion as that of $I_{P}$ . The effective angle of attack $\unicode[STIX]{x1D6FC}_{E}$ is derived following the same method as in § 3.1. In addition, considering the highly unsteady and multivariate nature of field measurements, a conditional sampling technique is applied in the current analysis to: (i) improve statistical demarcation of tip vortex behaviours with turbine operation/response parameters; (ii) elucidate underlying physical mechanisms governing turbine operational condition and tip vortex behaviours. Particularly, for the present analysis, the turbine yaw error (i.e. the misalignment angle between the wind direction and the rotor axis), turbine operational regions and types of disturbed tip vortex state are chosen as conditional sampling parameters.

Figure 15. The probability histograms of power fluctuation intensity ( $I_{P}$ ), tower strain fluctuation intensity ( $I_{S}$ ) and effective angle of attack ( $\unicode[STIX]{x1D6FC}_{E}$ ) for consistent and disturbed states of tip vortices under no yaw error restriction (a–c) and a restriction of yaw error ${<}3^{\circ }$ (d–f).

Figure 15 presents the probability histograms of power fluctuation intensity $I_{P}$ , tower strain fluctuation intensity $I_{S}$ and effective angle of attack $\unicode[STIX]{x1D6FC}_{E}$ for consistent and disturbed states of tip vortex events under different restrictions of yaw error. Specifically, no yaw error restriction is applied in figure 15(a–c) while a stringent restriction of yaw error ${<}3^{\circ }$ is employed in figure 15(d–f). For each histogram, twelve bins of equal size, covering from the minimum to maximum values of each turbine operation/response variable presented in the histogram, are selected to demonstrate the statistical distribution of the turbine variables under consistent and disturbed tip vortex states. A similar convention of bin size choice is employed consistently throughout the paper. Without a yaw error restriction, no significant difference in the $I_{P}$ histogram between the consistent and disturbed states (figure 15 a) is observed. However, there is a clear separation in the distribution of $I_{S}$ for consistent and disturbed states of tip vortices (figure 15 b). For the disturbed state, the distribution of $I_{S}$ appears to follow a normal distribution, while a significant portion of $I_{S}$ is clearly biased towards the lower values of $I_{S}$ for the consistent state. With an increased yaw error restriction, there is an improved separation of the $I_{S}$ histograms between consistent and disturbed states of the tip vortices, as shown by a comparison of figures 15(b) and 15(e). In particular, with increasing yaw restriction, the $I_{S}$ histogram of the consistent state approaches an exponential distribution, characterized as $0.62\text{e}^{-14.87I_{s}}$ through least square fitting. It is worth noting that an exponential distribution was identified for the relationship between the tip vortex stability and the turbulence intensity of the incoming flow in recent wind turbine LES studies (e.g. Ivanell et al. (Reference Ivanell, Mikkelsen, Sørensen and Henningson2010) and Sarmast et al. (Reference Sarmast, Dadfar, Mikkelsen, Schlatter, Ivanell, Sørensen and Henningson2014)), which may shed some light on the underlying mechanism of the trend observed for $I_{S}$ here. As a comparison, with an increasing yaw restriction, the $I_{S}$ histogram of the disturbed state resembles a normal distribution with the mean value moving towards higher $I_{S}$ . The least square fit of the histogram yields a normal distribution with a mean value of 0.13 and a standard deviation of 0.06. In contrast to the $I_{S}$ histograms, the $I_{P}$ histograms (figure 15 a,d) and $\unicode[STIX]{x1D6FC}_{E}$ histograms (figure 15 c,f) do not seem to be strongly affected by the yaw error restriction. Similarly, the normalized turbine power $P^{\ast }$ and tower strain $S^{\ast }$ are not appreciably influenced by the yaw error restriction, and therefore are not shown in figure 15 for brevity. To summarize here, figure 15 suggests a correlation between the tip vortex behaviour and tower strain fluctuations which represent fluctuations in the inherent strength of the vortices. In addition, these trends improved with yaw error restriction, indicating a definite effect of wind direction misalignment which needs to be minimized for further investigation. Therefore, for the following analysis in this paper, the yaw error is restricted to be less than $3^{\circ }$ , consistent with the restriction imposed in figure 15(d–f).

To further elucidate the correlations between the tip vortex behaviour and the turbine operation/response parameters, a restriction on the regions of turbine operation is applied to the analysis to de-couple the effects caused by the turbine control unit (TCU) operation, and results are presented in figure 16. Figure 16(a–e) shows histograms when the turbine operates in region 2 or below, during which TCU is designed to maximize power extraction with the available sub-optimal wind speeds by setting blade pitch to the minimum. For comparison, figure 16(f–i) presents histograms for regions greater than 2, where the turbine operation is regulated to maintain a relatively constant output power and the rotational speed of the turbine blades to protect the turbine from overload and structural failure. According to the changing TCU operation, the distributions of the consistent and disturbed states of the tip vortices as functions of turbine operation/response parameters vary substantially, as shown in the figure.

Figure 16. The probability histograms of power fluctuation intensity ( $I_{P}$ ), tower strain fluctuation intensity ( $I_{S}$ ), effective angle of attack ( $\unicode[STIX]{x1D6FC}_{E}$ ), turbine power ( $P^{\ast }$ ) and tower strain ( $S^{\ast }$ ) for consistent and disturbed tip vortex states under a restriction of yaw error ${<}3^{\circ }$ for (a–e) turbine operational regions ${\leqslant}2$ and (f–j) turbine operational regions ${>}2$ .

Figure 16(a) shows the power fluctuation $I_{P}$ histogram, in which considerable separation is observed between the consistent and disturbed states of the tip vortices when turbine operation is restricted to the regions ${\leqslant}2$ . Compared to figure 15(d), the centre of the $I_{P}$ histogram of the disturbed state clearly shifts towards higher values of $I_{P}$ , and its distribution approximates a normal distribution with a peak value of 0.09 and a standard deviation of 0.05. In regions ${\leqslant}2$ , the turbine power is directly proportional to the thrust on the turbine, thus a fluctuation in power is manifested as a fluctuation of the tower strain. As a result, the distribution of tower strain fluctuation $I_{S}$ presented in figure 16(b) shows similar trends as those of figure 16(a). Moreover, compared to figure 15(e), the distribution of the disturbed state is less clear with a restriction on regions ${\leqslant}2$ , while the $I_{S}$ distribution for consistent state becomes more concentrated to the region of very low $I_{S}$ . Restricting turbine operation to regions ${\leqslant}2$ limits the effective angle of attack $\unicode[STIX]{x1D6FC}_{E}$ to high values (i.e. 99 % incidence above $5^{\circ }$ ), as shown in figure 16(c), where no clear separation is observed between the histograms of the consistent and disturbed states. Figure 16(d,e) shows the histograms of normalized turbine power $P^{\ast }$ and tower strain $S^{\ast }$ in regions ${\leqslant}2$ . Similar to those for all regions, no appreciable separation between the consistent and disturbed state is observed.

When the turbine operates in regions ${>}2$ , as shown in figure 16(f–j), all histograms show a noticeable discrepancy compared to those presented in figure 16(a–e). One essential cause for such a discrepancy is the TCU auto-adjustment. When operating in regions ${>}2$ , the turbine is able to generate power close to (or even exceeding) the rated power, therefore the TCU curbs the power fluctuation to protect the turbine from excessive thrust loads while still maintaining the designed power output. As a result, figure 16(f) shows that the $I_{P}$ distribution in regions ${>}2$ is largely concentrated in the lower values of $I_{P}$ compared to figure 16(a). Specifically, more than 50 % of the consistent states and more than 75 % of the disturbed states of tip vortices are observed in the range of $0<I_{P}<0.025$ . In region ${>}$ 2, due to the effect of power regulation and blade pitching, the correlation between power and strain fluctuations diminishes, evidenced by the significant difference between $I_{P}$ histogram (figure 16 f) and $I_{S}$ histogram (figure 16 g) in this region. Moreover, a separation for consistent and disturbed tip vortex states is observed in figure 16(g). The least square fit of the $I_{S}$ histogram of the disturbed state yields a normal distribution with a mean value of 0.12 and a standard deviation of 0.04, similar to that shown in figure 15(e) without a turbine region restriction. Regarding the effective angle of attack $\unicode[STIX]{x1D6FC}_{E}$ , the restriction of the turbine to higher regions causes the distribution of $\unicode[STIX]{x1D6FC}_{E}$ to spread towards lower values as opposed to that of regions ${<}2$ . More remarkably, such region restriction leads to clear separation between the consistent and disturbed states, with disturbed tip vortices occurring at smaller values of $\unicode[STIX]{x1D6FC}_{E}$ and the consistent state concentrated mainly above $\unicode[STIX]{x1D6FC}_{E}>5^{\circ }$ . In line with trends observed for $\unicode[STIX]{x1D6FC}_{E}$ , the histogram of the normalized tower strain $S^{\ast }$ (figure 16 j) also exhibits a clear separation between consistent and disturbed states with a restriction of turbine regions (i.e. regions ${>}2$ ), due to the inherent connection among blade angle of attack and forces on the turbine blades and tower structures. As for the normalized turbine power $P^{\ast }$ (figure 16 i), the restriction of regions ${>}2$ shifts the distribution of $P^{\ast }$ to the range of $0.5<P^{\ast }<1$ for both consistent and disturbed states. A slight separation between the distributions of the two states is observed in comparison with the corresponding figure of regions ${<}2$ (figure 16 d), but is not as appreciable as the trends shown for $\unicode[STIX]{x1D6FC}_{E}$ and $S^{\ast }$ . To summarize, the conditional sampling based on turbine operational regions yields clearer correlations between tip vortex behaviour and turbine operation/response parameters, manifested as separation of the distributions of $I_{P}$ , $I_{S}$ ; $P^{\ast }$ , $S^{\ast }$ and $\unicode[STIX]{x1D6FC}_{E}$ according to the consistent and disturbed states of the tip vortices. Nevertheless, the trends of such separation of distributions are dependent on specific turbine operational regions. In particular, no separation is observed for $P^{\ast },S^{\ast }$ and $\unicode[STIX]{x1D6FC}_{E}$ in lower turbine regions ( ${\leqslant}2$ ).

To further elucidate the intricate connection between disturbed tip vortex patterns and turbine operation/response, a conditional sampling of specific types of disturbed state is implemented in addition to the yaw and turbine operational region restrictions. Specifically, we choose to focus on the Type I disturbed state in the analysis here for the following reasons. Firstly, the underlying aerodynamic origin of the Type I disturbed state is strongly connected to turbine performance. For example, the reduction of turbine power generation causes a drastic weakening of tip vortices, which further results in the disappearance of the tip vortex signature in the near wake under highly turbulent atmospheric conditions. Therefore, it is reasonable to expect that the conditional sampling based on the Type I disturbed state would improve the correlation of tip vortex behaviour with turbine power and tower strain which is inherently connected to the power generation. Secondly, the Type I disturbed state corresponds to complete disappearance of the voids, whose flow features can be distinguished from those of Type II and III in a non-ambiguous way. Figure 17 shows the histograms of the effective angle of attack $\unicode[STIX]{x1D6FC}_{E}$ , normalized turbine power $P^{\ast }$ and normalized tower strain $S^{\ast }$ for consistent and Type I disturbed tip vortex states under the yaw and region restrictions. The histograms of $I_{P}$ and $I_{S}$ do not yield a significant difference compared to those in figure 16, and therefore, are not presented here for brevity. As the figure shows, in the lower turbine regions ( ${\leqslant}2$ ), the distribution of the Type I disturbed state (figure 17 a) is slightly shifted to the region of low $\unicode[STIX]{x1D6FC}_{E}$ in comparison to that of all disturbed states shown in figure 16(c). A similar trend is also observed for $P^{\ast }$ (figure 17 b). Note that the conditional sampling at this stage (i.e. yaw error, turbine region and disturbed state type) substantially reduces the number of samples available for statistical analysis, which makes some histograms appear choppy. This issue limits the further analysis of the data based on conditional sampling, and we expect to resolve this issue through more data recording in future deployments. In higher turbine regions ( ${>}2$ ), as shown in figure 17(d–f), the histograms generally resemble those shown in figure 16(h–j), indicating that the majority of disturbed tip vortices in higher turbine regions are in the Type I state. Nevertheless, with a restriction on the type of disturbed state, there is a measurable increase of separation between the distributions for the disturbed and consistent states in the $\unicode[STIX]{x1D6FC}_{E}$ , $P^{\ast }$ and $S^{\ast }$ histograms. Such a separation increase is manifested by 10 %–15 % of the samples of the disturbed state shifting towards lower values and the distribution of the consistent state staying relatively unchanged in comparison to the corresponding ones in figure 16.

Figure 17. The probability histograms of effective angle of attack ( $\unicode[STIX]{x1D6FC}_{E}$ ), turbine power ( $P^{\ast }$ ) and tower strain ( $S^{\ast }$ ) for consistent and Type I disturbed tip vortex states under a restriction of yaw error ${<}3^{\circ }$ for (a–c) turbine operational regions ${\leqslant}2$ and (d–f) turbine operational regions ${>}2$ .

In addition to the histograms of turbine operational/response parameters, the direct correspondence between the tip vortex behaviour and turbine operation/response is examined by marking the incidences of disturbed states of tip vortices in the time series of these parameters. Note that, under field conditions, the characteristics of tip vortices are inevitably influenced by multiple physical variables, and therefore, it is difficult to establish a one-to-one correspondence between tip vortex behaviour and a specific turbine operational/response parameter unless stringent conditional sampling is imposed. Figure 18 presents two sample time series of turbine operation/response parameters marked with regions corresponding to the occurrence of the disturbed turbine states. The first sample displays the variation of  $\unicode[STIX]{x1D6FC}_{E}$  in a period of approximately 350 s with the incidences of all types of disturbed states marked by the grey vertical bands (figure 18 a). The specific time sequence is chosen such that the turbine operation is confined to regions ${\leqslant}2$ (approximately 96 % of the time here), yaw error is restricted to ${<}3^{\circ }$ and the average value of $I_{P}$ for the time period is around 0.1. These restrictions allow us to sample the data only in the region around the probability peak of the disturbed state, as shown in figure 16(a). As shown in figure 18(a), the grey vertical bands occur almost exclusively in the time periods around local minima of $\unicode[STIX]{x1D6FC}_{E}$ , indicating the consistent generation of tip vortices is likely to be disturbed when the utility-scale turbine operates under low $\unicode[STIX]{x1D6FC}_{E}$ and experiences sharp changes of $\unicode[STIX]{x1D6FC}_{E}$ . The second sample shows the change of $S^{\ast }$ in a period of 1790 s with incidences of the Type I disturbed state marked by the grey vertical bands (figure 18 b). This sample time series, corresponding to a time period with the lowest wind speed fluctuations among all of the datasets, is selected to allow clear demonstration of the one-to-one correspondence between tip vortex behaviour and turbine operations. In addition, similar to that in figure 18(a), a yaw error restriction ( ${<}5^{\circ }$ ) is imposed on the data to minimize the effect of yaw misalignment on the results. Note that the yaw error restriction is relaxed and no turbine region restriction is imposed here in comparison to previous cases to retain as many Type I disturbances as possible. Figure 18(b) illustrates that most Type I disturbed states tend to occur in the vicinity of the local minima associated with a sudden large drop of $S^{\ast }$ . Such a drop in $S^{\ast }$ is strongly correlated with a significant loss of the lift generated by the turbine blades, resulting in drastic weakening of the tip vortices (i.e. a major cause of the Type I disturbed state of tip vortices). The general trend observed here is consistent with the histograms shown in figure 17(f). In addition, the time series suggests that Type I disturbances have a higher tendency to occur in the periods when the turbine operations or the incoming wind fluctuations cause a significant lowering of turbine loading.

Figure 18. Samples of time series of (a) effective angle of attack ( $\unicode[STIX]{x1D6FC}_{E}$ ) with incidences of disturbed states marked using grey vertical bands and (b) normalized tower strain ( $S^{\ast }$ ) with incidences of the Type I disturbed state marked using grey vertical bands.