Aircraft wake vortex and turbulence measurement under near-ground effect using coherent Doppler lidar

Songhua Wu; Xiaochun Zhai; Bingyi Liu

doi:10.1364/OE.27.001142

1. Introduction

Wake vortex are large rolling air masses generated by aircraft because of lift. This turbulence is hazardous during the landing and take-off phases of the flight, as the aircraft in these phases operates close to its stall speed and close to the ground where there is very little margin for recovery [1,2]. On the other hand, for safety reasons, most airports assume a worst-case scenario and use conservative separation, which means the interval between aircraft landing or taking off often amounts to several minutes. Regulations specify minimum separation between aircraft and consequently limit the capacity of airport. With the aid of precise measurement of wake vortex and accurate atmospheric conditions, more efficient interval will be set to increase capacity [3–5].

ICAO (International Civil Aviation Organization) recognizes two methods of measurement for wake vortex, that is sound tomography and coherent Doppler lidar (CDL), and wake vortex in clear air can only be derived from lidar measurement up to now. Wake vortex characterization and monitoring based on different technologies [6–23] and different prediction models of wake vortex decay [25–31] are two major topics in previous literatures. The 2-μm pulsed coherent Doppler Lidar (PCDL) was used most widely in the previous wake vortex study [16]. Basically, the wake vortex trajectory can be visually determined using measurement data set. Köpp et al. [8] presented the method of velocity envelope (VE method) to retrieve wake vortex parameters under the condition of high signal to noise ratio (SNR) and relatively long pulse duration from 2-μm PCDL data. Smalikho et al. [18,19] used 1.55-μm Stream Line PCDL to detect the wake vortex, and because of its lower SNR, they proposed the method of radial velocity (RV method), employing the array of radial velocity to determine wake vortex position. The circulation, representing the intensity of wake vortex, is more challenging to be estimated because of the lack of true knowledge [13,20]. As for lidar measurement, the average value from radius area of 5 m – 15 m is usually used to represent wake vortex circulation as a whole [8]. There are some approaches focusing on circulation determination. The combination of the velocity envelope from measurement and the wake vortex velocity profile from model such as Burnham-Hallock model can be used to retrieve circulation [8,12,14]. This method requires the high accuracy of wake vortex core location. Compared to the retrieval results directly from measurement data set, the use of wake vortex model can remove the outlier to some aspects. Other methods using spectrum-based mathematical models, which need much larger computational load, were developed to retrieve wake parameters using different fitting methods such as maximum likelihood method [15,17,24]. In these algorithms, the spectral signature model takes the lidar and signal processing response function into consideration, making more accurate results which are suitable in lower SNR condition and for wake vortex from smaller aircrafts.

The wake vortex behavior out of ground effect is possible to be computed based on theoretical models. The depletion of wake vortex near-surface is very complicated, and temperature, humidity, wind shear and turbulence can change the drop rate of vortex and cause the cell to twist and contort unpredictably [27,29]. Therefore, we need better understanding of the dynamics of wake multi-vortex systems as well as the interaction between wake vortex and the ground to make accurate predictions of wake vortex development.

In order to investigate the near real-time approach to mitigate wake vortex using 1.55-μm pulsed coherent Doppler lidar and to study the wake vortex evolution near ground effect (NGE), field observations of the wake vortex were carried out from 2014 to 2017 at Beijing Capital International Airport (BCIA) [22]. The first phase of the campaign included the development and demonstration of the core techniques for wake detection, so called Wake Vortex Visualization Demonstrator (V2D), consisting of the scanning mode and signal processing technologies. Because of the limitation of observation sites, the wake vortex was probed and analyzed at the comparably high altitude above 100 m within a time window of tens of seconds. The second phase particularly focused on the investigation of the wake vortex under NGE. This paper gives a thorough overview on the second experimental observation. The lidar setup and experimental campaign are described in Section 2. Section 3 presents the basic retrieval methods of wake vortex and atmospheric turbulence using PCDL. The results are described in Section 4. A conclusion is given in Section 5.

2. Experimental setup and field campaign

In virtue of the small size, short life span and quick evolution of wake vortex, PCDL for vortex detection requires high spatial and temporal resolution. The PCDL system Wind3D 6000 shown in Fig. 1(a), manufactured by Leice-Lidar Transient Technology Ltd., is based on all-fiber laser technology and the heterodyne detection technology. A comprehensive description of the PCDL principle has been described in recent literatures [32,33]. An eye-safe pulsed 1.55-µm laser source was built based on Master Oscillator Power-Amplifier (MOPA) architecture with a large core fiber and excellent beam quality of M² of 1.1. The pulsed energy is approximately 150 $μ J$ and the pulse repetition frequency is 10 kHz. The pulse width produced by the acoustics optical modulation (AOM), which is also the width of time window for obtaining the lidar signal power spectrum, is adjustable from 100 ns to 400 ns, thus the spatial resolution can be varied from 15 m to 60 m. We operate the PCDL with a pulse width of 100 ns for this study, corresponding to the longitudinal size of probing volume of 15 m. The elevation angle resolution $Δ φ$ is ${0.2}^{\circ} - {0.3}^{\circ}$ in this experiment, so the transverse size of probing volume at range R is $R Δ φ$ (the unit of $Δ φ$ is in rad), where R is the distance between PCDL and analyzed probing volume. The transverse size at R = 200 m, for instance, is about 0.70 m ~1.05 m. The PCDL includes a real time display of the light-of-sight wind velocity and wind profile. The specifications of the PCDL are listed in Table 1.

Fig. 1 (a) A schematic photograph of PCDL system Wind3D 6000 (b) lidar observational transverse mode: Range Height Indicator (RHI) (c) sketch map of wake vortex observation under NGE.

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Table 1. The specifications of the PCDL and wind profiler lidar.

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The background atmospheric conditions are essential for the dissipation of wake vortices. A wind profiler lidar, Leice-Lidar WindMast WP350, was collocated with scanning PCDL and to provide atmospheric dynamic parameters for analyzing the effect of wind and atmospheric turbulence on aircraft wake vortex, also for wake vortex prediction simulation model. On the other hand, it is also a promising tool for airport low-level wind shear observation [34]. It measures wind profile from 40 m to 350 m using the Velocity-Azimuth-Display (VAD) configuration with very high spatial resolution of 1 m and high sampling rate of 1 Hz. Table 1 lists the specifications of the wind profile lidar.

For wake-vortex measurements, the pulse length of PCDL leads to a long-range gate which limits the spatial resolution. A Range Height Indicator (RHI) scan strategy with high resolution of scanning elevation angle, shown in Fig, 1(b), is adopted to compensate the resolution decrease caused by the long pulse duration. In RHI scanning mode, the laser beam scans in a plane perpendicular to the flight path of aircraft with fixed azimuth angle and changeable elevation angles. The minimum and maximum of the elevation angle are determined based on experimental requirement.

Figure 1(c) shows the sketch map of PCDL location during BCIA 2017 campaign. The wake vortex during the landing under crosswind conditions is the main factor for site selection. Owing to the prevailing northly wind at BCIA in winter, the meteorological station in the south of 18L/36R runway, marked with “lidar”, was selected to install the PCDL, approximate 974 m to the 18L/36R touchdown zone. The azimuth angle of RHI scanning was set to $230^{\circ}$ and the corresponding distance between A and B was 1110 m. For aircraft following standard approaching angle, the altitude of landing aircraft at point B was about 55.5 m, which was covered by the scan range. Table 2 lists the specific experimental configuration. The scanning rate is $1^{\circ} / s$ and the elevation range is from $- 1^{\circ}$ to $15^{\circ}$ , and the scan duration is 13 s – 14 s, meeting the demands for wake vortex ground effect characteristics investigation.

Table 2. Experimental configuration for RHI scanning mode.

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3. Methodology

Figure 2 shows the flow chart of data processing of wake vortex characteristics. In order to implement autonomous batching processing, accurate analyzed time period for specific case study must be determined firstly. On the one hand, fixed analyzed time period is inappropriate especially for different air traffic flow during different time interval. On the other hand, simulation prediction requires longer wake vortex evolution process where the circulation should decay to less than 140 $m^{2.} / s$ for heavy airplane or 80 $m^{2.} / s$ for the light one. Therefore, the analyzed time period automatically adjustment is preferred to meet those two aspects. In this campaign, the 01/36R landing flights information were obtained beforehand to determine the start and end time of observation. Data matching between aircraft type database and captured case study were then evaluated to judge whether further PCDL scanning measurement should be used or not.

Fig. 2 Flow chart of lidar observation and data batching process.

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3.1 Determination of wake vortex core position using radial velocity and spectrum

In order to locate and analyze the wake vortex evolution in real-time processing, we use both radial velocity and FFT spectrum of PCDL measurement. When the PCDL scans across a wake vortex, the anomaly of radial velocity can be found due to the Doppler broadening by the turbulence inside the vortex, shown in Fig. 3(a). The colors indicate the averaged radial wind speed along the laser beam where positive value represents the radial velocity has the same direction as laser beam. The color inside the vortex region indicates the averaged tangential speed and background wind in each detection volume. Therefore, the radial velocity is a straightforward indicator not only for the existence of wake vortex, but also an indicator for wake vortex distance from the PCDL. We introduce the function $D_{v} (R_{k})$ as:

D_{v} (R_{k}) = | V_{\max} (R_{k}) | + | V_{\min} (R_{k}) |,

where

V_{\max} (R_{k})

and

V_{\min} (R_{k})

are the maximum and minimum radial velocity, respectively, at each range

R_{k}

,where

R_{k} = R_{0} + k Δ R

is the distance from lidar,

R_{0}

is the minimal measurement range,

k = 0, 1, 2, ... K - 1

. Figure 3(b) shows the

D_{v} (R_{k})

with two pronounced bimodal distribution. Therefore, the

D_{v} (R_{k})

is firstly used to judge whether the wake vortex exists or not in one scanning measurement. Then the wake vortex range bins where the two peaks appear are determined then, as shown in Fig. 3(b) with black dot lines.

Fig. 3 Wake vortex location determination (a) the two-dimensional radial velocity distribution when an A388 crossed the scanning plane during Jan. 31 2017 at BCIA (b) Corresponding function $D_{v} (R_{k}; n)$ .

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After determination of wake vortex range bin, the FFT spectrum are further used to determine the exact elevation angles. The specific description of FFT spectrum can be obtained in paper [33]. Taking left wake vortex for example, Figs. 4(a) and (b) show the spectrum distribution at fixed range bin and different elevations from left wake vortex (in Fig. 3(a)) and ambient wind area which is derived from scan measurement without wake vortex disturbance, respectively. It can be seen because of the existence of wake vortex, the spectrum in Fig. 4(a) has a distinct discrepancy compared with the one from ambient measurement in Fig. 4(b). In order to compare the spectrum difference in detail, Figs. 4(c) and 4(d) show the spectrum of left wake vortex and ambient area at elevation angle of $7 {.6}^{\circ}$ and $4 {.0}^{\circ}$ , respectively, and the spectrum difference is also shown in yellow line. It is illustrated that the spectrum peak, representing the dominant radial velocity in one range bin, can be shifted due to wake vortex tangential velocity distribution. Above left wake vortex core position, as shown in Fig. 3(a), the radial velocity due to wake vortex existence becomes larger compared to the one in ambient wind area. Correspondingly, the spectrum peak of left wake vortex in red line shown in Fig. 4(c) is shifted to smaller spectral bin point compared to ambient one in blue line. Conversely, the radial velocity below left wake vortex has a negative radial velocity shown in Fig. 3(a), resulting in spectral peak right shift, as shown in Fig. 4(d). Furthermore, the wake vortex has a significant effect on the spectral width broadening [14]. Therefore, the spectral difference between adjacent RHI scans of wake vortex and ambient atmosphere is promising to visually locate the wake vortex position.

Fig. 4 (a) Left wake vortex spectrum distribution at fixed range bin and different elevation, (b) ambient spectrum distribution from scan measurement without wake vortex disturbance, (c) spectrum of left wake vortex and ambient at elevation angle of $7 {.6}^{\circ}$ (above left wake vortex core position), (d) same as Fig. 4(c), but for elevation angle of $4 {.0}^{\circ}$ (below left wake vortex core position).

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Figures 5(a) and 5(b) show spectrum difference obtained from wake vortex affected range bin and corresponding ambient measurement. The spectrum arrays at whole elevation angles and fixed wake vortex located-range bin are chosen as the interested area. The x-axis is the spectral bin point, and the y-axis is the different elevation angles. Taking Fig. 5(a) for example, the upper part of left wake vortex has a positive tangential velocity, leading to the shift of spectral peak to the lower part of the spectral bins. Therefore, the spectrum difference has “positive to negative” distribution at specific elevation angle, consistent to the area marked with red square in Fig. 5(a). Based on the spectrum difference distribution, the maximum and minimum value of spectral power at each elevation angle can be determined, shown with black and red dot line, respectively in Figs. 5(a) and 5(b). The cross point at maximum and minimum lines are regarded as the wake vortex core position, shown with black dashed lines.

Fig. 5 (a) the spectrum difference obtained from the left wake vortex range bin and corresponding ambient measurement, (b) same as Fig. 5(a), but for right wake vortex.

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3.2 Circulation determination and scaling correction

As mentioned in Sect 1, the circulation wake vortex is much more challenging to be estimated due to lack of true knowledge. Figure 6(a) illustrates the components of a lidar spectrum for a single sampling volume where the dominant Doppler velocity is represented by a shift in the spectral peak. Since wake vortex tangential velocities are most apparent as a widening of the spectrum, given a certain threshold from the measured Doppler spectrum shown in Fig. 6(a), the velocity enveloped can be found. In order to obtain the velocity envelope closest to the tangential velocities of the wake vortex, a floating threshold which is a function of elevation angle has been described in [12,16]. In that case, with the use of the Gaussian temporal window and radial velocity model function based on Burnham Hallock vortex model, the Doppler spectrum model can be obtained using conditional ensemble averaging. Then an iterative procedure is proposed for the circulation estimation from measured Doppler spectra. However, the SNR in this study is defined as the ratio of the peak value of FFT spectrum signal in each range bin to the Root Mean-Square (RMS) of background noise signal [33], which is different compared to [12,16]. Furthermore, different procedure in FFT spectrum and definition of temporal window make it more complicated to retrieve circulation following mentioned equations and steps as mentioned in [12,16]. As the value of threshold is determined by the level of fluctuations of the noise spectrum component [16]. A floating threshold based on SNR level is determined herein, which is similar as the studies in [14]. Specifically, a threshold is selected as n% of the peak velocity of the FFT spectrum shown in Fig. 6(a). The closest intersections to the peak velocity marked with V_min and V_max is defined as the negative and positive envelope, respectively. Following the method in [8], the background wind is calculated as the mean radial velocity of the measured one in front and behind the wake vortex shown in Figs. 6(b) and (c), which needs to be subtracted from the velocity envelopes before circulation calculation. It is noted that the results shown in Figs. 6(b) and (c) are linear interpolated with elevation angle resolution of $Δ φ_{1} =0 {.1}^{\circ}$ , and the elevation angle $φ = l Δ φ_{1},$ $l = 1, 2, 3, ...120$ .

Fig. 6 (a) Spectrum taken from Fig. 5(a) for the case when data was measured above the left vortex core and selected minimal and maximal value of the radial velocity distribution in the sensing volume. (b) Radial velocity as a function of the range and elevation, the rea and black curves represent the ranges in front of and behind the wake vortex, respectively. (c) radial velocity as function of elevation angles in front of (red line) and behind (black line) the wake vortex, and the mean background wind velocity (blue line). The x-axis is elevation angle number l.

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Figure 7(a) shows the velocity envelopes along four range bins where wake vortex can be indicated in Figs. 7(a2) and 7(a3). The sensitivity test of calculated circulation on threshold n% shows that the estimated circulation is not sensitive to the choice of threshold ratio at n>5, where obvious fluctuation at n<5 results from the noise peak disturbance. It thus gives insight into a compromise and reasonable method between accurate systematic broadening correction and fast vortex evaluation [8,16]. The comparison of velocity envelope of wake vortex with (solid line) and without (dot-line) background wind subtraction can be seen in Fig. 7(b). Figure 7(c) shows the wake vortex circulation along the core radius. An integration method is applied to decrease the error of estimation of vortex circulation [16]. Furthermore, since scanning plane is not perpendicular to 18L/36R runway because of obstacle blocking in this experiment, the detected velocity from velocity envelope is the projection of wake vortex true tangential velocity on scanning plane, angle correction is required for circulation calculation. In this case, the circulations of these two wake vortices are calculated from the mean value within the distance of 5 m and 15 m from the vortex core position, corresponding to $359 .8$ m²/s and $410 .5$ m²/s after angle correction for left and right wake vortex, respectively.

Fig. 7 (a) Velocity envelopes along elevation angles within 8-11 (from top to bottom) range bins. The red (blue) curves show the positive (negative) envelopes corresponding to the maximal (minimal) value of the radial velocity distribution in the sensing volume. (b) the velocity envelope of left and right wake vortex before (dot-line) and after (solid line) background wind velocity subtraction. (c) circulation of a pair of wake vortex as a function of the radial distance to the core position.

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In case of the core position of wake vortex lower than 15 m, the missing parts of vortex is corrected using Burnham-Hallock (BH) model, which describes the tangential velocities of a single wake vortex at each radius as a function of total circulation parameter $Γ$ and a core radius $r_{0}$ [35], where:

v_{0} = \frac{Γ}{2 π} (\frac{r}{r^{2} + r_{0}^{2}}),

Figures 8(a) and 8(b) shows the distribution of wake vortex circulation with radius and corresponding BH model fitting with NGE and without NGE, respectively. The fitting results match the measurement well and reasonable for circulation correction. After BH model fitting correction, the circulation can be calculated and is consistent with the circulation definition.

Fig. 8 (a) BH model fitting using PCDL measured data without NGE, (b) same as Fig. 8(a), but for the case with NGE. (c) simulated tangential velocity distribution before (blue) and after (red) scaling correction where PCDL scans downward and wake vortex moves downward (d) same as Fig. 8(c), but for the case when PCDL scans downward and wake vortex moves downward.

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Another factor for circulation correction which should be considered is the distortion of vortex. Because of the relative movement between the wake vortex and the scanning laser beam, the measured size of vortex will be compressed or stretched, so that the circulation will be underestimated or overestimated. In the processing of PCDL measured data set, the movement of the core position can be obtained by a series of descending and ascending scans, thus the trajectory and speed of vortices can be estimated. Consequently, this information can be used to correct the compressed or expanded wake vortex to obtain its exact dimension and circulation.

We simulated this scaling effect based on PCDL scanning mode. A simulated tangential velocity field of wake vortex with $Γ =500$ m²/s and $r_{0} = 2 .5$ m is generated using BH model, and the PCDL measurement is configured with the same parameters as the field experiment shown in Table 2. The wake vortex movement speed is set to 1.0 m/s, and the initial wake vortex location is X₀ = 248 m, Y₀ = 55.5 m, respectively. Figures 8(c) and 8(d) shows the tangential velocity simulation results at different conditions. It is shown that in the case of both the wake vortex and PCDL laser beam move downwards, shown in Fig. 8(c), the size of wake vortex is stretched. The truth radius should be smaller than the measured one. The circulations before and after scaling correction are 612 m²/s and 460 m²/s, respectively, overestimating to some extent about 32%. On the contrary, when the wake vortex movement and PCDL scanning direction is opposite, shown in Fig. 8(d), the size of wake vortex is compressed and the circulation is underestimated at about 20%. Therefore, it is important to make scaling correction to study wake vortex evolution more accurately. The effect of different parameters on circulation evaluation will be analyzed in detail in Sect. 4.1.

3.3 Retrieval of crosswind and atmospheric turbulence based on RHI structure function

The crosswind and atmospheric turbulence are two of the most important factors influencing the dissipation of wake vortex. The concurrent atmospheric background wind field and wake vortex features are of great significance for the analysis of wake vortex behavior [36]. Herein the velocity structure function method based on RHI mode is used [9]. The whole RHI slide is filtered out if there are wake vortex to avoid the superposition effect of aircraft vortex on the accuracy of the atmospheric turbulence. Figure 9(a) shows the averaged radial velocity $V_{D}$ distribution using RHI scanning mode. The crosswind velocity profiles are calculated by the Eq. (3) as follows and shown in Fig. 9(b),

< V_{c} (h) >_{E} = {(N_{s} L)}^{- 1} \sum_{n = 1}^{N_{s}} \sum_{h - δ < h_{k l} < h + δ}^{L} V_{D} (h_{k l}, n) {(\cos φ_{l})}^{- 1},

where

N_{s}

represents the number of scans used for averaging, herein we retrieved the turbulence parameters from lidar data measured during 20 scans, corresponding measurement period of about 5 min.

L

is the number of estimates in a layer of

Δ h = 2 δ = 50

m thickness at one scan. The summation is performed over the subscripts

n

,

k

and

l

satisfying the condition

h - δ < h_{k l} < h + δ

. The two-dimensional distribution of the mean radial velocity and its fluctuations are calculated using Eqs. (4)-(5) and shown in Figs. 9(c) and 9(d), respectively. where:

< V_{D} (R_{k}, φ_{l}) >_{E} = < V_{D} (h_{k l}) >_{E} \cos φ_{l},

V_{D}^{'} (R_{k}, φ_{l}, n) = V_{D} (R_{k}, φ_{l}, n) - < V_{D} (R_{k - 1}, φ_{l}) >_{E},

where the ranges

R_{k} = R_{0} +k Δ R

,

R_{0} = 120

m,

Δ R =15

m,

k = 0, 1, 2, ... K - 1

, and the elevation angles

φ_{l} = l Δ φ

,

Δ φ =0 {.2}^{\circ} ~0 {.3}^{\circ}

,

l = 0, 1, 2, ... 60

in this experiment.

Fig. 9 (a) The radial velocity distribution using RHI scanning mode (b) the mean horizontal wind component (c) The two-dimensional distribution of the mean radial velocity and (d) radial velocity fluctuation during 20:11-20:15 Jan. 23 2017 at BCIA without wake vortex disturbance.

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After the determination of radial velocity fluctuation $V_{D}^{'} (R_{k}, φ_{l}, n)$ , the estimates of the raw structure function of the radial velocity Doppler Lidar estimate $D_{r a w} (s, h)$ and the contribution from the estimation error of the velocity estimates $D_{e} (s, h)$ at lag s and height h from measured data set can be then derived [9,37].

D_{r a w} (s, h) = {(N_{s} L)}^{- 1} \sum_{n = 1}^{N} \sum_{h - δ < h_{k l i} < h + δ}^{L} {\hat{D}}_{r a w} (r_{i}, h_{k l i}, n),

D_{e} (s, h) = {(N_{s} L)}^{- 1} \sum_{n = 1}^{N} \sum_{h - δ < h_{k l i} < h + δ}^{L} {\hat{D}}_{e} (r_{i}, h_{k l i}, n),

{\hat{D}}_{r a w} (r_{i}, h_{k l i}, n) =[V_{D}^{'} (R_{k} + r_{i}, φ_{l}, n) - V_{D}^{'} (R_{k}, φ_{l}, n)]^{2},

{\hat{D}}_{e} (r_{i}, h_{k l i}, n) =[e (R_{k} + r_{i}, φ_{l}, n) - e (R_{k}, φ_{l}, n)]^{2},

Then the structure function after error contribution subtraction, $D_{w g t - c a l c u l a t e} (s)$ at height h, is fitted to the corrected von Kármán model $D_{w g t - m o d e l} (s)$ where the PCDL volume averaging effect has been taken into consideration.

D_{w g t - c a l c u l a t e} (s) = D_{r a w} (s) - D_{e} (s),

D_{w g t - m o d e l} (s) = ε^{2 / 3} G_{s} (s, Δ R, L_{i}),

G_{s} (s, Δ R, L_{i}) = 0.497 C_{K} s^{2 / 3} \int_{0}^{\infty} \frac{d ξ (1 - \cos ξ) \exp [- {(ξ Δ R / s)}^{2} / (2 π)]}{{[ξ^{2} + {(0.746 s / L_{i})}^{2}]}^{5 / 6}},

To retrieve turbulence energy dissipation rate (TEDR) and turbulence integral scale $L_{i}$ , the genetic algorithm is used to solve the optimum solution. Although PCDL is promising to improve our understanding of turbulence variability in atmospheric boundary layer, attention should be paid on its fundamental assumption [38]. Keeping in mind that the TEDR can be determined using structure function method on the assumption of locally homogeneous and isotropic turbulence, and the structure function is only depending on TEDR in the inertial subinterval of turbulence [9]. Therefore, the choice of fitting lag interval should be carefully addressed since only the structure function corresponding to inertial subrange is applicable to model fitting procedure. In this study, turbulence characterization under near ground is evaluated. It is well known that the integral scale of turbulence is proportional to the height under near ground. Fitting procedure using unrealistic initial value in genetic algorithm can induce large errors. For instance, the groundless fitting lag interval, such as larger than 100 m, result in overestimation of integral scale and underestimation of TEDR, which is not in agreement with fundamental laws of behavior of atmospheric turbulence parameters near the ground. Furthermore, the divergence parameter, characterizing the difference between measured and theoretical structure function, is used as follows [39,40]:

γ = {I^{- 1} \sum_{i = 1}^{I} {[D_{w g t - c a l c u l a t e} (i Δ r) / D_{w g t - m o d e l} (i Δ r) - 1]}^{2}}^{1 / 2},

where

Δ r = 2 m

and

I = 10

. Following this process, the structure function estimates of turbulence using 20 RHI scans on 20:11-20:15 January 23 2017 at BCIA at the height of 75 m is calculated. Figure 10 shows

D_{w g t - c a l c u l a t e} (s)

and

D_{w g t - m o d e l} (s)

in black dots and red line, respectively, where the structure function using different models are also shown. From the fitting of the

D_{w g t - c a l c u l a t e} (s)

, we derive the standard deviation of radial velocity

σ = 0.54

m/s and the integral length scale

L_{i} = 110.1

m, and the

ε = 0.001

m²/s³ can be calculated from Eqs. (14)-(15) as shown:

Fig. 10 Structure function estimates of turbulence using 20 RHI scans on 20:11-20:15 Jan. 23 2017 at BCIA with the height of 75 m. Curves shows calculations of the corrected structure function (black dots), the von Kármán model (black line), the Kolmogorov model (blue line) and the corrected von Kármán model (red line) taking the volume average effect of lidar detection into consideration.

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ε = {[\frac{2^{1 / 3} π}{\sqrt{3} Γ (1 / 3) Γ (4 / 3)}]}^{3 / 2} \frac{σ^{3}}{L_{0}} = 0.933668 \frac{σ^{3}}{L_{0}},

L_{i} = \frac{\sqrt{π} Γ (5 / 6)}{Γ (1 / 3)} L_{0} = 0.7468343 L_{0},

Also, the accuracy investigation of this method can be completed with inter-comparison with measurement results of independent turbulence devices. Generally, the sonic or cup anemometers have a very high accuracy for turbulence measurement and can be regarded as reference. Banta et al. [40] experimentally studied the representativeness of this method and concluded that the lidar estimate has a small bias and relative error is less than 25% for TDER estimation, which is quite acceptable for analysis of the influence of turbulence on wake vortex evolution.

4. Results

4.1 Simulation: effect of scaling effect on circulation calculation

As mentioned in Sect. 3.2, both the PCDL specification and wake vortex characteristics have significant effects on circulation scaling correction. Therefore, simulation is needed to evaluate the contributions of those factors on scaling effect. In order to describe the parameters clearly, Fig. 11 shows the schematic diagram of lidar scanning. Taking scanning from bottom to top with increasing elevation angles for example, at time $t_{0}$ , the single wake vortex is detected, the elevation angle of laser beam and distance between lidar and vortex position are $θ_{0}$ , $R$ , respectively, and the coordinate of the core position marked with black dot is $(X_{0}, Y_{0})$ , herein $X_{0} = R \cos θ_{0}$ , $Y_{0} = R \sin θ_{0}$ . At time $t_{0} + Δ t$ , the corresponding elevation angle of laser beam is $θ_{1}$ , and the cut-off point between laser beam and wake vortex is marked with red dot with coordinate of $(X_{1}, Y_{1})$ , $X_{1} = R_{1} \cos θ_{1}$ , $Y_{1} = R_{1} \sin θ_{1}$ , $R_{1} = {(R^{2} + r_{m}^{2})}^{1 / 2}$ , $r_{m} = Δ θ {(X_{0}^{2} + Y_{0}^{2})}^{1/2}$ . We define $V_{s c a n}$ as the PCDL scanning velocity, the sign represents the scanning direction where “-” is the scan piece from top to bottom with decreasing elevation angles and “+” is the one from bottom to top with increasing elevation angles, and $Δ t = Δ θ / V_{s c a n}$ , $Δ θ = θ_{1} - θ_{0}$ . Assuming wake vortex moves downward in this case, the core position of wake vortex at $t_{0} + Δ t$ moves to position $(X_{2}, Y_{2})$ .

Fig. 11 The schematic diagram of lidar scanning, assuming the lidar scans from bottom to top and the wake vortex moves downward.

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According to circulation definition, if the measured tangential velocity $V_{t} (t_{0} + Δ t)$ at time $t_{0} + Δ t$ is accurate, the circulation can be expressed as $Γ (t_{0} + Δ t) = 2 π r (t_{0} + Δ t) V_{t} (t_{0} + Δ t)$ . If we don’t take wake vortex movement into consideration, which is the case in previous studies, $r (t_{0} + Δ t) = r_{m}$ . However, wake vortex moves and is actually affected by many factors such as the atmospheric crosswind and the interaction with the other vortex and so forth. As shown in Fig. 11, the distance between core position $(X_{2}, Y_{2})$ and $(X_{1}, Y_{1})$ is the truth radius $r_{t}$ at $t_{0} + Δ t$ , and

X_{2} = X_{0} + Δ t \cdot V_{c r o s s w i n d},

Y_{2} = Y_{0} + Δ t \cdot V_{w v},

r_{t} = \sqrt{{(X_{2} - X_{1})}^{2} + {(Y_{2} - Y_{1})}^{2}},

where

V_{c r o s s w i n d}

is the crosswind velocity at direction X and is positive when it blows from lidar direction,

V_{w v}

is the wake vortex movement speed at height direction Y, similar to

V_{s c a n}

, the sign of “-” and “+” represent downward and upward actions, respectively. Therefore, the difference between measured and circulation

Δ Γ (r)

is calculated as follows:

Δ Γ (t_{0} + Δ t) = 2 π V_{t} (t_{0} + Δ t) \cdot Δ r,

where

Δ r = r_{m} - r_{t}

. In the case of the crosswind velocity is negligible and wake vortex moves along wake vortex core transverse direction,

Δ r

can be expressed as:

Δ r = \frac{V_{w v} \cdot Δ t}{\cos θ_{0}},

Δ Γ (t_{0} + Δ t) = \frac{2 π V_{t} (t_{0} + Δ t) \cdot V_{w v} Δ θ}{V_{s c a n} \cos θ_{0}},

As can be seen in Eq. (21), when the $V_{w v}$ and $V_{s c a n}$ has the same signs, indicating same movement direction, $Δ Γ (t_{0} + Δ t) > 0$ , meaning the measured one is overestimated, which is consistent to the analysis in Sect. 3.2.

Table 3 lists the specific simulation parameters in determination of wake vortex circulation from PCDL measurement. Simulated tangential velocities based on BH model are used to represent the measured data set from PCDL with initial value of $Γ =500$ m²/s and $r_{0} = 2 .5$ m. The initial values are the basic setting, and the variation range of each factor will be used to analyze the circulation sensitivity on this factor, the variation step is also listed in Table 3.

Table 3. Simulation parameters in determination of wake vortex circulation from PCDL measurement.

View Table | View all tables in this article

According to Eqs. (19)–(21), the simulation results are shown in Fig. 12. In this case, the circulation is the mean of circulation values from radius of 5 m −15 m. It is concluded that lower lidar scanning velocity (Figs. 12(a) 12(b)), faster wake vortex vertical velocity (Figs. 12(c) and 12(d)) can result in much larger errors in circulation without scaling correction. Meanwhile, the error in the case where $V_{w v}$ and $V_{s c a n}$ has the same sign, shown in Figs. 12(a) 12(c)), is more obvious compared with the opposite cases shown in Figs. 12(b) and 12(d)). Different wake vortex location (X, Y) can make the $θ_{0}$ in Eq. (21) different essentially. In Fig. 12(e), smaller X at fixed Y makes $θ_{0}$ larger, causing larger errors in circulation. In Fig. 12(f), Y has relative stably effect on circulation.

Fig. 12 Scaling correction simulation at different lidar scanning velocity (a) (b), wake vortex vertical movement (c) (d), wake vortex location (e) (f).

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Figure 13 shows a wake vortex case study of Airbus A388. Figure 13(a) is the trajectory of wake vortex without crosswind effect. The evolution animation of the radial velocity distribution can be viewed in Visualization 1. The distance between left and right wake vortex is increasing especially after the rebound phase. Figure 13(b) shows the movement velocity of wake vortices at Y direction. It is noted that the x-axis represents the time when the lidar scanning plane firstly detects the wake vortex after the landing aircraft flies over 18L/36R runway. It is different from the vortex age which is defined as the time when the aircraft intersected the scanning plane [20] because lidar automatic scanning observation was carried out during this campaign, it cannot record the time after over-flight exactly without special equipment such as camera. Camera is essential to visualize lidar scanning and aircraft landing more accurately. Figures 13(c) and 13(d) illustrate the circulation evolution of the left and right vortex before and after scaling correction, respectively. The tortuous variation of circulation in Fig. 13(c) indicates overestimation or underestimation effect. On the other hand, the circulation at rebound phase can be affected by the secondary vortex and other complicated ground effect, which may enhance turbulence and cause the broadening of spectral width. As a result, the circulation can be overestimated in one sense. Compared the results in Figs. 13(c) and 13(d), the scaling correction makes the circulation more accurate and reliable. Since the lowest height of right wake vortex is about 29 m, the NGE is less obvious, so the corrected circulation is decreased linearly. However, the lowest height of left wake vortex is about 22 m, the rebound phase makes the circulation overestimated, shown in Fig. 13(d).

Fig. 13 (a) Trajectories of left (red squares) and right (black squares) wake vortex axes (see Visualization 1) (b) wake vortex vertical movement velocity (c) circulation evolution before scaling correction and (d) circulation evolution after scaling correction.

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4.2 Case study: effect of atmospheric turbulence on wake vortex evolution under NGE

Figure 14 shows the spatial and temporal distribution of standard deviation of LOS velocity $σ_{v}$ , crosswind velocity, TEDR and the integral scale of turbulence, respectively on 24 January 2017 at BCIA. The spatiotemporal and statistics of parameter $γ$ is illustrated in Fig. 15. It is shown that within near ground area at whole time period the parameter $γ$ varies from 10⁻⁴ to 0.5 (an average of about 0.09), and around 87% and 61% of the cases have $γ$ less than 0.2 and 0.1, respectively, implying that the data measured by vertical plane scanning lidar can obtain reliable information about turbulence estimation. Time-averaged turbulence parameter profiles is analyzed and shown in Fig. 16 where the cases with $γ > 0 .3$ is subtracted. It can be seen from Fig. 14 and Fig. 16 that the atmospheric turbulence has distinct diurnal variation. During early morning and night, the turbulence is relatively weak due to stable thermal stratification [41], and the maximum averaged TEDR is less than $2 .5 \times 10^{-3}$ m²/s³. Contrarily, intense atmospheric thermal convection during daytime corresponds to larger values in $σ_{v}$ and TEDR. The TEDR near the ground is larger than $3 .5 \times 10^{-3}$ m²/s³. The TEDR has overall decrease with increasing height during each analyzed time period. As can be seen in Fig. 14(d) and Fig. 16(c), the integral scale has comparable value (22m −29 m) to its height below height of 35 m. Compared to TEDR behavior near ground, the integral scale has more complicated trend with height. A slight increase with height can be seen during early morning and daytime period. But for the case at night, the integral scale decreases with height above 26 m. Less data set at higher height are available due to RHI scanning area limitation, which could induce more uncertainty for structure function measurement. On the other hand, the effect of atmospheric inhomogeneity and nonstationary at stable condition has a significant effect on model fitting procedure, especially referring to the choice of fitting lag interval and hypothetical applicability. More detailed studies on stable stratification atmospheric should be evaluated [42].

Fig. 14 Spatiotemporal distributions of the (a) standard deviation of velocity (m/s) (b) crosswind velocity (m/s) (c) turbulence energy dissipation rate and (d) integral scale of turbulence obtained from measurements by the PCDL on 24 Jan. 2017 at BCIA.

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Fig. 15 (a) Spatiotemporal distribution of the parameter $γ$ obtained from measurements by PCDL on 24 Jan 2017 at BCIA, (b) corresponding histogram of parameter $γ$ .

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Fig. 16 Time averaged turbulence parameters (a) integral scale (b) TDER and (c) $σ_{v}$ during 00-06 LST (black dots), 09-18 LST (blue dots) and 19-24 LST (red dots), respectively.

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Considering the efficiency and processing time for the data batching processing, the turbulence parameter retrieval at wake vortex generated height is of great priority for further statistics analysis. In order to analyze the effect of atmospheric turbulence on wake vortex evolution under NGE, 24 heavy aircrafts are chosen on 24 January 2017. Different parameters are defined and then normalized using theoretical initial values of the vortex parameters described below [36]:

b_{0} = (π / 4) B_{a},

Γ_{0} = M g / (ρ b_{0} V_{a}),

w_{0} = Γ_{0} / (2 π b_{0}),

t_{0} = b_{0} / w_{0},

where

b_{0}

is the initial distance between the cores of the right and left vortex,

Γ_{0}

is the vortex initial circulation out of its core,

w_{0}

is the descent speed of a pair of vortex in an unperturbed atmosphere, and

t_{0}

is the time during which the vortex move down to a distance equal to the initial distance between the vortex cores. In Eqs. (23)-(24),

B_{a}

is the aircraft wingspan,

g

is the gravitational acceleration,

ρ

is the air density at the flight altitude,

M

is the mass, and

V_{a}

is the speed of the aircraft. Table 4 lists the parameters of different aircraft type used in statistics analysis.

Table 4. Specific parameters of different aircraft type used in statistics analysis.

View Table | View all tables in this article

Based on the aircraft vortex parameters mentioned above, Fig. 17 shows the normalized wake vortex characteristics where the squared-marked line represents the mean of parameters at specific time periods. The normalized distance between the cores of the wake vortex shown in Fig. 17(a), is closed to the theoretical values of initial distance b₀. Different from the trend for out ground effect (OGE) cases [36], the distance increases with time generally because of the wind shear existence. The tilt angle of a pair of vortex $ς$ is usually an indicator of inhomogeneity of the wind distribution. In Fig. 17(b), the tilt angle has relative wide distribution, but $ς > 0$ is more frequent than $ς < 0$ , and the mean values at each period are always larger than 0 and increase slightly with time. The phenomenon is different from OGE cases [36]. Specifically, the cases when crosswind blows from PCDL account for about 71% of all cases, and because of the wind logarithm profile at near-surface layer, the downwind wake vortex is affected by the opposite shear force, and usually rebounds earlier and higher than the upwind wake vortex, causing positive nadir angles. Figures 17(c) and 17(d) also indicate the asymmetrical effect of crosswind on upwind and downwind wake vortex where the upwind wake vortex is less affected by crosswind. Figures 17(e) and17(f) shows the normalized core altitude and normalized vertical component of the vortex core movement speed, respectively. It can be seen that the downwind wake vortex has earlier rebound time and higher rebound height than upwind wake vortex, and the rebound processing of upwind wake vortex is less significant. Figures 17(g) and 17(h) shows the normalized circulation evolution of upwind and downwind wake vortex, respectively. As mentioned in Fig. 13, the time in this paper is different from the vortex age. The first detected wake vortex scan fragment cannot capture the exact wake vortex in initial generated moment. It means that the first circulation in Figs. 17(g) and 17(h) often represents the wake vortex after certain time period decay. One scan duration is 13 s – 14 s in this study, furthermore, wake vortex decays faster near ground compared to the evolution under out ground effect (OGE), it is possible that the first detected circulation is smaller than the initial circulation calculated by Eq. (15). The red, blue square-marked line represent the averaged cases value at $T E D R < 4 \times 10^{- 3}$ and $T E D R \geq 4 \times 10^{- 3}$ The circulation attenuation of upwind wake vortex is more related to atmospheric turbulence compared to downwind wake vortex, and larger turbulence makes wake vortex decay faster. But for downwind wake vortex, the turbulence has less obvious effect on wake vortex decay. These normalized parameters show the different evolution process and features of upwind and downwind wake vortex under NGE, which is different from the cases under OGE [36].

Fig. 17 Measurement results from selected heavy aircraft types on 24 Jan. 2017 at BCIA (a) the normalized distance between the cores of the wake vortex (b) the tilt angles of a pair of vortex (c) the normalized transverse distance (d) normalized transverse component of the vortex core movement speed (e) the normalized core altitude (f) normalized vertical component of the vortex core movement speed (g) normalized circulation for upward wake vortex and (h) normalized circulation for downward wake vortex.

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5. Conclusions

Aircraft wake vortex, the small-scale phenomenon of clear air dynamics, can only be detected by Doppler lidar and analyzed quantitatively. In this paper, aircraft wake vortex observation under NGE using PCDL at BCIA during 2017 campaign are studied. A set of real-time signal processing methods for wave vortex detection using PCDL are developed, and proved its feasibility and effectiveness through field experiments. The core techniques, so called Wake Vortex Visualization Demonstrator (V2D), particularly the scanning mode and signal processing technologies have been developed and demonstrated based on the Doppler lidar spectrum analysis. As for wake vortex trajectory determination, the combination of radial velocity and a robust spectrum subtraction method is firstly proposed to indicate the occurrence of vortices in real time. The velocity envelope method with reasonable threshold selection is used to calculate wake vortex circulation. BH model is specially used to correct the tangential velocity under NGE. The underestimate or overestimate of wake vortex circulation due to RHI scanning mode is delicately simulated and analyzed. It can be found that the PCDL specification and wake vortex characteristics can contribute to the scaling effect in different degrees. The scaling correction method is proposed and successfully tested using PCDL measurement.

In addition, the simultaneous retrieval of wake vortex and atmospheric turbulence with one lidar measurement has laid the foundation for the future “detection, prediction and decision-making” system at the airport. The effect of crosswind and atmospheric turbulence on wake vortex under NGE cases are studied and compared with previous literatures. The normalized parameters show significant difference on upwind and downwind wake vortex, and the asymmetrical effect of crosswind and atmospheric turbulence on upwind and downwind wake vortex are obvious, which is different from the case under OGE.

Funding

Boeing-COMAC Sustainable Aviation Technology Centre; Ocean University of China.

Acknowledgments

We thank our colleagues for their great support during the field experiments at BCIA, including Hongwei Zhang, Qichao Wang, and Xiaoying Liu from Ocean University of China (OUC) for preparing and conducting the experiment; Dr. Helen Lee and Dr. Zheng Fan with Boeing Company, Dr. Zhongmin Hu, Dr. Daikai Lin and Dr. Shuai Zhang with COMAC for their in-sight discussions; Director Wei Zhang and Jianjun Zhang from the weather center of Huabei Air Traffic Management Bureau for coordination at BCIA; Xitao Wang, Yilin Qi and Rongzhong Li from Leice-Lidar Transient Technology Ltd. for preparing and operating the lidar.

Disclosures

The authors declare that there are no conflicts of interest related to this article.

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Qualification	PCDL Wind3D 6000	Wind Profiler lidar WindMast WP350
Wavelength, μm	1.55	1.55
Pulse repetition rate, kHz	10	20
Sampling rate, GHz	1	1
Data update rate, Hz	4 (fastest)	1
Pulse width, ns	100 - 400	120
Pulse energy, $μ J$	150	12
Measurement range, m	40 - 6000	20 - 350
Range resolution, m	15 - 60	15 physically; 1 by algorithm
Blind area, m	adjustable	25
Scanning speed, m/s	adjustable	-
Speed measurement uncertainty, m/s	$\leq 0.1$	$\leq 0.1$
Radial velocity measurement range, m/s	$\pm 37.5$	$\pm 37.5$
Power Consumption, W	<300	90
Weight, kg	~75	<30

Distance to touchdown zone A	974
Azimuth, ^o	230
Distance to runway 18L/36R, m	248
Distance between A and B, m	1110
Scanning rate, ^o/s	1
Elevation range, ^o	−1 - 13
Elevation angle resolution, ^o	0.2 – 0.3
Detection radial range, m	120 - 600
Duration of measurement, s	~0.3
Scan duration, s	13 - 14
Transverse resolution (R = 300), m	1.03 - 1.57
Probing pulse duration, ns	100
Longitudinal resolution, m	15
Detectable lowest height, m	5 - 6
Distance to touchdown zone A, m	974
Sampling interval ( $T_{s}$ ), ns	1
Range gate length ( $Δ R {=cT}_{s} / 2$ ), m	0.15

Parameter, P	Initial value, P₀	Variation range	Parameter variation step, $Δ P$
$V_{s c a n}$ , ^o/s	−1.0	[-2 −0.5] [0.5 2]	0.1
$V_{w v}$ , m/s	−1.0	[-2 2]	0.1
$X_{0}$ , m	248	[100 600]	2
$Y_{0}$ , m	55.5	[20 100]	2
$Γ_{0}$ , m²/s	500	Based on aircraft type	Based on aircraft type
$r_{0}$ , m	2.5	Based on aircraft type	Based on aircraft type

Aircraft type	Number, N	$B_{a}$ , m	$M$ , ton	$V_{a}$ , knot	$b_{0}$	$w_{0}$	$Γ_{0}$	$t_{0}$
A332	10	60.3	180	140	47.3	1.43	424	33.2
A333	4	60.3	185	146	47.3	1.41	418	33.7
A388	4	79.8	386	140	62.6	1.75	687	35.8
B763	2	47.6	136	140	37.3	1.73	407	21.5
B788	2	60.0	166	140	47.1	1.33	392	35.5
B789	2	63	186	140	49.5	1.35	419	36.7

Qualification	PCDL Wind3D 6000	Wind Profiler lidar WindMast WP350
Wavelength, μm	1.55	1.55
Pulse repetition rate, kHz	10	20
Sampling rate, GHz	1	1
Data update rate, Hz	4 (fastest)	1
Pulse width, ns	100 - 400	120
Pulse energy, $μ J$	150	12
Measurement range, m	40 - 6000	20 - 350
Range resolution, m	15 - 60	15 physically; 1 by algorithm
Blind area, m	adjustable	25
Scanning speed, m/s	adjustable	-
Speed measurement uncertainty, m/s	$\leq 0.1$	$\leq 0.1$
Radial velocity measurement range, m/s	$\pm 37.5$	$\pm 37.5$
Power Consumption, W	<300	90
Weight, kg	~75	<30

Aircraft wake vortex and turbulence measurement under near-ground effect using coherent Doppler lidar

Abstract

1. Introduction

2. Experimental setup and field campaign

3. Methodology

3.1 Determination of wake vortex core position using radial velocity and spectrum

3.2 Circulation determination and scaling correction

3.3 Retrieval of crosswind and atmospheric turbulence based on RHI structure function

4. Results

4.1 Simulation: effect of scaling effect on circulation calculation

4.2 Case study: effect of atmospheric turbulence on wake vortex evolution under NGE

5. Conclusions

Funding

Acknowledgments

Disclosures

References

Supplementary Material (1)

Cited By

Figures (17)

Tables (4)

Equations (25)

Optics Express