Flow pattern similarities in the near wake of three bird species suggest a common role for unsteady aerodynamic effects in lift generation

Abstract

Analysis of the aerodynamics of flapping wings has yielded a general understanding of how birds generate lift and thrust during flight. However, the role of unsteady aerodynamics in avian flight due to the flapping motion still holds open questions in respect to performance and efficiency. We studied the flight of three distinctive bird species: western sandpiper (Calidris mauri), European starling (Sturnus vulgaris) and American robin (Turdus migratorius) using long-duration, time-resolved particle image velocimetry, to better characterize and advance our understanding of how birds use unsteady flow features to enhance their aerodynamic performances during flapping flight. We show that during transitions between downstroke and upstroke phases of the wing cycle, the near wake-flow structures vary and generate unique sets of vortices. These structures appear as quadruple layers of concentrated vorticity aligned at an angle with respect to the horizon (named ‘double branch’). They occur where the circulation gradient changes sign, which implies that the forces exerted by the flapping wings of birds are modified during the transition phases. The flow patterns are similar in (non-dimensional) size and magnitude for the different birds suggesting that there are common mechanisms operating during flapping flight across species. These flow patterns occur at the same phase where drag reduction of about 5% per cycle and lift enhancement were observed in our prior studies. We propose that these flow structures should be considered in wake flow models that seek to account for the contribution of unsteady flow to lift and drag.

1. Introduction

Bioinspired flight is currently one of the major research areas in aeronautics and robotics. Recent advances in the development of small unmanned aerial vehicles (UAVs) and flying robots have prompted much research in the aerodynamics of flapping wings [1,2]. In the low Reynolds number region where these vehicles operate, stationary wing configurations typically suffer from low performance. However, birds, bats and insects that use flapping wings exhibit high performance [3,4]. These natural flyers have a flexible wing configuration, which grants them the ability to fly in several flight modes and the capability of generating vortex structures that result in large values for both lift and drag [4].

Weis-Fogh [5] studied the role of steady and unsteady aerodynamics in the flight performance of insects. He suggested, through qualitative study, that for certain types of fliers in specific flight modes, unsteady aerodynamics plays a major role in the lift generation process. To measure the aerodynamic forces on complex lifting surfaces with unsteady motions, one has to analyse the properties of the vortex structures or wakes formed by the body [6]. In the past few decades, wake patterns behind flapping birds' wings (the so-called ‘gaits’) have been described using idealized models in order to better characterize flow dynamics. These wakes have been described by theoretical models and later reinforced by visualization techniques. The vortex ring gait suggests that each wingbeat is aerodynamically active only during the downstroke phase where tip vortices connect the starting and stopping vortices; thus, creating an elliptical vortex ring. During the upstroke phase, there is no shedding of vorticity into the wake [7]. The continuous vortex gait suggests that vorticity is shed continuously throughout the upstroke and downstroke phases from the wingtips without strong concentrations of starting or stopping vortices. The wake is populated by tip vortices of nearly constant circulation. The vortex ring gait was described in hovering flight [8] and slow forward flight [9], while at higher flight speeds the continuous vortex gait dominates [10–13]. It has been shown that the description of these gaits as discrete is somewhat incomplete; there is not an abrupt change between the two gaits, instead the change is gradual over the speed range [6,14–16].

Advances in technology have allowed for quantitative measurements of wakes and estimating aerodynamic forces using particle image velocimetry (PIV) [17,18]. This method has been applied to a number of flying species where measurements were taken at distances between 8 and 22 chord lengths [6,16,19–22]. These measurements have been applied to calculate the momentum balance using the quasi-steady aerodynamic assumption [11], leading to estimation of lift and drag (see review by Spedding & Hedenström [23]) experienced during flapping flight. Using this approach, prior interactions of the near wake are neglected, allowing for the assumption that the flow did not dissipate significantly in the streamwise direction and the wake is self-preserving at the far-wake region [24]. Neglecting the unsteady effects, however, is not entirely justifiable for most flight conditions encountered in the low Reynolds number region [25,26]. At low Reynolds numbers, the flow may develop wake–wake interactions that can potentially cause cancellation of vorticity and reconnection of vortex lines. Recently, Johansson et al. [27] argued that the unsteady flow has an impact on the flight cost. These findings can significantly modify the qualitative and quantitative properties of fluid flows [6]. For a recent description of the work published on the fluid dynamics at the wake region behind flying birds and bats, we refer the reader to fig. 1 of Kirchhefer et al. [28].

The feasibility of recent advances in accurate three-dimensional fabrication has led to the development of robotic wings. Bird models have been used to shed light on the interaction between the bird's wings and the surrounding flow field and the forces exerted by flapping wings on the wake [29,30]. These models complemented the former observations and the commonly described aerodynamic performances of birds using quasi-stationary flow conditions; e.g. the flapping motion of the wing. Although these investigations of mechanical wings provide a basic insight into flow conditions and the development of aerodynamic forces over moving wings, they cannot simulate the natural flapping, including the peculiar motion, flexibility, feathers, muscles, etc., that are characteristics of birds. Therefore, one has to mainly rely on studies of living animals to reveal the actual kinematics and aerodynamics of bird flight.

Flapping wings and flight performance have also been investigated using computational fluid dynamics simulations in order to understand the complex flow mechanism behind flapping wings. The challenge of performing this task is twofold: modelling the wing, and simulating the unsteady wake during flapping flight. While the aeroelasticity of birds' wings was addressed thoroughly, as well as the motion of wings in fluids [31], the coupling between the phenomena with regards to bird aerodynamics is still lacking. Gordnier et al. [32] solved the flow behind a flexible flapping wing using a large eddy simulation modelling approach. Yet, the wings were modelled as experiencing pure plunging motion, which does not replicate the wing motion found in nature. Persson et al. [33] solved the aerodynamics of a flapping wing using lower fidelity panel method and higher order accurate discontinuous Galerkin Navier–Stokes simulations. They have demonstrated the wake evolution based on the unsteady flow field generated from an elliptical aerofoil, yet without considering aeroelastic effect. Gardiner et al. [34] simulated the wing flapping of geese to study wing kinematics and estimated lift and drag. Recently, Song et al. [35] reconstructed a hummingbird's wing motion using high-speed images generating a motion-simulated wing. Yet, the flexibility, feathers and muscle activity were not considered.

Ruck & Oertel [36] used an aeroelasticity model simulating the wing's flexibility and motion while solving the unsteady turbulent flow field and its effects on aerodynamic performance of flapping wings using the RANS approach. At reduced frequency (defined as k = πfc/U_∞, where f is the flapping frequency, U_∞ is the mean forward velocity and c is the wing root chord) of 0.22, which is similar to that of many birds flying at cruising speed, the tip and root vortices were found to dominate the wake pattern. Throughout the entire downstroke phase, a dominant root vortex (formed from the wing root, [37]) was found while the vortex sheet separated more quickly at the tip. It was not until the upper reversal point that the root vortex began to separate. The small-scale vortex structures that are shed continuously, and the bound vortex [38] that is present throughout the downstroke and upstroke phases, decreased the strength of vortices as well as spanwise flow structures. Behind the body, secondary vortex structures were observed with minimal strength when compared to the vortices generated by the wings, and thus it was concluded that their effects could be neglected [36]. This flow can be compared with the continuous vortex gait where vorticity is shown to follow only the path of the wingtips at large, spanwise distances from the origin of the wake. However, this model shows that there are more complexities in the near wake than are described by models developed by far-wake analysis.

We hypothesize that the near-wake flow structures comprise features associated with unsteady aerodynamics that occur at the transition from upstroke to downstroke (USDS); thus, modifying the drag and lift components as estimated by quasi-steady theory [26] (which neglects the unsteady contribution). We performed a controlled study on the near-wake flow behind freely flying birds. Three species were chosen for the experiment to increase the number of species for which PIV data are available, and to allow for comparison among birds of different body forms and flight styles. High spatial and temporal resolution was accomplished using a long-duration time-resolved PIV system [28]. High temporal resolution allows for many measurements of the same wingbeat cycle while high spatial resolution allows for more accurate description of the qualitative and quantitative characteristics of the wake.

2. Methods and experiments

2.1. Animals

Three distinct wild-captured birds were tested: European starling (Sturnus vulgaris), western sandpiper (Calidris mauri) and American robin (Turdus migratorius). Morphological parameters of the birds, as well as parameters of the experiment, are summarized in table 1. The individual birds were excellent wind tunnel fliers that we selected from groups of birds that were used in previous experiments (starling [39], robin [40] and sandpiper [41]). Because these birds had been extensively trained to perform multi-hour flights for migration studies, they were very familiar with the wind tunnel and would fly reliably in a steady position for PIV measurements. We performed a few days of habituation flights to allow the birds to adjust to the PIV set-up before collecting data, but the birds did not require extensive additional training. For starling safety, goggles (Yamamoto Cogaku Co. YL 600) were fitted to the bird while flying in the wind tunnel. A set of optoisolators operated by six infrared transceivers were integrated into the PIV system (upstream from the laser sheet location) in order to prevent direct contact between the bird and the laser sheet. The optoisolators triggered the laser only when the bird was flying upstream further from the PIV field of view. The robin and sandpiper would not wear the goggles comfortably, but isolation from the laser sheet and triggering system ensured the safety of the birds.

Table 1.

Morphological characteristics of the birds flown along with the experimental parameters.

bird	weight (g)	wingspan (cm)	chord (cm)	wind speed (m s−1)	wingbeat frequency (Hz)	Reynolds number	Strouhal numbera	reduced frequency
starling	78	38.2	6	13.5	12.5	5.4 × 104	0.16	0.17
robin	78	42.8	10.6	12	13.3	8.6 × 104	0.25	0.37
sandpiper	30.3	25.5	4.5	10	13.1	3.1 × 104	0.28	0.19

^aStrouhal number = fA/U_∞, where f, wingbeat frequency; A, wingtip amplitude; U_∞, freestream velocity.

2.2. Wind tunnel

The experiments were performed in the hypobaric climatic wind tunnel at the Advanced Facility for Avian Research (AFAR) at the University of Western Ontario (see [28] for more details). The wind tunnel is a closed loop type with an octagonal test section of 2 m length preceded by a 2.5 : 1 contraction. The turbulence intensity at the test section was smaller than 0.3% with a uniformity of 0.5%. The wind tunnel allows the control of speed, pressure, temperature and humidity. The bird is introduced into the test section through a 0.5 m open jet section located between the downstream end of the test section and the diffuser. The flight conditions for all birds were at atmospheric pressure, a temperature of 15°C and relative humidity of 80%.

2.3. Coordinate system

The coordinate system used for the wake is a right-handed Cartesian system, where x,y,z correspond to the streamwise, normal and spanwise directions. x is directed downstream, y is directed upwards and z is determined according to the right-hand rule. The streamwise and normal velocity components are denoted by u and v, respectively.

2.4. Particle image velocimetry

A long-duration time-resolved PIV system [42] was employed for the wake flow measurements. The PIV system consisted of a 80 W double-head diode-pumped Q-switched Nd : YLF laser at a wavelength of 527 nm and two CMOS cameras (Photron FASTCAM-1024PCI) with spatial resolution of 1024 × 1024 pixel² operating at a rate of 1000 Hz. The PIV system was capable of continuously acquiring image pairs at 500 Hz using two cameras for 20 min. Olive oil particles, 1 µm in size [43] were introduced into the wind tunnel using a Laskin nozzle from the downstream end of the test section, thus it did not cause disturbance to the flow or to the bird.

One of the CMOS cameras was used for the PIV, while the other CMOS camera was used for measuring the wingbeat kinematics simultaneously with the PIV. The PIV camera's field of view (FOV) was 12 × 12 cm² for the starling and sandpiper experiments corresponding to 2c × 2c, where c is the starling mean chord length and 2.6c × 2.6c for the sandpiper. The PIV FOV for the robin data was 14 × 14 cm² (1.4c × 1.4c). The velocity fields were computed using OpenPIV [42] with 32 × 32 pixel² interrogation windows and 50% overlap, yielding a spatial resolution of 32 vectors per average chord, equal to 1.8 vectors mm⁻¹. The wake was sampled in the streamwise-normal plane at 2 ms intervals (500 Hz), therefore, both the downstroke and the upstroke phases were temporally resolved. Table 2 summarizes the collected datasets obtained during the experiments based on the PIV system for the three birds. The number of wake features corresponds to vector maps where wake signature behind the bird's wing were identified and were used for the analysis of the wake features. The measured wake locations correspond to the distance between the bird's wing trailing edge, as measured from the centre of the PIV FOV. To determine the location of the light sheet with respect to the bird's wing or body, a 30 Hz Nikon Coolpix L16 camera was mounted downstream of the test section pointing towards the location where the bird would trigger the laser. A spatial calibration was performed before the experiment. These images enabled us to determine the location of the light sheet relative to the wing during the experiments. The light sheet location provided information regarding the PIV measurement plane with respect to the wing's spanwise distance from the body; this was normalized by the semi-spanwise distance, b.

Table 2.

A summary of the datasets collected during the bird flight experiments.

bird	total no. of vector maps	total no. of maps with wake features	PIV downstream location (c)	light sheet location
starling	1000	400	3–4	mid-span (∼b/2)
robin	700	300	2–3	mid-span (∼b/2)
sandpiper	2600	500	3–4	mid-span (∼b/2)

2.5. Kinematics

Wingbeat kinematics were recorded using a high-speed CMOS camera operating at 1000 Hz with a spatial resolution of 1000 × 1000 pixel². The FOV was equal to 46 × 46 cm², corresponding to an area of 9c × 9c for both the sandpiper and the starling while for the robin it was 74 × 74 cm² (7c × 7c). From the images, we calculated the wingbeat frequency, angle of attack and angular velocity of the wing. The kinematic images were synchronized with the PIV images in order to provide a direct relationship between the wake formed by the wing motion and its kinematics. In addition, a floor-mounted GoPro Hero camera (Woodman Labs, Inc.) operating at 60 Hz was used to record the spanwise position of the bird with respect to the laser sheet illumination. These images provided the identification of the measured PIV plane and its location relative to the wing, so that the wake velocity fields were associated with the spanwise location across the wing. The floor-mounted camera was not synchronized with the PIV or the kinematic measurements; therefore, the two time histories were synchronized manually based on the presence of the laser light in the images. Once synchronized, spanwise positions were assigned to the wake data acquired at 500 Hz based on interpolation from the simultaneously recorded spanwise positions.

2.6. Error estimation

An error analysis based on the root sum of squares method was applied to the velocity data and the wing kinematics. The errors were estimated as: 2.5% for the instantaneous velocity values, 10% for the instantaneous vorticity and 4% for the circulation, which was calculated, based on the vorticity field [44]. The error introduced in the kinematic analysis resulted from the spatial resolution of the image and the lens distortion leading to an estimated error of 5% in the wing displacements.

2.7. Data selection

The data presented in this manuscript were selected based on the following criteria: the bird did not accelerate or decelerate, it did not change altitude during flapping, the PIV measurements were taken behind the bird's wing semi-span location (see table 2) and the wing motion was clearly identified in the kinematic images.

3. Results

3.1. Kinematics

The kinematic aspects of the wing motion are briefly described herein for the purpose of orienting the wake features with wingbeat phases. A detailed description of the kinematics during flapping flight of the starling can be found in Kirchhefer et al. [28]. The description of an entire wingbeat cycle requires that the flow be divided into phases as well as noting the location of the wake with respect to the wing; e.g. the distance between the edge of the measured plane and the wing. Figure 1 presents images in sequential order from right to left as the bird flies through one full wingbeat cycle during forward flight (upstream, against the wind). Upstroke is considered from position ‘a’ to ‘c’. Downstroke is from position ‘c’ to ‘e’. The transition occurs at ‘c’, ‘a’ and ‘e’, where the wing changes its motion direction. We denote the transition from downstroke to upstroke as DSUS corresponding to ‘a’ and ‘e’ and the transition from USDS corresponding to ‘c’.

Figure 1.

Sequence of instantaneous images describing a full wingbeat cycle of the western sandpiper.

One may partition the wingbeat in a more arbitrary manner in order to emphasize drastic changes during transition. As suggested by Weis-Fogh [5], the classical partition of the wingbeat phases to DS and US may not be accurate when describing the wing kinematics when unsteady flow patterns are present. Therefore, we defined the motion of the wing from right to left; ‘a’ to ‘b’ is the lower upstroke region, ‘b’ to ‘c’ is the upper upstroke region. On the other hand, we can observe ‘b’ to ‘d’ as the USDS transition phase. Similarly, ‘c’ to ‘d’ and ‘d’ to ‘e’ are the upper and lower downstroke region, respectively; therefore ‘d’ to the next sequential image to follow ‘e’ will describe the DSUS transition.

The wingbeat frequencies of the flapping wings for the three birds were similar (table 1). Dividing the entire wingbeat cycle into two main regions: upstroke and downstroke, shows that for the three birds, the period for both phases is approximately equal (table 3). Yet, if one chooses to classify the entire cycle from a transitional point of view, where the USDS is defined as the period for which the mid-wing is above the horizontal body plane and the DSUS is the period where the mid-wing is below the plane, then the USDS was approximately 60% of the cycle while the DSUS was 40%. Although the transition phases are characterized in a somewhat arbitrary manner, the time distribution between the phases demonstrates that the birds spend more time with their wings above the horizontal body plane as opposed to below. Presumably, the bird has to generate sufficient lift to support its weight. The flapping speed of the wingtips is relatively fast during the downstroke phase; e.g. for the sandpiper, the time taken for the upstroke phases of the four cycle, respectively are 0.045, 0.04, 0.057 and 0.042 s, whereas the time taken for the downstroke phases of the four cycle, respectively, are 0.03, 0.033, 0.033 and 0.035 s, which causes high vertical momentum (∝ lift) and some horizontal (∝ thrust) impulses. To repeat the procedure, the bird has to recover from the downstroke phase by slowing down the speed of the wing followed by a twisting motion that raises the wings up again.

Table 3.

Kinematic parameterization of the flapping phases of the three bird species used in PIV and kinematic studies.

bird	frequency (Hz)	DS (%)	US (%)	USDS (%)	DSUS (%)	amplitude (chord)	tip wing speed (m s−1)
starling	11.1–14.1	48 ± 6	52 ± 2	56 ± 2	44 ± 2	2.8 ± 0.5	0.03
robin	12.7–14.3	50 ± 3	51 ± 5	58 ± 1	42 ± 1	2.1 ± 0.3	0.05
sandpiper	11.4–14.1	47 ± 3	53 ± 3	60 ± 1	40 ± 2	4.7 ± 0.5	0.05

A quantitative description of the wings' kinematics is shown in figure 2. We extracted the wingtip motion of the birds using freeware motion analysis software Kinovea (https://www.kinovea.org). A point very close to the wingtip was tracked in all the three birds for four continuous wingbeat cycles. The number of wingbeat cycles is calculated by normalizing the total evaluation time with the wingbeat period. The displacement of the wingtip for each time step, which corresponded to 0.002 s, was calculated from the high-speed images in pixels and calibrated to metres. Figure 2a shows the non-dimensional wingtip displacement plotted against the number of cycles, respectively, for the sandpiper, starling and robin. We used the respective wing chord length of the birds to non-dimensionalize the wingtip translation. It appears that irrespective of the species, a similar trend is followed by the wingtip kinematics for all the birds. The wingtip displacement reflects an evolving sinus-like curve function. In the plots, each crest of the curve corresponds to the transition from USDS and each trough of the curve corresponds to the transition from DSUS. After the USDS/DSUS transition, a start of a stroke is followed by an upper/lower region of a stroke until mid of the side curve, which belongs to mid stroke. In the end, each stroke is followed by the transition to another stroke and the cycle continues. It is important to note that the wingtip displacement value is not constant for each wingbeat cycle. The observed maximum wingtip translation at the start or end of the stroke and the side curve length of an upstroke or downstroke differ for each wingbeat cycle. The translational speed of the wingtip is calculated as the difference between the subsequent displacement distances over the time step and plotted against the number of cycles in figure 2b for each species. To facilitate the direct comparison between the changes of flapping wing speed with the structure of the wakes behind the downstream of the wing, translational wingtip speed is plotted over the downstream wake distances in figures 4, 5 and 6 and is discussed in more detail in the Discussion. The respective chord length of the birds is used to non-dimensionalize the downstream distance. The wingbeat cycle plotted at a distance far downstream at the right end of the figures happened first, as the wake produced at the earlier wingbeat cycle travels far. A significant feature of the wing speed plots is the broad region shown at the crest of each curve (transition from USDS), whereas the troughs (transition from DSUS) are relatively narrow with sharp transitions.

Figure 2.

Wingbeat kinematics: (a) non-dimensional amplitude of the wingtip versus number of wingbeat cycles and (b) non-dimensional wingtip translation speed versus number of wingbeat cycles.

Figure 4.

Near-wake flow features of the western sandpiper while flying in a flapping mode. (a,b) Owing to the length of the wake, the figure is divided into two segments: the bird flew from right to left, from the top figure (starting at distance x/c = 60 towards x/c = 0). (i) Wake reconstruction—contour maps; top figures on each segment. Contours represent the values of spanwise vorticity and the vectors depict the two-dimensional, two-component velocity field in the near wake. The map covers complete three consecutive wingbeat cycles. (ii) Wingtip displacement—represented by blue curve and cumulative circulation—represented by red curve. The wingtip displacement is plotted against downstream chord length to directly correlate with the respective wake. The circulation is calculated based on the spanwise vorticity, and calculated per PIV realization and summation is done over the wingbeat cycles.

Figure 5.

Near-wake flow features of the European starling while flying in a flapping mode. (a,b,c) Owing to the length of the wake, the figure is divided into three segments: the bird flew from right to left, from the top figure (starting at distance x/c = 70 towards x/c = 0). (i) Wake reconstruction—contour maps; top figures on each segment. Contours represent the values of spanwise vorticity and the vectors depict the two-dimensional, two-component velocity field in the near wake. The map covers almost four consecutive wingbeat cycles. (ii) Wingtip displacement—represented by blue curve and cumulative circulation—represented by red curve. The wingtip displacement is plotted against downstream chord length to directly correlate with the respective wake. The circulation is calculated based on the spanwise vorticity, and calculated per PIV realization and summation is done over the wingbeat cycles.

Figure 6.

Near-wake flow features of the American robin while flying in a flapping mode. (a,b,c) Owing to the length of the wake, the figure is divided into three segments: the bird flew from right to left, from the top figure (starting at distance x/c = 36 towards x/c = 0). (i) Wake reconstruction—contour maps; top figures on each segment. Contours represent the values of spanwise vorticity and the vectors depict the two-dimensional, two-component velocity field in the near wake. The map covers complete four consecutive wingbeat cycles. (ii) Wingtip displacement—represented by blue curve and cumulative circulation—represented by red curve. The wingtip displacement is plotted against downstream chord length to directly correlate with the respective wake. The circulation is calculated based on the spanwise vorticity, and calculated per PIV realization and summation is done over the wingbeat cycles.

A summary of the kinematic data for each wingbeat cycle is described in table 3 where the amplitude is defined as the height of the wingtip from the reversal point above the body centre to the reversal point below it. The wing's amplitudes normalized by the chords appear to be similar for the starling and robin, while the sandpiper is double in magnitude. The wingtip speeds for the sandpiper and robin were similar and the starling had a faster wing speed. This may suggest that the starling uses a different flight pattern compared with the robin and sandpiper.

To describe the wake evolution and how it was formed, it is important to note the location and position of the birds' wings with respect to the PIV imaging plane. This allows for the correlation between the point where the disturbance in the flow was created and the point at which the wake was measured. To associate the kinematic data with the PIV realizations the calculated convection velocity and the distance between the wing and the measurement plane were used. A detailed description of the calculation is provided in Kirchhefer et al. [28] and Ben-Gida et al. [39].

3.2. Flow measurements

The PIV yields two-dimensional two components vector maps. A sample of the velocity superimposed over the spanwise vorticity, ω_z, at the near-wake region is given in electronic supplementary material, S1. The spanwise vorticity, which is used as the characteristic quantity in the wake visualization, is calculated as:

3.1

where u and v are the streamwise and normal velocity components, respectively, and x and y are the streamwise and normal directions of the coordinate systems, respectively; defined based on the PIV field of view. To complement the wake vortices and the wake reconstruction (as described later), we have calculated the circulation. A detailed description on the calculation of circulation is given in the electronic supplementary material, S1. The circulation enables the association of some of the flow patterns with the different phases of the wingbeat cycle as one may expect to obtain net positive circulation as the bird gains lift (mostly during the downstroke phase), and net negative circulation over most of the upstroke.

3.3. Convection velocity

Convection velocity is calculated by comparing consecutive PIV realizations using a spatially averaged time correlation [28]. The data were sampled at 500 Hz allowing for flow features to be captured several times and for consecutive images to ‘overlap’ by approximately 75%. This overlap lends itself to use this correlation technique to quantitatively compare wake features to determine the degree to which they have convected through the flow. The correlation quantitatively describes the degree to which the two velocity fields are similar. The shift that results in the maximum correlation coefficient is thus the distance that the wake has convected through the flow. The convection velocity is then calculated by examining the distance the flow features travelled in the time between the two consecutive images.

In figure 3, consecutive vorticity maps that were extracted from the high-speed PIV image show the flow being convected from left to right through the field of view. One can observe that the same flow feature is captured in at least five images. Therefore, we can perform a correlation analysis to find the optimal matching between these images. Detailed description of the reconstruction methods is given in electronic supplementary material, S2.

Figure 3.

Consecutive vorticity maps extracted from the long-duration high-speed PIV demonstrating the wake evolution (blue, positive spanwise vorticity; red, negative vorticity).

3.4. Wake composites

Our main effort was to describe, visually, the wake evolution behind the birds during flapping flight and to observe the formation of flow features due to the wing's motion. This was performed throughout wake reconstruction over a long distance (i.e. a long time). The utilization of the long-duration time-resolved PIV system enables the reconstruction of the wake evolving behind the wings for a relatively long time (70 chord lengths in the case of the sandpiper) with high spatial and temporal resolution.

The wake reconstructions (figures 4(i), 5(i) and 6(i)) are based on PIV images taken from a stationary camera yielding Eulerian observation of the flow field. The reconstructions are complemented by the wingtip amplitude and cumulative circulation (figures 4(ii), 5(ii) and 6(ii)) as a function of the downstream distance as the birds fly in the wind tunnel. The birds flew from right to left; therefore, the downstream distance is measured as positive chord lengths. What appears as downstream essentially happened earlier, while what appears as upstream happened later. Owing to the length of the reconstructed wakes, each figure was divided into two consecutive segments, therefore, the beginning of the wake appears at the top portion of the figure and continues at the bottom segment of each figure. Throughout each wingbeat cycle, the birds' position did not change much relative to the measurement plane [39]. Thus, invoking Taylor's hypothesis [45] allows the assumption that the flow remains relatively unchanged as it passes through the measurement plane. This hypothesis implies that there is no significant time dependence of a spatial velocity distribution over the timescale required for observation. Lumley [46] has discussed the factors affecting the accuracy of Taylor's hypothesis. These factors include the criteria of Lin [47], which is that Taylor's hypothesis may be applied to spatially small structures of a turbulent shear flow, given the gradients in convection velocity are small over the size of a turbulent eddy. Additionally, Lumley [46] noted that the convection speed may be unsteady, since the small eddies of a turbulent flow are embedded in progressively larger eddies. Zaman & Hussain [48] showed that the hypothesis works well for an isolated coherent structure if a constant convection velocity, equal to the structure centre velocity, is used in the case of shear flows. To visualize an entire wingbeat cycle, a wake composite image is generated by offsetting each consecutive PIV image with the calculated instantaneous convection velocity and then overlapping the images, while keeping the closest section of the image to the bird; essentially, the youngest part of the wake. The beginning and end of the wingbeat cycle was determined by analysing the wing's kinematics (as described in the kinematic section) and associating these with their corresponding section of the wake. We found that each wingbeat cycle lasts between 12 and 18 chord lengths for the various wakes analysed. Each individual analysis comprised from 2 to 5 consecutive wingbeat cycles, thus enabling us to analyse the flow field behind the bird continuously and to identify significant trends. Each of the wakes shares many similarities but there are some key differences. Figures 4–6 demonstrate the evolution of the wakes behind the freely flying birds. The contours shown represent the vorticity field imposed on the velocity field, which is depicted as two-dimensional vectors, and the axes are scaled based on the specific bird's chord length, measured at the semi-span location. Each wake composition is associated with the cumulative circulation to emphasize the relationship between the wake features and the resulting cumulative circulation. The dashed vertical lines mark the point of transition from USDS and vice versa on the wake reconstruction maps. The initial circulation is calculated at the right side of the figure and accumulated towards the left side. This provides a qualitative description of how the bird modifies the wake through the wing motion to generate instantaneous lift over the different phases of the cycle, including unsteady lift [49].

Each bird demonstrates some unique features in wake topography, yet the general descriptions of the flow patterns as depicted in figures 4, 5 and 6 are similar. Generally, where the near wake of a flapping wing was measured, a vortex street is observed with some modifications, and complexity.

Herein we list the different flow features observed from the wake reconstructions for the three birds. The wingbeat cycles were divided into six different phases, in order to emphasize the variations in the flow features based on the wing's position. We choose to focus on certain patterns that are less predicted to be present at the wake as obtained from the vorticity velocity contours accompanied by the velocity field. These patterns have been observed by Kirchhefer et al. [28] and termed ‘double branch’ features, which correspond to concentrated regions of spanwise vorticity where four apparent layers, located at the same region, are observed; see, for example, figure 4: starting at the USDS transition towards the downstroke region between chords 25 and 35, figure 5: similarly, at the region between chords 10 and 17 and figure 6: between chords 9 and 14. It is noteworthy that these flow patterns which appear during the transition from USDS based on the classical partition to wingbeat phases correspond to the USDS phase as presented in the wing kinematics section (see figure 1). The presence of these patterns is presumably due to wing motion, and consequently, the formation of the flow around the wing and into the wake. The PIV method enables us to capture the two-dimensional velocity field, therefore, we can deduce one component of the vorticity; the spanwise vorticity. However, the spanwise vorticity carries the signature of the entire vorticity field. It carries information of the other vorticity components, which are partially projected in the spanwise direction assuming it is not a perfect vortical structure oriented in the streamwise direction [50]. It is plausible to assume that the double branch feature is a projection of a three-dimensional vortical pattern, which evolves in the near wake, changing its volume and the momentum along it. In the following, we summarize the apparent features, observed to be similar in the wakes of all three birds:

• — Lower upstroke region: double branch structures with backwash (reverse flow) above and below this region.

• — Transition from lower to upper upstroke: single branch region with a strong upwash below and backwash above the branch.

• — Upper upstroke: upwash below the wake and backwash above it. The starling and robin have downwash above this region at times. During the end of the upstroke, stronger vorticity values occur, typically more negative. A double branch feature begins right after a strong negative vortex.

• — USDS transition: double branch region. For the sandpiper, strong upwash throughout this region.

• — Upper down stroke region: continuation of the double branch region. Backwash flow below and in front of the region while downwash flow above it.

• — Transition from upper to lower down stroke: single branch region. Backwash above and below.

• — Lower downstroke region: downwash above, backwash to downwash below.

The terms downwash, upwash and rotational flow are used here to illustrate the position of the velocity vector field in respect to the wake. Downwash and upwash refer to the vector directions while rotational motion emphasizes the rotational motion the fluid experiences in the presence of the wake. The rotational motion is commonly observed along the path between pairs of positive and negative vorticity, this potentially can indicate a streamwise vortex tube as explained by Kirchhefer et al. [28]. These descriptions are directly linked to the coupling between the near wake and the bird's motion; when the bird flaps its wing downward, a bulk of fluid is pushed downward, and in consequence creates a rotational flow that eventually leads to a positive circulation for generating lift. Similarly, downward motion is followed by the upstroke phase. However, one can observe that these regions of motion are formed also in the transition zones, which indicates a more complex transport of momentum at the wake. The reconstructed wakes show similarities within the main features, while one can observe differences between the birds, due to their natural flight patterns and behaviour. A detailed description of the characteristics of the flow features for the individual birds appears in the electronic supplementary materials (S3).

3.5. Double branch types

From our observations, we distinguish between two types of double branch features: two layers aligned together in an angle relative to the horizon and two branches which deviate in space into two separate layers forming an arc and merging after a certain distance. One can observe that the first type appears at the USDS region, while the second type is less coherent and commonly appears to form at the upstroke region.

These peculiar patterns appear at the same location for the three birds as can be observed in figures 4(i), 5(i) and 6(i). A line is drawn around these patterns in order to emphasize their topological structure. Measurements of their dimensions in the streamwise and normal directions reveals that in a non-dimensional form, they have similar dimensions between the three birds' wakes: the first type has a dimension of five chord lengths in the streamwise direction and the second type about seven chord lengths on average. This result is independent of the length of the wingbeat cycle, because the duration of the cycle for the three birds is somewhat different. The characteristic length corresponds to 2–4 ms where this event is formed, which is about 5–7% of the entire wingbeat cycle. In the normal direction, these features appear to span over one chord length in both cases.

4. Discussion

We hypothesized that the near-wake flow structures of flying birds comprise features associated with unsteady aerodynamics. Our findings, which appear to be consistent in three different species of birds, suggest that employing some sort of flapping wing mechanisms (i.e. flaps at the trailing edge) will form unsteady flow features which may provide a more efficient design for small UAVs.

During the transition phase from USDS, the unsteady effects are most apparent; altering the drag and lift components compared to the originally estimated values assuming quasi-steady theory. It has been proposed that most of the lift generating forces is produced during the downstroke [5], as the change in fluid momentum per unit time. However, our analyses show that variations of lift and drag during flapping flight are observed over the entire wingbeat cycle (this study, [39,49]).

It was shown for similar data obtained for the starling [28], that the unsteady lift [49] and unsteady drag [39] components are not negligible. Both components, calculated directly from the near wake, were shown to have a prominent contribution at the transition phases; notably where the double branch is present. These findings complement the early works where power estimates of birds in flight were performed. These works estimated lift and drag of flying birds in gliding and flapping modes using quasi-steady theory [7,51,52]. While quasi-steady theory demonstrates how birds successfully develop sufficient lift to stay aloft and move forward, the unsteady portion of the flow is assumed to be negligible [53]. The wake structure, as reconstructed for various bird species from the far-wake region, show features that support the current models of continuous gait (as described in the Introduction). However, the near-wake reconstructions presented herein reveal flow structures within the transition phases that appear to be dissipated in the far wake.

Kirchhefer et al. [28] observed the presence of these ‘double branch’ vortices for two sets of starling wakes. At the transition phases, two distinct elongated regions of concentrated spanwise vorticity were present aligned in an angle with respect to the free stream. These regions of measurable vorticity were highlighted in comparison to the background vorticity and were comparable with the wake signature as characterized by the spanwise vorticity. Kirchhefer et al. [28] suggested that the double branch features are a signature of streamwise vortices interacting with one another in the wake similar to the observations made by Chen et al. [54]. An additional interpretation of the branches, as a streamwise vortical structure, may be a combination of tip vortex associated with finite wings, and what has come to be known as a ‘root vortex’ [20,55]. Furthermore, multiple streamwise vortices have been observed in computational simulations of an aeroelastic model [36], suggesting that these structures may be formed at various or even continually varying locations along the span. In both simulations and experiments, the presence of multiple streamwise vortices has been indicated, and can be considered a possible cause of the double branch feature in the near-wake region.

Careful examination of the wake indicates that the presence of the double branch in each of the investigated wakes occurs at the same phase of the wingbeat cycle. They occur mostly during the USDS phase developing towards the downstroke region. Although each bird has different functional and other characteristics (differ in size and weight), the wake evolution features similarities. This leads us to question the role these features play in the birds' efficiency with respect to generating lift, reducing drag and saving energy.

As lift is linearly proportional to circulation, we have chosen to calculate the circulation at the wake reconstructions to provide a quantitative description of the flow features, see figures 4(ii), 5(ii) and 6(ii) for the three birds wakes. The ‘double branch’ feature is associated with periods of an accumulation of net positive circulation. The net circulation estimated from the spanwise vorticity component is in line with the unsteady lift estimated by Stalnov et al. [49]. They showed that the unsteady lift terms appeared to have a significant contribution at the transition phase; USDS, at the location where the double branch features are formed. Similarly, it appeared that the unsteady drag has a prominent contribution at the transition phase of the wingbeat cycle [39].

The topological features of the entire wingbeat demonstrate a continuous gait, without breaks or abrupt changes within or between wingbeat cycles. The well-pronounced vortex structures (double branch) follow a semi-sinusoidal path that continues from the upper branch of the downstroke structure, becoming increasingly dominated by a lower branch, which tends to continue throughout the end of the upstroke. This is in good agreement with Ruck & Oertel [36], who described the upstroke as being dominated by a tip vortex structure that expands to the wing base and forces the root vortex to decrease.

The non-dimensional geometrical similarity in location and size of the vortical patterns may suggest a generic motion that aims to control lift and drag at this phase over the cycle. This result is somewhat surprising as the three birds are associated with different orders (Charadriiformes for sandpiper, Passeriformes for starling and robin) and families (Turdidae for robin, Sturnidae for starling) that have different functional and morphological features. Western sandpipers are continuously flapping, long-distance migrants with long, high aspect ratio wings and very short tails. American robins are short to medium-distance migrants with long tails, and they have an intermittent flapping flight style. European starlings are medium-distance migrants, with intermediate length tails, and they frequently flap-glide. In our experiments, the sandpiper flew in the wind tunnel in a straight line, maintaining altitude, and was able to fly for long times compared to the robin that did not maintain altitude as steadily. The starling flight during the flapping phase was more similar to the sandpiper, but more abrupt. Yet, despite these differences the flow structures appear to be similar.

It is proposed that the double branch flow pattern observed could be part of a more detailed picture that complements the continuous gait model as discussed by Rayner et al. [10]. The continuous gait model assumes constant circulation throughout the wingbeat cycle and in consequence considers steady motion that generates lift. However, we show here and in former work that the circulation varies over the wingbeat cycle, due to unsteady flow features as observed at the near-wake region. One may synergize the concept of continuous gait with the proposed vortex structure as suggested by Ruck & Oertel [36], to reflect the contribution of the unsteady flow to the estimation of flight performance [26]. It is mainly the transition portion of the wingbeat where we demonstrate its significance and function.

5. Conclusion

Three distinctive birds: European starling, western sandpiper and American robin, were flown in an avian wind tunnel. The near-wake characteristics of the birds were measured using a long-duration high-speed PIV system. The flow field measurements were performed at the near-wake region behind their wings. Using a cross correlation on the velocity fields, we have reconstructed the near wake behind the birds over a long distance (up to 70 chord lengths). These reconstructed wakes shed light on the flow patterns developed at the near wake and their role during the various wingbeat phases. We showed that during the transition phases, the flow pattern is significantly different compared with the upstroke and downstroke phases. The observed flow patterns depict a quadruple vorticity layer, which is not common in far field wakes. The presence of these flow patterns appears to be similar for the three birds. Furthermore, the geometrical features of these patterns are identical for the three birds when normalizing them with the chord length. We suggest that these flow patterns, which form during the transition phases, are associated with the unsteady aerodynamic forces generated during flapping flight. Such distinct wing motion which generates an unsteady flow may result in manifesting the aerodynamic forces; enhancing lift and reducing the total drag and in consequence could help researchers in understanding how certain bird species save energy during long-distance flights.

Ethics

The birds were captured under a scientific collection permit from the Canadian Wildlife Service (CA0256). Animal care and experimental procedures were approved by the University of Western Ontario Animal Use Sub-Committee (protocols 2006-011, 2010–2016) and conformed to standards set by the Canadian Council on Animal Care.

Data accessibility

All relevant data are given within the paper.

Authors' contributions

R.G. was responsible for the design of the experimental set-up, performed the experiments, analysed the data and prepared the manuscript. K.K. and H.B.-G. performed the data analysis and editing the manuscript. A.J.K. performed the experiments. G.A.K. assisted in the set-up design, assisted in data analysis and edited the manuscript. C.G.G. was responsible for the capture, care and training of the experimental birds, assisted with study design and data collection, and edited the manuscript.

Competing interests

We have no competing interests.

Funding

The authors gratefully appreciate the Canada Foundation for Innovation and Ontario Research Fund (grant no. 11743) for supporting the AFAR wind tunnel and other infrastructure. Funding was provided to C.G.G. through NSERC Discovery Grant (grant no. 311901).