Vortex wakes generated by robins Erithacus rubecula during free flight in a wind tunnel

Abstract

The wakes of two individual robins were measured in digital particle image velocimetry (DPIV) experiments conducted in the Lund wind tunnel. Wake measurements were compared with each other, and with previous studies in the same facility. There was no significant individual variation in any of the measured quantities. Qualitatively, the wake structure and its gradual variation with flight speed were exactly as previously measured for the thrush nightingale. A procedure that accounts for the disparate sources of circulation spread over the complex wake structure nevertheless can account for the vertical momentum flux required to support the weight, and an example calculation is given for estimating drag from the components of horizontal momentum flux (whose net value is zero). The measured circulations of the largest structures in the wake can be predicted quite well by simple models, and expressions are given to predict these and other measurable quantities in future bird flight experiments.

Figure 1

Composite colour-coded spanwise vorticity fields, ω_y (x, z), with velocity vectors superimposed at half their true spatial resolution for flight speeds U=4 and 8 m s⁻¹. Data are from the vertical centreplane. The vorticity is mapped asymmetrically about a 14-step colour bar to local extrema of −350 and 600 s⁻¹. The resolution of the colour bar matches the worst-case uncertainty in the measurements so that visible features are likely to exist. Regions corresponding to start and stop vortices are indicated by (+) and (−) arrows. At U=4 m s⁻¹ (wake wavelength, λ≅0.29 m), the stop vortices can be barely measurable, and instead a diffuse trail of vorticity marks the upstroke. At U=8 m s⁻¹ (λ≅0.57 m) the entire wake is composed of trails of weak transverse vorticity only. The figure shows the downstroke wavelength λ_d for each speed. The vorticity fields have been combined from consecutive frames in a sequence, starting from right to left, with the bird flying towards left as indicated by bird silhouette. Data are from bird#1, but bird#2 shows the same patterns.

Figure 2

Variation in peak vorticity magnitude |ω_y|_maxc/U (a) and measured circulation of the strongest starting (filled symbols) and stopping (open symbols) vortices Γ/Uc (b), rescaled by the mean wing chord c and mean speed U, as a function of flight speed U. The symbols represent mean±1 s.d. for bird#1 (squares) and bird#2 (circles), respectively. Sample sizes are (starting vortex, stopping vortex): (28, 16), (66, 55), (44, 43), (27, 40), (27, 40), (10, 18) for bird#1 at U=4–9 m s⁻¹, and (15, 15), (30, 33), (32, 46), (17, 32) for bird#2 at U=4, 6, 8 and 9 m s⁻¹, respectively.

Figure 3

Variation in circulation of the strongest starting (filled symbol) and stopping (open symbol) vortices as a ratio of the total same-signed vorticity in the same image (a), and as a ratio of the reference circulation Γ₁ required to support the weight by downstroke generated vortex loops (b), as a function of flight speed for bird#1 (squares) and bird#2 (circles). Symbols represent mean±1 s.d. Sample size as for figure 2.

Figure 4

Normalized circulations and peak spanwise vorticity as a ratio of the reference circulation Γ₁ for starting (filled circles) and stopping (open circles) vortices, rescaled by the mean wing chord c and flight speed U for bird#1 at U=5, 6, 7, and 8 m s⁻¹. The solid horizontal and vertical lines represent means for starting vortices and the dotted lines are means for stopping vortices, and their intersections approximately mark the centroids of the measurement population. Sample sizes as for figure 2.

Figure 5

The total positive circulation associated with one wingbeat, normalized by Γ₁, the reference circulation required for nominal weight support. Symbols as figure 3.

Figure 6

Wingbeat kinematics of robin #1 as a function of flight speed U. (a) Wing beat frequency, (b) amplitude, (c) downstroke fraction, (d) wing span reduction at mid upstroke in relation to mid downstroke, (e) reduced frequency, k. The number of sequences analysed for each speed were [6, 7, 6, 5, 8, 2] for U=[4, 5, 6, 7, 8, 9] m s⁻¹, respectively.

Figure 7

Predicted (continuous lines) and measured (symbols) circulations for five bird species for whom wake data are available. The lines come from equation (4.3), derived only from the continuous circulation required for lift in a steady uniform potential flow. Data are from Spedding et al. (1984, 2003b), Spedding (1986, 1987a) and this study.

Figure 8

A simple summary of kinematic data as a function of flight speed, U, for the thrush nightingale (solid blue) and robin (dotted red), both measured in similar wind tunnel experiments. The panels show wing beat frequency (Hz), normalized wingbeat amplitude, downstroke ratio and span ratio in (a–d). The data are shown only by the least squares linear fit line, except for f(U) in (a) where individual points are given as an example of the scatter around the fit. Figure 6 may be consulted for further details in the robin data.