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A family of vortex wakes generated by a thrush nightingale in free flight in a wind tunnel over its entire natural range of flight speeds

G. R. Spedding^1,*, M. Rosén² and A. Hedenström²

¹ Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1191, USA
² Department of Animal Ecology, Lund University, Ecology Building, SE-223 62 Lund, Sweden

View larger version (17K): [in a new window]   Fig. 1. The generation of a single, closed-vortex loop during a downstroke can, in principle, lead to a simple wake model geometry. The bird body (which has no aerodynamic significance) is represented by a stick supporting the wings. The assembly moves at constant speed, U. As the wings accelerate at the beginning of the downstroke (A), they shed vorticity into the near wake, which rolls up as a concentrated starting vortex. During the downstroke (B), the starting vortex remains connected to the two wingtip vortices, which elongate as the downstroke progresses. At the end of the downstroke, the wings decelerate, shedding vorticity into the wake along the trailing edge, and then vanish (C), taking no further part in the aerodynamics until they reappear at the beginning of the next wingbeat. The hypothetical deformed loop left at C then relaxes into, or can be modelled by, a planar ellipse, and the idealised model wake (D) is composed of a sequence of these, separated by spaces left by the inactive upstroke. Although this wake-generation mechanism is ostensibly simple, the details are not, and numerous assumptions about the formation, shedding and subsequent roll-up of vortex lines or tubes with complex curvature are built in. I, wake impulse; circular arrows indicate the local sense of rotation of the induced flow.

View larger version (11K): [in a new window]   Fig. 2. Constant-circulation wake. In (A), the effect of the (invisible) bird moving at speed U is to leave behind a pair of undulating vortices with constant circulation (1=2=constant), in which case potential cross-stream vortices denoted by broken lines have zero strength. Here the geometry is simplified for convenience so the wake appears as if the downstroke and upstroke portions were approximate ellipses and rectangles, respectively, as drawn in (B). Although the actual geometry assumed in most models (e.g. Rayner, 1986; Spedding, 1987b) is slightly more complicated, the fundamental principle remains that the wake impulse (I) from both down- and upstrokes points upward, contributing to lift, and hence weight support. Because the wingspan is reduced on the upstroke, the projection of area S1 onto a vertical plane will be larger than that of S2, and so the net impulse of the whole wake is forward, generating thrust.

View larger version (8K): [in a new window]   Fig. 3. The bird (tn) is trained to fly at constant speed, U, the independently controlled speed of the wind tunnel. Two Stanford DG 535 delay generators (dg1,2), configured to run off a single crystal base timing clock, generate synchronised timing pulses to control the dual-head Nd:YAG (pl) laser output flash timing (ta) and the asynchronous reset (tb) for the two CCD array cameras (tm1,2). The timing of the reset pulses is determined by the mean speed, U, and by the downstream displacement of tm2 from tm1, and is designed to remove the mean flow from the measured displacement field. Digital images are acquired at independent interface cards (ic1,2) and transferred directly to PC RAM. The laser timing pulses are gated (gb) with the summed output from an array of LED-photodiode pairs so that if any one or more beams are interrupted by the bird, laser output stops. (Modified from Spedding et al., 2003.)

View larger version (10K): [in a new window]   Fig. 4. Classification of all spanwise locations by character code (bottom) and the three named categories appearing in this paper, centre/body (lr), midwing (lx) and wingtip (ly).

View larger version (17K): [in a new window]   Fig. 5. Idealised predicted spanwise vorticity y(x,z) in vertical cross-sections through (A) the vortex loop and (B) the constant-circulation wake models of Figs 1D and 2, respectively. Although sections further towards the wingtip cut more obliquely through the presumed vortex lines, the effect on peak|y| measurements would be small, and in A the sections through the closed loop are shown with unchanged amplitude. (The circulation will be unchanged.) If the wake has continuous trailing vortices (as in the constant-circulation model), then at the centreplane|y|=0 (B). Midwing cuts may have more complicated cross-sectional geometries if, as anticipated, they cut through transition regions between down and upstroke-generated vortices.

View larger version (103K): [in a new window]   Fig. 6. (A—D) Four consecutive fields of y(x,z) with velocity vectors superimposed at half their true spatial resolution. The reference frame is moving with the mean flow, and so it is as if the bird had passed from right to left, leaving behind these traces in still air. The colour bar intervals correspond roughly to the measurement uncertainty. The colour bar is scaled asymmetrically about y=0, and the numbers at the ends show values in units of s-1. The circle-ended line shows the scale of the wingspan, 2b. The window size x,z is approximately 20 cmx18 cm. The circles drawn around locally maximum positive values of y(x,z) show the regions within which normalised circulation + is calculated. tot is calculated by including all above-threshold values in the same frame, regardless of whether they are within the local neighbourhood, or connected. Similarly, the negative peak is identified by the broken circle. The trailing vorticity attributable to the upstroke contains both negative and positive local peaks (large white arrows). In A these low-amplitude, positive peaks will be included in the sum for tot (because they have the same sign as the peak value), but in C, they will not. The development of an accounting procedure that correctly accounts for the real (as opposed to idealised) measured vorticity distributions is given in Figs 27 and 28 and their associated text.

View larger version (11K): [in a new window]   Fig. 7. The peak absolute value of the spanwise vorticity||max (circles), rescaled by the wing chord c and mean speed U as a function of time t in wingbeat periods T. The normalised circulation (squares) is also plotted on the second ordinate. Filled symbols, positive vortices; open symbols, negative ones. The first four time steps correspond to the data in Fig. 6. The time series represents successive sections of the wake passing through the observation window. The field is strongly asymmetric in both the peak vorticity and its integrated total strength.

View larger version (47K): [in a new window]   Fig. 8. A reconstruction from three consecutive frames of Fig. 6 to show the vortex wake over slightly more than one wingbeat cycle. The wake is shown as if left in still air by the bird passing from right to left. The silhouette is drawn approximately to scale and in the correct vertical (z) position but its horizontal (x) location should in fact be displaced by about 3 to the left (upstream) because the measuring station is that far downstream of the bird in the test section. During the time required for the wake to advect past the cameras (approx. 3T, or 0.21 s), the wake has moved downwards under its self-induced convection speed. The three component frames are matched approximately but the data are not edited or reinterpolated to improve the fit, and the borders are left outlined so their location is clear. The wingspan bar (2b) is placed to begin at the start of the downstroke. The wake wavelength is determined by the flight speed and wingbeat period and is shown as a double-arrowed bar. The relative time spent on downstroke and upstroke is given by the downstroke ratio, and can be verified from the wake picture. The colour bar and its scaling are as given in Fig. 6, and are fixed for all low-speed wake images (Figs 6, 8, 9, 11).

View larger version (124K): [in a new window]   Fig. 9. Magnified view of the rightmost starting vortex in Fig. 8. The apparent centre of rotation deduced from the arrows does not lie on the peak of the spanwise vorticity.

View larger version (17K): [in a new window]   Fig. 10. Profiles of the velocity components u(z) (A) and w(x) (B), where (x0,z0) is the location of the peak in y. The vertical dotted lines projected from z=z0 and x=x0 intersect the curves of u(z) and w(x) slightly offset from the u=0 and w=0 lines. Original data points are shown as diamonds (A) and triangles (B), joined by straight lines. Just noticeable are dotted line curves that join profiles either side of x0 and z0, respectively.

View larger version (112K): [in a new window]   Fig. 11. (A) Vertical cross-section through a midwing plane in the 4 m s-1 wake. Plotting conventions are as described in Figs 6 and 8, so relative bird motion is from right to left. The colour bar scaling is fixed to that established in the centre plane (Fig. 6), so saturation of the negative part indicates a relatively stronger stopping vortex contribution. (B) Vertical cross-section through the wingtip plane in the 4 m s-1 wake. A and B, together with Fig. 8, can be compared with the three idealised patterns of Fig. 5.

View larger version (14K): [in a new window]   Fig. 12. Variation in peak vorticity magnitude||max (circles) and circulation (squares) rescaled by the wing chord c and mean speed U for positive (filled symbols) and negative (open symbols) vortices in the slow-speed wake as a function of spanwise distance divided by the semispan y/b.

View larger version (16K): [in a new window]   Fig. 13. A possible representation of the slow-speed wake by a small number of vortex lines, based on data such as Figs 8, 10, 11, 12. The primary wake structure is a collection of loops, drawn as solid ellipses. They intersect the centre/body plane of observation along the major axis marked ad, which makes an angle d with the horizontal (downstroke; au, u, respectively, for upstroke). a is the measured strength of the starting vortex. b is the total measured strength of the more diffuse collection of vortex lines left at the end of the downstroke. c is small compared with both a and b, and the collection of rectangular upstroke wake vortices (broken lines) is an idealised cartoon version of the observed trace patterns that are quite disorganised and weak. Their primary effect is to disrupt the structure of the measured stopping vortex, which they do because vortex lines of opposite sense lie close together. When their strengths go to zero, a standard closed-loop wake model results. The projection of the downstroke wake length in x, d, onto the centreline is denoted by the double-headed arrow. U is the mean flight speed; bold arrow indicates direction of flight.

View larger version (95K): [in a new window]   Fig. 14. Composites of the wake at moderate speed U=7 m s-1. The plotting conventions are as previously given in Fig. 8. The colour bar scaling is fixed for all centreplane (A), midwing (B) and wingtip (C) sections.

View larger version (17K): [in a new window]   Fig. 15. Most likely wake topology deduced from all data at U=7 m s-1. The basic form is quite similar to the low-speed wake in Fig. 13 (the symbols and notation are the same), but the upstroke-generated portion (broken lines) is stronger, and more distinct from the downstroke-generated loops (solid ellipses).

View larger version (67K): [in a new window]   Fig. 16. (A) Composite for high-speed (U=10 m s-1) flight, close to the vertical centreplane, but slightly offset, showing the structure over an entire wavelength. (B) Closer to the true centerline. (C,D) Similar sections through proximal and distal midwing locations; (E,F) the same for the wingtip section.

View larger version (14K): [in a new window]   Fig. 17. Most likely collection of vortex lines for the high-speed wake, based on data such as shown in Fig. 16. Now the primary wake structures are primarily oriented in the streamwise direction and there is no preferred location for the comparatively weak cross-stream vortices y. The correctness of this structure can be determined by testing whether d=u. For an explanation of other symbols, see Fig. 13.

View larger version (117K): [in a new window]   Fig. 18. Single-frame view of the wake during brief gliding interval at 11 m s-1 flight speed. The velocity field is dominated by the induced downwash. The cross-stream vorticity, y(x,z), is mapped onto the discrete colour bar symmetrically from -120 s-1 to 120 s-1.

View larger version (14K): [in a new window]   Fig. 19. (A) The mean streamwise velocity as a function of vertical distance from the wake centre. The dotted line is a polynomial interpolation for estimating the integrated drag of the defect profile. The peak defect value, Ux/U0.01, is about one order of magnitude smaller than typical centreline downwash velocities in flapping flight at this speed. (B) Mean vertical velocity distribution with streamwise direction. The downstream coordinate, x, has its origin at the estimated bird position, approximately 17 chords upstream of the data plane. See text for further details.

View larger version (121K): [in a new window]   Fig. 20. Drag wake due to control manoeuvre in unsteady flight. The colour bar is symmetric, with extremes at y(x,z)=±200 s-1.

View larger version (11K): [in a new window]   Fig. 21. Mean wake defect from Fig. 20. The dotted line is a polynomial interpolated baseline for drag estimates. See text for further details.

View larger version (21K): [in a new window]   Fig. 22. Normalised circulations and peak spanwise vorticity for positive (filled circles) and negative (open circles) patches of vorticity in the slow-speed (U=4 m s-1) wake at the centre/body (A), midwing (B) and wingtip (C). (The absolute value of the negative quantities is actually plotted here, and in most subsequent figures.) The solid horizontal and vertical lines are drawn at the average values, and their intersection approximately marks the centroid of the cluster of points. See text for further details.

View larger version (20K): [in a new window]   Fig. 23. As Fig. 22, but for medium-speed flight at 7 m s-1. Note that the normalised||max scale goes only to 5 (one third of the previous figure).

View larger version (17K): [in a new window]   Fig. 24. As Fig. 23, but with a further 3 m s-1 increment in U for high-speed flight at 10 m s-1.

View larger version (14K): [in a new window]   Fig. 25. The variation in peak vorticity magnitude||max (A) and total measured circulation (B), rescaled by the wing chord c and mean speed U, for starting (filled circles) and stopping vortices (open circles) as a function of forward flight speed U.

View larger version (17K): [in a new window]   Fig. 26. Normalised circulations of starting and stopping vortices over all U values and at three different spanwise locations: (A) centre/body, (B) midwing, (C) wingtip. The circulations are normalised by reference values that would be required for weight support at each U for wakes comprising constant-circulation straight-lines (0), and discrete, closed loops (1). The ratio between 0 and 1 depends on the downstroke ratio (as explained in the text), which is assumed to be held constant for this plot. Values are means ± S.D.

View larger version (16K): [in a new window]   Fig. 27. Total integrated circulation tot from all positive (filled circles) and negative (open circles) vorticity in the observation window, plotted as a function of flight speed U. Although no single window contains the entire wake structure, each selected window, centered on peak values of either sign, contains all of the vorticity shed either at the beginning of the downstroke, or at the end of the downstroke and beginning of the upstroke. (A) The fraction of the total circulation that is not contained in the strongest vortex cross-section is very much higher in the stopping (negative) vortices than in the starting (positive) vortices. (B) The total negative vorticity would be sufficient for weight support, but not the positive component. The sum of the two, which ought to be zero (recall the convention of plotting the absolute value of the negative components), is not.

View larger version (15K): [in a new window]   Fig. 28. As Fig. 27B, but + (filled squares) now includes all traces of above-threshold positive vorticity found in the neighbourhoods of the predominantly negative signed vorticity. Neither component is significantly different from the other (the sums balance), and both are within experimental uncertainty of sufficiency for weight support (tot=1).

View larger version (18K): [in a new window]   Fig. 29. (A) The variation in peak vorticity magnitude||max, rescaled by the wing chord c and mean speed U, with flight speed U for positive (starting) vortices (closed symbols) and negative (stopping) vortices (open symbols) for three different spanwise locations: centreplane (circles), midwing (squares) and wingtip (triangles). (B) Same plotting conventions for the circulation of the patch of vorticity associated with||max. Values are means, and ± S.D. are shown for the centreplane values only.

View larger version (18K): [in a new window]   Fig. 30. The variation in normalised circulation as a function of flight speed U and spanwise location. Symbols as in Fig. 29.

View larger version (56K): [in a new window]   Fig. 31. A summary of three wake patterns deduced from vertical slice data at slow (A), medium (B) and high (C) speeds, respectively. The wakes are shown deliberately idealised and simplified to suggest the most important elements of a wake-based model. The three samples do not represent discrete wake topologies, and the transition from one to another is gradual, largely through changes in the vorticity shed during the upstroke. The tubes represent surfaces of constant vorticity magnitude, and are coloured blue or red according to whether they originated with down- or upstroke. The wakes have been rescaled to occupy approximately the same (streamwise, x) length on the page. In practice, the high-speed pattern at 11 m s-1 has a streamwise extent of almost 3 times that of the low-speed wake at 4 m s-1. (Many thanks to Michael Poole for this figure.)

View larger version (16K): [in a new window]   Fig. 32. (A) The Ellipse—Rectangle (E—R) wake is the simplest single model geometry that describes the wakes found over all flight speeds. Two planar wake areas are shed by the downstroke and upstroke, and they are elliptical and rectangular in shape, respectively (B). In order to calculate and test vertical forces, only the projections onto the horizontal plane need be considered. (C) A weighting function Cu(U) varies between 0 and 1 from Umin to Umax to gradually change the relative contribution from the upstroke (rectangular) component. , wavelength; , wake element inclination angle; , downstroke ratio; h, height. The d- and u-subscripts refer to down- and upstrokes.

View larger version (14K): [in a new window]   Fig. 33. Predicted/measured wake parameters for the thrush nightingale, and their contribution towards the total wake impulse. (A—C) show the horizontal wake length (, A), inclination angle (, B) and projected area (S, C) for the downstroke (solid diamonds) and upstroke (open diamonds) segments. In (D), alternative estimates of the wake circulation are available from either the strongest measurable single vortex (v, open circles), or from the mean total circulation of either positive or negative patches of vorticity (tot, closed circles). Based on the wake reconstructions in this paper, and on the assumptions of the E—R model geometry, the best estimate comes from a weighted sum of the two, shown by the dash-dot line. In (E) the fraction of weight support provided by the wake model is plotted for all flight speeds. The magnitude of the error bars will be similar to those shown in Fig. 28. Thus all points lie within ±20% of one. Iz, vertical impulse; W, weight; T, wingbeat period; U, flight speed; c, wing chord.