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First published online September 5, 2008
Journal of Experimental Biology 211, 2909-2918 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.018192
The near and far wake of Pallas' long tongued bat (Glossophaga soricina)
1 Department of Theoretical Ecology, Lund University, Sölvegatan 37, SE-223
62 Lund, Sweden
2 Department of Biology, Bielefeld University, D-33501 Bielefeld, Germany
3 Department of Aerospace and Mechanical Engineering, University of Southern
California, Los Angeles, CA 90098-1191, USA
* Author for correspondence (e-mail: christoffer.johansson{at}teorekol.lu.se)
Accepted 8 July 2008
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Summary |
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 TOP Summary INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Key words: bats, Glossophaga soricina, flight, aerodynamics, wake, DPIV
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INTRODUCTION |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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; Hedenström et
al., 2006b; Rosén et
al., 2007; Spedding et al.,
2003b). On the other hand, the time-varying properties of even
fairly simple, three-dimensional model flapping wings can result in very
complex pressure distributions on the wing surfaces with a corresponding high
complexity of the ensuing wake (Parker et
al., 2007; von Ellenrieder et
al., 2003). In contrast to the bird wakes, data from bat flight
have also shown a rather complex wake pattern
[(Hedenström et al.,
2007) see also Tian et al. for some preliminary results
(Tian et al., 2006)]. The
general wake topologies at three different flight speeds (U=1.5, 4
and 6.5 m s–1) have been described by Hedenström and
colleagues on the basis of wake velocity and vorticity fields for a small bat
species, Glossophaga soricina
(Hedenström et al.,
2007). At the lowest speed studied, 1.5 m s–1,
the wings generate a strong start vortex, shed at the trailing edge of the
wing at the beginning of the downstroke
(Fig. 1)
(Hedenström et al.,
2007). As the wing stroke progresses, a trailing tip vortex is
shed from the wing tip and there is also a companion trailing vortex, of
opposite sign to the tip vortex, shed at the wing root, showing that each wing
generates its own vortex loop. At the end of the downstroke the wing goes
through a pitch-up motion, flipping the wing upside down, which results in the
shedding of a distinct combined stop/start vortex for the down- and upstroke
(Fig. 1)
(Hedenström et al.,
2007). The downstroke generates a downward- and somewhat
backward-directed jet, for weight support and some thrust to overcome drag.
During the upstroke the wing moves backwards relative to the still air with
reversed circulation compared with the downstroke, thus also resulting in a
backward- and downward-directed jet, for thrust and some weight support. At
the end of the upstroke the wing goes through a pitch-down motion, shedding a
combined stop/start vortex for the up- and downstroke
(Fig. 1)
(Hedenström et al.,
2007).
|
)
(see also Results below). At the inner wing the downstroke is initiated by the
wings generating an induced upwash followed by a strong start vortex and
trailing patches of start vorticity. As at 1.5 m s–1, both
tip and root trailing vortices are found
(Fig. 1). When the wing reaches
the end of the downstroke the inner wing sheds a diffuse stop vortex. The
downstroke generates a downward- and backward-directed jet resulting in weight
support and thrust. During the upstroke the wing span is reduced but at the
end of the upstroke the wing extends and a weak vortex ring, inducing an
upwash (Fig. 1), is visible at
the outer wing position (Hedenström
et al., 2007) (see also Results below). The inner wing sheds
negative-signed vorticity throughout the upstroke, associated with a downwash
during the upstroke. The upstroke therefore generates weight support for most
of its duration, except at the outer wing towards the end of the upstroke.
The more complicated a wake structure, the more likely it is to twist and
bend and deform as it evolves in the wake behind the animal. The deformation
as vortex elements are immersed in the velocity fields induced by themselves
and their neighbours is very likely to increase the geometrical complexity. If
these deformations are associated with interactions between either like-signed
(pairing and merging) or opposite-signed vortices (cancellation) then the
topology will also change. Such interactions could arrest the natural
development that would have occurred in an otherwise quiet ambient. For
example, the roll-up of wingtip vortices that usually occurs within a few
chord lengths of the wing trailing edge behind a steady wing may be modified
because elements of other smaller scale structures are incorporated too. This
kind of effect varies with Reynolds number (Re=Ul/
,
where l is a characteristic length and is the kinematic
viscosity) in the range of interest to small birds and bats
(10x104–60x104) because the types of
vortex shedding on the wing vary with Re, and the thickness of the
shed structures also varies (e.g. Ramasamy
et al., 2007).
In summary, it is likely that the bird or bat wake gradually becomes less
and less representative of what the flow near the wing looked like the further
downstream it is observed. It is somewhat remarkable that previous
measurements of bird wakes, that were made at downstream distances
(x) of approximately 15 mean chord lengths (c) behind the
wing trailing edge, could be recognized and modelled at all, and it is still
possible that these measured structures had deformed significantly from their
original shape [see studies by Spedding and colleagues for wake evolution
behind steady airfoils at moderate Re
(Spedding, 2003;
Spedding et al., 2006)]. Here
we present a more detailed analysis of the bat data than previously
(Hedenström et al.,
2007), including direct comparisons between near
(x/c>1.1) and far (x/c>16) wake
measurements. This will allow us to evaluate the scope and utility of far-wake
measurements in animal studies.
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MATERIALS AND METHODS |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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). The
bats were weighed before each experimental run and the average body masses are
presented in Table 1. The
morphometrics of wing planform were measured from in-flight photos using Image
J
(http://rsb.info.nih.gov/ij/;
Table 1), following the
procedures of Pennycuick (Pennycuick,
1989) at speed U=5 m s–1.
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The bats were trained to fly at a feeder (a metal tube, 2 mm in diameter),
providing honey-water, suspended from the ceiling of the Lund University wind
tunnel (supplementary material Fig. S1)
(Pennycuick et al., 1997).
Between feeding bouts the bats roosted on a net 6 m upstream from the test
section in the wind tunnel settling chamber. They fed spontaneously by flying
downstream into the test section, approaching the feeder via a U-turn
from the downstream direction. The bats were individually recognized from a
video recording showing a rear view. Between experiments, the bats were kept
in a room where they could fly freely and had access to fruit, honey-water,
Nectar Plus (Nekton, Pforzheim, Germany) and pollen grains ad
libitum. The temperature in the wind tunnel and roosting facility was
kept at 22–27°C and the humidity in the roosting facility was
maintained at >55%. The bats were clock-shifted 12 h so their active (dark)
period coincided with lab hours.
Digital particle image velocimetry
The wake measurements were performed using a customized DPIV setup with a
double-pulsed laser (Spectra Physics, Quanta Ray PIV II, dual head Nd:YAG, 532
nm; Mountain View, CA, USA) operating at 10 Hz repetition rate. The air was
seeded with fog (particle size 1 µm). Pairwise images (separated by
t=200–300 µs) were captured on a CCD array camera
(Redlake, Megaplus II ES 4020; Lommel, Belgium) operated in binning mode
(10242 pixels), and transferred via a digital interface
(IO Industries, DVR Express 1.23; London, Ontario, Canada) directly to a SCSI
disk array (RAID 0) hosted on a PC. To avoid stray light the camera was
equipped with an optical bandpass filter of 530±10 nm (Thorlabs, FB
530-10; Göteborg, Sweden). The velocity components u, v and
w in the streamwise (x), spanwise (y) and vertical
(z) directions were measured in combinations of streamwise
[x–z] and spanwise [y–z]
imaging planes. The streamwise [x–z] planes were
oriented vertically and parallel with the flow downstream of the flying bat at
different x and y locations. The spanwise positions are
defined as: outer wing (lz), mid-wing (ly), inner wing (lx) and mid-body (lr)
(supplementary material Fig. S2). For the near-wake measurements the left edge
of the image was 4 cm downstream of the wing trailing edge (or
x/c
1.1) and for the far-wake measurements it was 62 cm
downstream of the wing trailing edge (or x/c16).
Near-wake wing measurements were performed at flight speeds (wind tunnel mean
speed, U) ranging from 1.5 to 7 m s–1 in 0.5 m
s–1 increments. Far-wake measurements were performed at
flight speeds from 4 to 7 m s–1 in 0.5 m s–1
increments. At lower speeds the wake had convected too far downwards for the
experimental setup. The transverse [y–z] (Trefftz)
plane was vertical and spanwise, positioned approximately 12 cm downstream of
the wing trailing edge (x/c=3.2), or approximately in the centre of
the streamwise images. This setup results in the bat image being faintly
visible in the transverse correlation image and so the streamwise distance
between the bat and the light sheet was selected to keep the wings of the bat
out of phase with the wake. Transverse and near-wake mid-body experiments were
performed at three different flight speeds, 1.5, 4 and 6.5 m
s–1. Particle image displacements were calculated using
correlation image velocimetry (CIV) algorithms
(Fincham and Spedding, 1997;
Fincham and Delerce, 2000).
From the velocity fields we calculated vorticity (
) in the streamwise
plane as:
 | (1) |
 | (2) |
). Circulation (
) was estimated according to Spedding
et al. (Spedding et al.,
2003b). The circulations for positive (+,
anti-clockwise) and negative (–, clockwise) patches of
vorticity are labelled as `start' and `stop' vortices for the streamwise
measurements and `root' and `tip' vortices for the transverse measurements,
respectively. The total circulation of start
(tot+) and stop
(tot–) vortices was also measured in each
image by integrating over the entire image. At low speeds, in cases when more
than one start or stop vortex was visible in the same image, the strongest
vortex core other than the one used for the measurements above was removed
from the estimated total circulation in the image.
Kinematics
Two synchronized high-speed cameras (Redlake, MotionScope PCI 500, 250 Hz,
1/1250 s) recorded the bats from side and dorsal views, simultaneously with
the DPIV recording during the far-wake experiments. We used infrared
illumination (VDI-IR60F, Video Security Inc., Kaohsiung, Taiwan) to avoid
disturbing the bats and to minimize interference with the DPIV measurements.
The cameras were equipped with infrared filters [Schneider Optics, BW09249 092
(89B); Van Nuys, CA, USA] to eliminate the bright green flashes from the
laser. Coordinates of digitized points on the wings and body of the bats from
the two views were transformed into three-dimensional coordinates by direct
linear transformation (DLT), using freely available Matlab® routines
(courtesy of Christoph Reinschmidt,
http://isbweb.org/software/movanal.html).
Based on the movements of these points, wingbeat frequency (f) and
amplitude (A) were calculated (a detailed analysis of the kinematics
will be presented elsewhere; M.W., L.C.J., A.H., R.v.B. and Y.W., unpublished
data).
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|
), a vortex dipole with an upward-directed induced flow was
observed at the end of the upstroke (eu) at speeds equal to and above 3 m
s–1. The vertical contribution of this negative lift was
calculated from the circulation of the negative vortex core
(eu–) in the streamwise plane
[x–z] of the near-wake vorticity fields. Furthermore,
the streamwise diameter (dxz, the distance between the
centres of peak positive and negative vorticity) and angle relative to the
horizon (
xz) were measured for speeds from 4 and
6.5 m s–1 (Fig.
2A). The diameter (dyz) and angle relative to
the horizon (yz) were also measured in the
transverse plane [y–z]
(Fig. 2B) at the two available
speeds (4 and 6.5 m s–1). The negative vertical force
(Fv) generated by this vortex dipole was then calculated
from the impulse (Ieu) according to:
 | (3) |
is the air density, Teu is the formation time
and assuming an ellipsoidal, horizontally projected area of the vortex ring,
Seu:
 | (4) |
The formation time, the time it takes to generate the vortex ring, was
estimated as the horizontally projected length of the vortex ring in the
flight direction divided by the forward flight speed as:
 | (5) |
Statistics
Before the analysis the dependent variables and the covariate were
loge-transformed to remove non-linearity of the data (see below)
and skewness in the distribution (Grafen
and Hails, 2002). The mean values for the measurements at each
combination of conditions were used as the independent data points, which were
weighted using the inverse of the standard error of the mean (s.e.m.). The
number of data points for each of the factors is presented in the
supplementary material as are the resulting degrees of freedom for each test
(supplementary material Tables S1–S7). All analyses were performed using
SPSS 15.0 (SPSS Inc., Chicago, IL, USA) with significance level set at
0.05.
|
|c/U),
normalized circulation of the main start or stop vortex
(||/Uc), normalized total positive or negative
circulation in the vorticity field
(|tot|/Uc), or the relative
contribution of the main start or stop vortex to the total circulation of
start or stop vortices (/tot) as dependent variables.
The model was constructed using individual as a random factor and sense of
circulation (start or stop) and wing position (lz, ly, lx or lr) as fixed
factors. Flight speed was used as a covariate and the model included all main
effects and all second-order interactions between factors. Using a linear
model on loge-transformed data is equivalent to modelling the raw
data using a power function. This is reasonable since
||/Uc is expected to be proportional to
U–2
(Rosén et al., 2007).
The same holds for ||c/U, which is
proportional to ||/Uc (Pearson
correlation=0.988). Differences between near and far wake were determined using the far-wake data and a subset of the near-wake data covering the same speed range. For this test a GLM with the same variables as in the near-wake-only analysis was performed but including wake position (near or far) as a fixed factor.
Differences between the wing tip and wing root vortices in the transverse
data were determined using a GLM with normalized peak vorticity
(||c/U) or circulation
(||/Uc) of the vortices as dependent variables.
Flight speed was set as covariate, vortex type (tip or root) and stroke phase
(mid-downstroke, mid-upstroke and beginning of downstroke) as fixed factors
and individual as a random factor.
SPSS calculates estimated marginal means (EMMs), which are the model estimates at the mean value of the covariate for the different factors in the model. The EMMs help to illustrate some of the results.
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RESULTS |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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). Composite streamwise [x, z] velocity fields for
the near wake at 2, 3, 5 and 7 m s–1 and for the far wake at
5 and 7 m s–1 for the outer (lz) and inner wing (lx)
positions are given in Figs 3,
4,
5,
6, selected to complement
previously published wakes. In the following section we will emphasize certain
characteristics and point out previously undescribed features of the wake.
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|
At U=2 m s–1 the wing motion was similar to that at 1.5 m s–1 (see above), but the upstroke was more vertical relative to still air than at 1.5 m s–1. The wake in the streamwise plane [x, z] contained two start vortices and only one stop vortex, a pattern found both at the inner (Fig. 4) and at the outer wing positions (Fig. 3). This pattern was also found at 2.5 m s–1 for one of the bats, while the other bat displayed the same wake pattern as at 3 m s–1 (see below). At low speeds (1.5–2.5 m s–1) the start and stop vortices in the wake were distinct (Figs 1, 3 and 4), and in contrast to the higher speeds the stop vortex was also distinct at the inner wing position.
For U=3–7 m s–1 the wake followed the same
qualitative pattern as described by Hedenström and colleagues
(Hedenström et al., 2007)
for speeds of 4 and 6.5 m s–1 (see above). At the inner wing
(Fig. 4), the beginning of the
downstroke was associated with an induced upwash followed by a large start
vortex and then trailing patches of start vorticity (+). The
timing of the inner wing upwash in the stroke cycle was determined by studying
the transverse plane [y, z], which showed a downwash at the end of
the upstroke and an upwash at the beginning of the downstroke for the inner
wing (lx) and body positions (lr). At these higher speeds of 3 to 7 m
s–1, the stop vortex shed at the inner wing was more diffuse
than at slower speeds, and had a relatively lower circulation,
–/tot–. A vortex
ring producing a weak upward-induced flow is known to be shed at the outer
wing at the end of the upstroke
(Hedenström et al.,
2007), but with an associated vertical force of only 0.4% and 1%
of the weight of the animal at 4 and 6.5 m s–1,
respectively.
|
tot+|) and stop
(|tot–|) vortices decreased,
as did peak vorticity (|+| and
|–|) and circulation of the main start
(|+|) and stop
(|–|) vortices, with increasing flight
speed (Table 2; see
supplementary material Figs S3 and S4 for the raw data). Also, the strength of
the main start vortex relative to the total circulation of the start vortices
(+/tot+) in the streamwise
plane [x, z] did not change significantly with speed
(Table 2). However, when
analysing a subset of the near-wake data, we found a significant negative
trend in the +/tot+ for speeds
>3 m s–1 (Table
2).
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There were significant differences between the spanwise wing positions
(Table 2) with a trend of
decreasing strength of the main start (+ and
+) and stop (– and
–) vortices in the streamwise plane [x, z]
going from the outer wing towards the centre of the body
(Fig. 7B). This trend was
present in both the near and the far wakes
(Fig. 7A). The rate of decrease
in strength from the outer wing to the centre of the body differed for the
start and stop vortices, as indicated by the significant interaction between
the sense of circulation and wing position, with a more pronounced trend for
the stop vortex than for the start vortex
(Table 2,
Fig. 7). However, the total
circulation of start (tot+) and stop
(tot–) vortices in the streamwise [x,
z] plane did not differ between wing positions
(Table 2).
The transverse [y, z] images (Fig. 1) showed a tip vortex as well as a vortex of opposite sense at the wing root (root vortex) at all speeds studied (1.5, 4 and 6.5 m s–1) throughout most of the wingbeat cycle. The ratio between the root and tip vortex strength was approximately 0.5 at the studied speeds. Only at the end of the upstroke was the root vortex absent at speeds of 4 and 6.5 m s–1. At the beginning of the downstroke the `root' vortex was not located at the wing root, but further out on the wing and it migrated towards the wing root as the stroke progressed. Wingbeat phase, as well as the interaction between tip/root and phase, were significant factors in the statistical model, showing that the peak vorticity magnitude and circulation varied over the stroke cycle and did so differently for the tip and the root vortices (Table 3).
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Near-/far-wake comparison
The far wake (Figs 5 and
6) showed similar patterns to
the near wake, with a few notable differences. The peak vorticity of the main
start (+) and stop (–) vortices was
lower in the far wake than in the near wake
(Table 4). However, the
circulation of the main start and stop vortices was higher in the far wake
than in the near wake (Fig.
7A), but there was no difference in the total streamwise [x,
z] start or stop circulation between the near and far wake
(Table 4). Taken together, this
suggests that the strength of the main start and stop vortices in the far wake
was higher relative to the total circulation (/tot)
in the images. However, although there was such a trend in the data, the
result was not significant (Fig.
7; Table 4). The
difference between near and far wakes was most pronounced for the stop
vortices shed at the inner wing (Fig.
7), where the stop vortices, which had a rather diffuse
distribution in the near wake (see Fig.
4), had rolled up into a more distinct structure when reaching the
far-wake position (Fig. 6).
This is manifested in a significant difference in the circulation for the
different wing positions between the near and far wakes, as indicated by the
interaction between near/far and wing position
(Table 4).
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Individual differences
In none of the tests performed was `Bat' or any of the interactions
including `Bat' significant (Tables
2,
3,
4), suggesting that any
differences between the two individuals were small.
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DISCUSSION |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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+) and stop vortices
(–), with higher values measured in the near wake than
in the far wake, as expected based on simple diffusion of vorticity (e.g.
Tritton, 1988). The results
thus display the same trend as experimental results from fixed wing studies
(Spedding et al., 2006). The
total circulation in the image of start (tot+) or
stop (tot–) vortices did not differ between
the near and far wake (Table
4). This is also in line with previous studies on fixed wings
(Spedding et al., 2006), and
suggests that it can be informative to study far wakes, as is commonly the
case when working on unrestrained live flying animals, but that not all
measurements will be affected similarly. The estimates of circulation of the
main start and stop vortices showed, somewhat counter-intuitively, higher
values in the far wake than in the near wake. This was primarily because the
rather diffuse stop vortex shed at the inner wing became more concentrated in
the far wake (Fig. 7A). The
merger of two like-signed vortices (e.g.
Melander et al., 1988;
Meunier and Lewecke, 2005) is
accompanied by an increased circulation of the new merged object, compared
with each of its components (the total circulation is conserved), and the
increase in circulation of trailing vortices as they entrain vorticity from
their surroundings has also been shown in the near wake of an oscillating wing
(Birch and Lee, 2005). The near wake is much more readily tied to the generating wing kinematics and it also contains details of vortex structures that could easily be missed in the far wake. For example, the vortex ring generated by the outer wing at the end of the upstroke was clearly visible in the near wake, and although it was also visible in the far wake (when it was known where to look) it had often been moved by convection out of the field of view. Hence, studying only the far wake may lead to an over-simplified view of the wake structure.
Double `start' vortices at 2 m s–1
At 2 m s–1 we observed a novel vortex wake (Figs
3 and
4). Here, the wake contained
two consecutive vortices of start (positive sign) sense but only one stop
vortex, as seen both at the inner and at the outer wing position. This wake
pattern is found at a flight speed where the upstroke is almost vertical
relative to still air, which based on kinematics occurs at 2–3 m
s–1 (0.43<Strouhal number,
St=fA/U<0.75) in this species
(Lindhe Norberg and Winter,
2006). The upstroke may thus generate thrust or negative thrust,
depending on the sign of circulation around the wings. However, when the
upstroke is vertical, weight support should be negligible or even negative and
the downstroke alone must generate full weight support. At 2.5 m
s–1, the wake of the two bats differed, with one displaying
the characteristics of 2 m s–1 flight speed and the other the
characteristics of 3 m s–1, suggesting some variation between
individuals due to small differences in movement patterns of the wings. In the
absence of transverse [y, z] velocity field data at this flight
speed, we cannot determine how this wake pattern connects in three dimensions
or at exactly which phase of the stroke the `start' vortices are formed.
Therefore we can only speculate about the origin of the double `start'
vortices. One possibility is that it represents two phases of the build-up of
the circulation around the wing, one attributed to the rotation of the wing at
the end of the upstroke/beginning of the downstroke and the second attributed
to the linear acceleration of the wing. A second possibility is that the
second `start' vortex represents the shedding of a trailing edge vortex built
up during the first part of the downstroke. Shedding of trailing edge vortices
has been observed in heaving plate experiments at high St and/or high
angles of attack (e.g. Jones and Platzer,
1997; Lewin and Haj-Hariri,
2003), both criteria being fulfilled by the bats at this flight
speed (Hedenström et al.,
2007). However, measurements directly above the wing surface in
this species have shown a continuous shedding of trailing edge vorticity
during the downstroke at 1 m s–1
(Muijres et al., 2008) and it
needs to be confirmed whether the pattern is indeed qualitatively different at
2 m s–1.
Inverted rings with negative lift – control or unavoidable cost?
Kinematic studies of flying bats have provided a basis for aerodynamic
hypotheses (Aldridge, 1986;
Aldridge, 1987;
von Helversen, 1986;
Lindhe Norberg and Winter,
2006; Norberg,
1976a; Norberg,
1976b), including the prediction of negative circulation at the
outer wing during the end of the upstroke
(Norberg, 1976a;
Norberg, 1976b). This was
confirmed by Hedenström and colleagues
(Hedenström et al.,
2007), but not further explored in quantitative detail. In fact,
the circulation around the wing during the end of the upstroke differs in sign
between the inner and outer part of the wing at medium (4 m
s–1) and high speeds (6.5 m s–1).
Qualitatively, this means that at some position along the span a vortex core,
a distinct patch of streamwise vorticity, of the same sense as a `normal' tip
vortex is being shed (blue-filled circle in
Fig. 8A), while at the tip of
the wing the vortex has opposite-signed circulation (orange-filled circle in
Fig. 8A). Because the inner
part of the wing generates a downwash, the vortex structure generated here
will move downwards. At the same time the outer wing generates an upwash
resulting in an upward displacement of the vortex structure generated there
(Fig. 8B). This should result
in the vortex shed at mid-span being separated into two vortices when moving
downstream, which is what is observed in most of the images
(Fig. 8C). In a minority of
cases, the two vortices are still connected (similar to the blue-filled
circles in Fig. 8A). Shedding
of trailing vortices along the span is quite common in engineered wings as a
result of changes in the pressure distribution over the wing (due to extended
flaps, etc.). But in most cases these vortices are the result of changes in
the magnitude of the bound circulation rather than its sign.
|
At the upper turning point of the wing stroke not only the outer part of the wing but also the inner wing and body generate upward-induced flows. This happens after the outer wing has shed its negative-lift-generating vortex ring and is starting to develop circulation for the downstroke (Fig. 4). For the inner wing the stop vortex at the end of the upstroke encircles the upward flow together with wing root cores formed mid-wing at the beginning of the downstroke by the outer wing and the start vortex of the downstroke. In other words, the upward-directed flow seen at the inner wing and body occurs during the beginning of the downstroke (see above and Fig. 4). In videos of the lateral view the tail/legs move upwards relative to the body, forming a negative geometric angle of attack and the inner wing membrane `bulges' downwards showing a loss of lift or production of negative lift, consistent with the observed wake. Consequently the circulation around all the sections of the wing changes sign during some phase of the stroke cycle. This suggests that the circulation observed in the streamwise plane [x–z], which represents the change in circulation, is able to capture the total circulation generated during a wing beat and can be used to calculate the force balance in these bats.
One ring or two?
At all speeds studied, each bat wing generated its own vortex loop as shown
by the presence of the wing root vortices in the transverse [y, z]
plane, confirming previous observations
(Hedenström et al.,
2007). When a wing flaps by rotation about a hinge (the wing
root), there are large differences in the relative magnitude of the air flow
from root to tip. At the root, the flow can be imagined to be almost steady as
local vertical wing section speeds are small compared with the mean forward
speed. The relative magnitude of the variation due to the flapping motion
itself [and associated local section Reynolds numbers
(Rosén et al., 2007)]
increases towards the tip. At a local wing section the circulation will also
vary in direct proportion to the local incident velocity (subject to
modification from local twist, camber, flexibility and thickness) and if the
bound circulation changes then so must the circulation deposited into the
wake. This section-by-section, quasi-two-dimensional concept of wing
circulation makes the formation of two separate rings behind flapping wing
pairs quite a likely outcome, and many such complicated wake structures have
been reported in the insect flight literature (e.g.
Aono et al., 2008;
Brodsky, 1991;
Grodnitsky and Morozov, 1993).
However, the shedding and subsequent roll-up of shed vorticity is not easy to
predict and may be very different from a quasi-two-dimensional process.
Here, the measured spanwise variations in wake circulation are consistent
with the observation that each bat wing makes (at least) one ring of its own.
Far-wake measurements of birds in similar circumstances do not show such
circulation gradients and have not found significant drops in wake circulation
at the centreline. However, a recent study of swift wakes shows a reduction of
the induced downwash behind the body relative to that of the wings
(Henningsson et al., 2008),
which should be indicative of wing root vortices. There are no conclusive data
from transverse planes in bird wakes, and although the existing models based
on far-wake measurements of bird flight have single loops for each wing pair,
it may be that higher resolution data in transverse planes and closer to the
animal might show this to be an oversimplified concept.
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Acknowledgments |
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Footnotes |
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Author's present address: Department of Mechanical and Aeronautical
Engineering, University of Pretoria, 0002 Pretoria, South Africa 
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References |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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