Kinematics and hydrodynamics of swimming in the mayfly larva
Department of Anatomy, University of Cambridge, Downing Street, Cambridge CB2 3DY, UK
e-mail: jhb1000{at}cam.ac.uk
Accepted 17 December 2003
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Summary |
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Key words: larva, swimming, kinematics, vortex wake, drag, starting manoeuvre, mayfly, Chloeon dipterum
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Introduction |
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Modern wake studies began with the vortex theories of Rayner
(1979) and Ellington
(1984
), which attempted to
describe how energy is organised in the wake. The essence of these theories is
that bursts of vorticity released from the propulsor surface should be
composed of closed vortex loops, often in the form of small-cored vortex
rings, and the first structures of this kind were demonstrated (using
stereophotography of neutrally buoyant bubbles) in bird flight
(Spedding et al., 1984
). Wake
visualisation studies have confirmed that fish also transfer momentum into the
water in a regulated manner although the precise structure of the wake depends
on speed, swimming style and use of the caudal, dorsal and pectoral fins
(McCutchen, 1977
;
Blickan et al., 1992
; Muller et
al., 1997
,
2001
;
Wolfgang et al., 1999
;
Wilga and Lauder, 1999
;
Lauder, 2000
;
Liao and Lauder, 2000
; Drucker
and Lauder, 1999
,
2000
). As Videler
(1993
) postulated, the wake
generated by a caudal fin swimmer consists of a chain of linked vortices in
the form of a reverse von Karman street, but slow pectoral fin swimming and
turning in sunfish (Lepomis macrochirus) produces discrete, unlinked
ring vortices (Drucker and Lauder,
1999
,
2000
).
A recent study using a simple dye technique for wake visualisation showed
that an invertebrate, undulatory swimmerthe damsel-fly
larvasheds discrete ring vortices to the side of the swimming path, one
ring vortex per half-stoke (Brackenbury,
2002). This type of wake lacks a caudally directed thrust jet and
is similar to that described in the eel (Anguilla anguilla;
Muller et al., 2001
), which,
like the damsel-fly larva, uses a high-amplitude undulation generating high
lateral body velocities. In both cases, the ring vortices propagate away from
the body at a very large angle (
70°) relative to the rear. Two other
insect swimmers, the culicid larva and pupa (Brackenbury,
1999
,
2001
), also generate discrete
ring vortices with each half-stroke but they propagate backwards much closer
to the swimming line. Neither of these insects uses the undulatory method of
swimming, but instead the body is subjected to simple side-to-side bending.
The present study describes an invertebrate undulatory swimmer, the mayfly
larva, that pushes water almost directly to the side rather than behind the
body and, in this respect, resembles the damsel-fly larva. But, unlike the
latter, which is a relatively slow swimmer, the mayfly larva swims as fast as
specialised dytiscid water beetles of the same size. Therefore, among the
questions to be asked in this study is how an apparently ineffective method of
swimming can generate such high forward speeds.
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Materials and methods |
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Locomotory activity is generally of two kinds: horizontal swimming across
the bottom, with the longitudinal axis of the body held a few millimetres
above the bottom, and open-water swimming, upwards, downwards or in the
horizontal direction. In the first series of visualisation experiments, a thin
layer (approximately 1 mm) of milk was carefully laid on the bottom of the
container through a syringe, and larvae swimming across the bottom left behind
a trail of `footprints' as evidence of their wakes. These trails were filmed
from directly above the container, care being taken to exclude trails caused
by physical contact between the undersurface of the body and the tracer. In
practice, the latter could be readily identified: when a larva swam clear of
the bottom, there was a clear delay between its passage over any particular
point on the bottom and the eventual appearance of a footprint at that point.
This delay represented the time for the wake disturbance to travel from the
fish to the bottom. In cases of direct contact, movements of the larva
produced immediate disturbances of the milk layer. In a second series of
experiments, a more accurate method was used to visualise the wakes of larvae
swimming in open water by dispensing tracer into the water in the form of a
narrow (0.51.0 mm) streamer released from the barrel of a plungerless
syringe mounted vertically above the container, with the tip of its needle
just penetrating the surface and discharging slowly under gravity. The speed
of descent of the streamers was 45 mm s1, equivalent
to approximately 5% of the speed of the jets visualised in the wakes. In these
experiments, the insects were recorded from the side of the container. In a
third series of experiments, observations were made on insects performing
starting manoeuvres from a position of rest on the bottom of the container. In
some cases, the bottom was covered with a layer of milk in an attempt to
visualise flows associated with these manoeuvres. Recording was performed, in
separate experiments, from either above or from the side of the container.
Altogether, approximately 120150 individuals were used in these three
sets of experiments. Most of these were used in order to obtain a qualitative
understanding of the relationship between kinematics and wake generation.
Quantitative data were obtained from a sub-sample of 50 individuals
showing the greatest clarity of visual detail.
A final series of experiments was designed to measure the hydrodynamic drag
on the bodies of dead insects. The insect was impaled on a stiff, 10
µm-diameter wire, the end of which was bent into a right-angled `hook'
(Fig. 1A). The other end of the
wire was connected to a Grass FT03 force displacement transducer, the signal
from which was displayed on a Grass 7D pen recorder. A steady flow regime was
achieved by mounting a 12 cm-diameter vessel, containing water to a depth of 5
cm, on a two-speed turntable. Within approximately 1 min of starting the
turntable, the water in the container attained solid body rotation. The
impaled insect was immersed 2 cm below the surface of the water, at a distance
of 4.5 cm from the centre of the container and orientated in line with the
flow. At this point, the flow velocities were estimated to be 9.5 cm
s1 and 25.0 cm s1 at the lower and higher
turntable speed settings, respectively, and their values were confirmed by
dropping dye immediately in front of the insect's head and filming its motion
around the streamline. No account was taken in subsequent calculations for the
slight curvature of the streamlines in the vicinity of the insect's body. In
each experiment, duplicate measurements were made at both flow velocities,
allowing 2 min for equilibration of the readings.
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The force measurement system was calibrated by rotating the transducer plus holder through 90° and suspending small weights from the end of the wire holder. The flow resistance of the immersed length of wire lying just above the mounted insect was measured by repeating the flow experiments using a simple length of wire (i.e. minus hook and insect), immersed to a depth of 2 cm. This value was then deducted from the original recordings. In total, successful duplicate measurements were obtained for 11 specimens, several others being discarded when the orientation of the insect altered during the course of the experiments.
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Results |
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Mayfly larvae swim either on their sides or in the upright position, and the wake created by the movements of the body leaves a different impression on the bottom layer of dye depending on which mode is used. Fig. 2 shows an example of the impression left by the wake of a larva swimming side-on to the bottom. Visual inspection from the side of the container showed that, as was often the case, the larva was moving parallel to the bottom with its body held clear of the bottom by a few millimetres. Initially, the area cleared of dye consists of a sinuous wave coinciding with the fin tip path (Fig. 2a). The main motion of the water thereafter is outwards away from the mid-line of the swimming path, and, for an individual half-stroke, this continues for 250300 ms. The `mature' wake impression consists of a ladder-like series of segments cleared of dye and separated from their neighbours by thin, more or less transverse lines of dye (Fig. 2b). Each segment corresponds to the wake generated during a single half-stroke, and the mean direction of the apparent flow within each segment was approximately 81° relative to the rear of the swimming line (Table 1). The pattern of impressions created by the wake of a larva swimming close to the bottom in upright mode was quite different. In this case, the dye was affected solely by the ventral half of the wake and consisted of a line of roughly circular areas, each of which started as a pinpoint and expanded within 4060 ms to a circle with a mean diameter (measured transversely to the swimming line) of 0.49±0.08 BL (N=29; Fig. 3). The frequency of these circular impressions was 28.3±2.8 s1 (N=11), which is not significantly different from the stroke frequency. The implication is that the chain of circular events was produced by alternate half-strokes performed to the ventral side of the body.
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Unpredictable ground effects, and the fact that the bottom-layer technique
can only produce a two-dimensional impression of a three-dimensional wake,
meant that the findings of these experiments were not in themselves conclusive
but could only be used to help interpret the results of the second series of
open-water experiments. Fig. 4
shows an encounter between the wake of a larva swimming in open water and a
dye streamer. In Fig. 4a, the
larva is moving downwards in a `seven o'clock' direction and the tail fin is
within 20 ms of the completion of its dorsad swing. Approximately 40 ms on
from Fig. 4a, a wake element
intercepted the dye streamer and propagated outward from the swimming line.
This element was a discrete ring vortex, and
Fig. 4b shows dye being drawn
into the trailing edge of the ring vortex, then travelling along the vortex
axis and beginning to outline the leading edge. A further 0.22 s later
(Fig. 4c), the dye has
re-circulated into the main body of the vortex, revealing the vortex core. A
second example of a dye-infiltrated vortex is shown in
Fig. 5: the ellipsoidal shape
of the vortex, the ring core and fluid flow into the trailing edge of the
vortex are all evident. The swimming paths of the larvae in these experiments
only rarely coincided with a streamer for long enough to allow consecutive
ring vortices to be visualised, but one example is shown in
Fig. 6. In total, approximately
40 individual ring vortices were identified that had penetrated a dye streamer
`head-on', allowing measurements of external radius parallel to the ring plane
(rp), external radius in the direction of the vortex axis
(ra), ring radius (r) and axial jet velocity
(jet;
Fig. 7A). Although the vortex
cores could be seen with relative ease and the opposite core centres could be
approximately located by eye it was not possible to obtain a reliable estimate
of core diameter. As was the case with ring vortices produced in the wakes of
swimming culicids (Brackenbury,
2001
), Vjet was measured from the consecutive
positions of the dye front as it moved along the vortex axis after becoming
drawn into the trailing edge at the start of the visualisation process. The
movement of the dye front was most clearly discernible once it had reached the
level of the ring plane, and this maximal value for axial
jet is given in
Table 1. This is the distance
travelled by the dye front, in open-water fixed co-ordinates, in the
particular 20 ms interval coinciding with its passage through the ring plane.
Note that the ring vortex travels away from the swimming line at its own
self-induced velocity and therefore the value given in
Table 1 represents a summation
of the propagation velocity and the axial flow velocity due to internal
circulation within the vortex. In three instances, it was possible to
establish a crude velocity profile of the dye front as it progressed along the
vortex axis. The data points in Fig.
7B are given in vortex-fixed co-ordinates and therefore plot the
re-circulatory component of the vortex jet. Velocity increases from zero at
the trailing edge, reaches a maximum at the ring plane and decreases as dye
re-circulates along the leading edge. This pattern is similar to that observed
in culicid ring vortices and is approximately what would be expected in a
`classic' ring vortex. The mean value of Vjet at the ring
plane for the three examples shown in Fig.
7B is approximately 4 cm s1, i.e. half the
jet value shown in
Table 1, which includes the
propagation velocity. Although the data for comparison are limited, they
suggest that approximately half the jet velocity is due to the propagation of
the ring vortex and half is due to internal circulation, a result again
roughly in agreement with findings on culicid ring vortices.
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The momentum axis of the ring vortices, measured in the stroke plane
(; Fig. 7A, right), did
not differ significantly during horizontal or upward swimming
(Table 1). These values were
also not significantly different from the `apparent' momentum axis values
measured in the bottom-layer experiments.
Hydrodynamic drag
Original recordings from a single individual are shown in
Fig. 1D, and data from all 11
experimental subjects are summarised in
Fig. 1C. By extrapolation from
Fig. 1C, the estimated drag at
the normal swimming speed of 20.8 cm s1 was approximately
6.5x105 N. Reynold's numbers entered into
Fig. 1C are based on the body
length minus the tail bristles [0.71± 0.04 cm (N=6)].
Transient manoeuvres
Mayfly larvae resting on the bottom display two kinds of escape manoeuvre
in response to a threatening stimulus. In terms of the end result, the
manoeuvres could be described as `rapid start' and `rapid turn about',
although the two are very closely related. The threatening stimulus used in
this study was a mild mechanical shock applied to the right side of the head
or thorax. A rapid start begins with a dorsiflexion, which pulls the legs up
from the substrate and arches the body so that the tail fin is brought into
contact or near-contact with the dorsal surface of the head and thorax (20 ms
position, Fig. 8A).
Simultaneously, the larva rolls onto its left side and the anterior part of
the body yaws to the left: these movements are particularly clear when the
larva is seen in dorsal view (Fig.
8D). As a result, by 40 ms from the start of the manoeuvre, the
larva becomes pointed in a new direction. This part of the manoeuvre,
characterised by dorsiflexion, can be termed stage 1. Extension (stage 2) now
drives the body in the new direction (40 ms and 60 ms stages in
Fig. 8A,D). The turning angle
(yaw angle) varied from 40° to 160°, with a mean value of
112.4±33.8° (N=39; Fig.
8D). At the end of stage 2, a ring vortex was released from the
body and this propagated in a direction approximately opposite to the line of
exit of the larva from the manoeuvre. Subsequent swimming movements carried
the larva away on its side with the long axis of its body held parallel to the
bottom with its centre held 0.34±0.09 BL (N=8), or
approximately 3 mm, above the bottom (Fig.
8A, 60 ms stage). Although the manoeuvre involves some movement of
the body in the vertical plane during stage 1, the rapid start is essentially
a turn and escape to the side. The durations of stages 1 and 2 were
25.5±7.6 ms (N=20) and 32.5±8.5 ms (N=20),
respectively.
Stage 1 of the turn-about manoeuvre is identical to stage 1 of the rapid start. But, by the end of stage 2 (extension), the body has rolled back to its upright position and the legs, which have been trailing to this point, are re-extended to make renewed contact with the bottom (60 ms and 80 ms positions in Fig. 8B). As it lands on the bottom, the larva performs a partial dorsiflexion, restoring the abdomen to its normal resting configuration: this upward flick of the tail fin sheds a single ring vortex that propagates 19.2±9° (N=6) forward of the vertical (Fig. 8C, right). Since the reaction of the larval body to this vortex is downwards and backwards, it can be seen as a `braking' vortex, counteracting the force of the initial propulsive vortex released at the end of stage 2.
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Discussion |
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The wake structure of the final-instar mayfly larva is similar to that
previously described in the damsel-fly larva
(Brackenbury, 2002). In both
larvae, swimming movements produce a series of discrete ring vortices, one
vortex per half-stroke, which are shed to alternate sides of the mean swimming
line and propagate away from the body at a high angle relative to the rear:
approximately 80° in the case of the mayfly and 70° in the case of the
damsel-fly. Culicid larvae and pupae also generate a double row of discrete
ring vortices but these convect along a line much closer to dead aft:
approximately 26° (Brackenbury,
2001
). The ability of culicid pupae to steer their vortices much
more favourably to the rear appears to be related to their swimming
kinematics; swimming is based not on an undulatory wave but on up and down
bending of the body, which induces large body rotations in the pitching plane
(Brackenbury, 1999
).
Consequently, although the abdomen sweeps through a full circle about the
head, the body rotations continuously re-align the tail fin so that it beats
in a foreaft direction (relative to the direction of swimming) rather
than up and down. The ring vortex is shed when the tail fin has reached its
most caudal position relative to the body, and the vortex propagates primarily
backwards rather than to the side of the swimming path. By contrast, the ring
vortex of the mayfly and damsel-fly larvae is released when the tail fin is at
its most lateral position, and it propagates almost directly to the side. None
of the above insects produces an aft-flowing jet such as that seen in the wake
of continuously swimming fish that use the caudal fin for swimming and that
consists of a reverse von Karman vortex street of linked vortices with a jet
zigzagging between (Blickan et al.,
1992
; Muller et al.,
1997
; Wolfgang et al.,
1999
). Insect wakes are more like that described in the
intermittently swimming Danio Brachydanio rerio
(McCutchen, 1977
) and the
continuously swimming eel (Muller et al.,
2001
). The latter authors also cite other examples of swimming
organisms generating laterally propagating ring vortices including
Brachydanio albolineatus, a water snake (Natrix natrix) and
a leech.
The digital particle image velocimetry images obtained by Muller et al.
(2001) showed a double vortex
shed to the side of the swimming line with each half-stroke that was
interpreted as a ring vortex. The ring vortex was formed by contributions from
a body wave and a tail wave, the latter being essentially a stopstart
vortex associated with fin tip reversal at the stroke transition. The body
wave generates semi-circular flow between the anterior crests and posterior
troughs in the body contour, the vortex being massaged caudally along the body
before joining the tail flow (Muller et
al., 2001
; Wolfgang et al.,
1999
). The large sideways component of momentum in the ring
vortices of eels results in part from the high lateral velocities of the body
surface associated with the transmission of the high-amplitude body wave. This
condition also applies to mayfly and damsel-fly larvae, both of which have
high tail beat amplitudes (mayfly, 0.26 BL; damsel-fly, 0.41 BL). According to
Muller et al. (2001
), the
eel-like swimming pattern is a compromise between thrust and efficiency, where
neither of these factors is particularly high. The propulsive efficiency of
damsel-fly swimming, calculated independently from hydromechanical modelling
and flow field measurements, was 0.650.67 compared with values of
0.70.8 in continuously swimming fish
(Alexander, 1999
). The
propulsive efficiency of mayfly larvae is probably low since only 1417%
of the estimated force generated in reaction to the ring vortex is directed
forwards.
Despite this, the larvae swim at speeds equivalent to those of specialised
diving beetles of comparable body length
(Nachtigall, 1977). During
level swimming, a momentum balance must exist between the larva and its wake.
The downward component in the wake must balance the upward momentum in the
body, exactly counteracting the force of gravity. Backward momentum in the
wake must be balanced by forward momentum in the body overcoming the force of
drag. Is there sufficient forward momentum in the visible wake of swimming
mayfly larvae to account for forward movement?
Following the argument outlined in the previous study of damsel-fly
swimming (Brackenbury, 2002),
the momentum (M) of an axi-symmetric ring vortex can be given by:
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Taking values of r, ra, Vjet and
Ø from Table 1 and a
t value of 18 ms yields a forward thrust of
6.0x105 N. The measured drag on the bodies of dead
mayfly larvae, extrapolated to the normal swimming speed, was
6.5x105 N, a value very close to the drag on the
bodies of dytiscid beetles with similar body lengths and swimming speeds
(Nachtigall, 1977): for
example, Agabus bipustulatus (body length 9.5 mm; speed 20 cm
s1; Re 1900; drag
7x105 N) and Agabus chalconatus (body
length 8.3 mm; speed 17 cm s1; Re 1400; drag
5x105 N). Nachtigall found that drag was
proportional to velocity2, but only for larger dytiscids swimming
at Reynolds numbers of 5000 and above. This is well above the range of
Reynolds numbers relevant to mayfly larval swimming where, as
Fig. 1C shows, Newton's Law of
resistance (drag µ velocity2) does not predominate.
The similarity between thrust and drag estimates in mayfly larvae appears to satisfy the need for a momentum balance during swimming, but these data cannot be taken at face value. It seems unlikely that the drag on the body of a dead larva is the same as that experienced by a living insect, with its continuously changing profile. The drag estimated will have been influenced by the slight curvature of the streamlines in the vicinity of the body: over the insect's body length, the mean direction of flow will have changed by approximately 10°. A further source of error may be inherent in the wake model, which is based on a `classic' small-cored ring vortex; although the ring radius and the external radii of the vortex could be readily ascertained, it was not possible to measure the core radius. With these qualifications in mind, it can at least be concluded that the results of the present study are consistent with the findings in the previous studies of a momentum balance in swimming culicid and damsel-fly larvae.
Rapid-start manoeuvre
Two rapid-start manoeuvres have been identified in damsel-fly larvae: the
`flex' and the `twist' (Brackenbury,
2002). The flex resembles the C-start of fish both kinematically
and hydrodynamically and consists of a rapid flex/unflex movement in the
horizontal plane. The twist is more complex, involving some movement in the
vertical plane, which rolls the insect onto its side. In both cases, the
insect exits from the manoeuvre at an angle of up to 160° from the
original heading. A twisting damsel-fly larva dorsiflexes then flexes to one
side, rolling the body onto its side (stage 1); it then extends (stage 2),
accelerating the body in the new direction. It will be seen that this sequence
of events is almost identical to that outlined in
Fig. 8 for the mayfly larva. In
both larvae, the tail fin makes brushing contact with the head at the end of
stage 1, and extension results in the shedding of a single ring vortex
approximately opposite to the line of body exit from the manoeuvre. The mayfly
manoeuvre, however, is three times as fast: stages 1 and 2 together last 58 ms
compared with 156 ms in the damsel-fly larva. The kinematics of damsel-fly
rapid starts was found to be comparable, both in the timing and the
geometrical changes in body shape, with the C-start of larval salmon
(Oncorhynchus tshawystscha; Hale,
1996
). The lowest body length limit investigated by Hale was 1.5
cm, and in this case the combined duration of stages 1 and 2 was 150200
ms. This is comparable to the speed of response of a 2 cm-long damsel-fly
larva but is much slower than the response of a 1 cm-long mayfly larva.
The mayfly larval `turn about' cannot simply be interpreted as rapid start that fails to translate in continuous swimming. Before the end of stage 2, the larva has prepared for renewed contact with the ground by re-extending its legs and rolling its body back to the upright position. As a final adjustment, it then flicks the tail to produce a stopping vortex (Fig. 8C). All these features indicate that the `turn about' is a calculated manoeuvre, intended solely to turn the larva away from the stimulus, but falls short of an attempt at escape. The behavioural parameters that govern the threshold between `turn' and `escape' are not known but presumably depend on the nature and intensity of the stimulus.
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Acknowledgments |
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References |
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