Escape manoeuvres in damsel-fly larvae: kinematics and dynamics

John Brackenbury

Department of Anatomy, University of Cambridge, Downing Street, Cambridge CB2 3DY, UK

(e-mail: jhb1000{at}cam.ac.uk)

Accepted 15 October 2002


    Summary
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 Summary
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
The kinematics and hydrodynamics of rapid escape manoeuvres executed by final-stage larvae of Enallagma cyathigerum were investigated using videography combined with a simple wake-visualisation technique. Two kinds of escape manoeuvres were identified: first, a `rapid flex', comparable with the rapid C-start of fish, and, second, a `rapid twist' that involves a helical contraction of the body inducing motion in the yaw, pitch and roll planes. In both cases, the initial flexion phase is concerned with re-orientating the body, the extensional phase with acceleration of the body in the new direction. The behaviour of the caudal fin during twist indicates considerable independence of movement and aspect control within the three constituent lobes. Dye deposited beneath the resting larvae showed a thrust jet shed into the wake at the end of the extension phase. The estimated momentum of the ring vortex containing the jet was similar to that imparted to the body at the start of the translational phase. Similarities between the swimming dynamics of damsel-fly larvae and fish are discussed, as well as the wider implications of these findings to other aquatic invertebrates whose normal, steady swimming appears to be based on unsteady manoeuvres.

Key words: larva, escape manoeuvre, unsteady swimming, caudal fin, kinematics, vortex wake, control of locomotion, damsel-fly, Enallagma cyathigerum


    Introduction
 TOP
 Summary
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
Escape manoeuvres present the locomotory system of a swimming animal with a severe test because their successful execution demands a change in direction, which may sometimes be up to 180°, combined with rapid acceleration, all within the duration of one or two strokes of the body or the fins or both. Drucker and Lauder (2001aGo) used the term `manoeuvrability' to cover a variety of unsteady locomotor behaviours involving controlled dynamic instability of the body. Such behaviours include turning, braking, negotiating obstacles, controlling the vertical position of the body in the water and stopping and starting. In many fish, an escape manoeuvre is essentially a start coupled with a turn, and the best documented of these is the rapid C-start, in which the body is rapidly flexed, usually away from the threatening stimulus, then rapidly extended to accelerate the body in the new direction (reviewed by Domenici and Blake, 1991Go, 1993Go, 1997Go; Blake et al., 1995Go). The two-stage response involves a re-orientational phase (the flex) and a translational phase (the extension) usually followed by a variable stage consisting of continuous or coasting swimming. Recent flow studies by Wolfgang et al. (1999Go) suggest that the C-start is a continuum in the generation of a thrust vortex, the first stage of which is the drawing of a jet into the C-shaped cavity formed by the flexing body. The kinematics and dynamics of the rapid flex are determined by the movements of the body and the caudal fin, although sometimes the pectoral fins may also be used to pivot the body in the vertical plane. A more specialised role for the pectoral fins in turning has been described by Drucker and Lauder (2001aGo) in the sunfish Lepomis macrochirus. This involves co-ordination between the near-side, or strong-side, fin, which produces a jet to rotate the body onto a new heading, and the far-side, or weak-side, fin, which produces a jet to drive the body away from the stimulus. As in the case of the C-start, the sequential division of the response into re-positional and translational phases is evident.

In a previous study on the hydrodynamics of steady swimming in damsel-fly larvae (Brackenbury, 2002Go), the author noted a rapid escape response similar in kinematics and dynamics to the rapid C-start of fish. Subsequently, a related, although more complex, rapid escape manoeuvre has also been identified that involves specialised movements within the three-lobed caudal fin. The present study was undertaken to analyse the dynamics of the escape responses of damsel-fly larvae against a background of the knowledge of steady swimming gained from the earlier investigation.


    Materials and methods
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 Summary
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
The experiments were carried out on final-stage larvae of Enallagma cyathigerum L., which were collected from permanent pools in the Fenland area to the northwest of Cambridge, UK. The larvae were maintained indoors at temperatures of approximately 18-22°C and individuals were used within a few days of capture. Swimming behaviour was filmed in daylight conditions using a Panasonic video camera (S-VHS format, horizontal resolution >400 lines at 25 frames s-1) delivering 50 fields s-1 (horizontal resolution of each field >200 lines) at shutter speeds of 0.001-0.0002 s. Video tapes were viewed on a cassette recorder with a single-field advance facility that allowed detailed examination of kinematic and flow events. Swimming trajectories and dye movements were traced by hand directly from the video screen.

During experiments, individual larvae were placed in a transparent container measuring 16 cmx8 cmx8 cm (width x depth x height) containing water to a depth of 6-7 cm. The method of flow visualisation follows that previously described (Brackenbury, 2002Go) using fresh cow's milk as a dye tracer. Both in the wild and in the laboratory, Enallagma cyathigerum larvae adopt a bottom-dwelling lifestyle because their bodies are denser than water. Steady locomotory behaviour is of two kinds: horizontal swimming, with the body held just clear of the bottom, and open-water swimming, which may be upwards, downwards or horizontal. In addition, swimming may be `fast', with the legs trailing to minimise drag, or slow, with the legs performing rhythmical paddling movements. Escape manoeuvres are nearly always followed up with fast, bottom swimming; consequently, the open-water dye-streamer technique employed in the earlier study (Brackenbury, 2002Go) was not appropriate and all results were obtained using the bottom-layer technique. A thin layer of milk (approximately 1 mm) was carefully laid down on the bottom of the container using a syringe, and larvae initiating an escape response left behind a trail as evidence of the wake. The trails were filmed from directly above the container, care being taken to reject any examples in which there was evidence of direct contact between the body and the tracer once the larva had begun its movement. In a second, shorter series of experiments, kinematic data were collected with the camera filming directly from the side of the container. In total, approximately 40 individuals were used to collect data and the results are presented as mean values ± 1 S.D. with the number of observations (N) in brackets.


    Results
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 Summary
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
Kinematics
Damsel-fly larvae exhibit two kinds of escape reaction to a light mechanical stimulus administered to the side or the front of the head. Although superficially alike, these reactions are kinematically distinct and appear to be expressions of different neuromotor programmes. The first, which may be termed the `flex', is the simpler of the two techniques, involving a rapid flex of the body to the opposite side from the stimulus followed by straightening then acceleration in the new direction (Fig. 1A). In a sample of 10 such manoeuvres, the turning angle varied between 30° and 160°, with a mean value of 80°. The flex is a two-dimensional movement confined to the yaw-plane of the body, is based on a single flexion/extension cycle and can be executed within 100 ms. Flexion is essentially a re-orientational stage concerned with swinging the head into the new alignment. This movement may also be assisted by the simultaneous flexion of the ipsilateral legs (20 ms and 40 ms stages in Fig. 1A). Extension initiates the translational stage, accelerating the head and the centre of the body in the new direction (Fig. 1B). As this stage begins (60 ms), all the legs are withdrawn from the substrate and begin to trail behind the body as in continuous swimming. The bending movements of the tail fin are similar to those previously observed during steady swimming (Brackenbury, 2002Go); throughout the manoeuvre, the three tracheal plates are pressed together in the median plane and experience identical degrees of bending along their length from base to tip. All three show maximum bending at the flexion line separating the basal and apical segments of the tracheal plate. The angle of attack of the fin tip (apical segment) reverses during the stroke transition (Fig. 1C), at which point there is contact or near-contact between the tail fin and the ipsilateral side of the head.



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Fig. 1. Kinematics of a simple flex manoeuvre in larva of Enallagma cyathigerum. (A) Successive 20 ms profiles seen from above as the larva reacts to a stimulus presented to the left anterior side of the body. (B) Angle of attack of the apical segment of the tail fin, represented by bars, during a simple flex manoeuvre. (C) Superimposed line representations of the longitudinal body axis corresponding to profiles in panel A. Open circles represent the head, crosses represent the centre of the body. In panels B and C, broken lines represent the motion of the head and tail ends of the body.

 

The second manoeuvre can be termed the `flex and twist'. As with the simple flex, a larva reacting to a stimulus applied to its left side appears to flex to its right (Fig. 2A, 3A) before extending in the new direction. In fact, the insect flexes to its left [an ipsilateral or `strong-side' flexure to adopt the terminology of Drucker and Lauder (2001aGo)], but this movement is masked by a simultaneous helical twisting of the body that induces pitching and rolling instability as well as yaw instability. The sequence of events, as viewed from above, is as follows. The first observable movement is a rapid dorsiflexion that elevates the tail and begins to pull the anterior end of the body and the legs away from the substrate (20 ms stage in Fig. 2A). Simultaneously, the caudal end of the body, including the tail fin, begins to twist clockwise, as viewed from behind (20 ms stage in Fig. 2A, curved arrows), and this twist is relayed cranially along the body axis, rolling the larva onto its right side (40 ms and 60 ms stages in Fig. 2A). Thus, the impression of right-side flexure is created by a combination of dorsiflexion plus the fact that the larva has rolled onto its right side. Already by this stage, the body is beginning to flex along its left side. Note that this is the opposite to the simple flex response where lateral bending is to the right not the left. The direction of the force experienced by the tail plates, as inferred from their angle of attack at this stage, is roughly opposite to the line of motion of the head (Fig. 2B, 3B), suggesting that the anterior part of the body is being pivoted about its centre of gravity into its new alignment. At the end of the re-alignment stage, the insect lies on its side, facing in the intended direction of escape, with its tail fin in contact with the head (60 ms stage in Fig. 2A). Extension then drives the body in the direction of escape 115.8±25.3° (N=20) away from the original heading (Fig. 7B). The latter stage is kinematically identical to the extension phase of the simple flex manoeuvre, and both culminate in the shedding of a thrust jet (see below) behind the retreating body. Front and side views of the twisting larva (Fig. 4) show the vertical displacements of the body and also give a clearer view of the onset of the left-side body flexure as soon as the insect has rolled onto its side (Fig. 4A, 60 ms stage). Throughout the manoeuvre, the geometric centre of the body remains close to the substrate and the larva exits from the manoeuvre (100 ms stage in Figs 2,3,4) with its body parallel to the bottom and its body centre separated from the bottom by a distance of 0.25±0.09 body lengths (N=12). Thus, the twist manoeuvre, like the simple flex, prepares the body for sideways escape with little or no vertical component.



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Fig. 2. Kinematics of a twist manoeuvre in larva of Enallagma cyathigerum. (A) Successive 20 ms profiles seen from above as the larva reacts to a stimulus presented to the left anterior side of the body. Curved arrows represent the rolling motion of the body, straight arrows indicate the direction of bending of the apical segment of the tracheal plate, relative to the basal segment, along the flexion line. The dorsal plate of the tail fin is shaded for ease of reference. (B) Superimposed line representation of the longitudinal body axis corresponding to profiles in A. Open circles represent the head. Broken lines plot the motion of the head and tip of the tail.

 


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Fig. 3. Kinematic and hydrodynamic events during a twist manoeuvre in larva of Enallagma cyathigerum. (A) Successive 20 ms body profiles seen from above. (B) Paths followed by the head (open circles), fin tip (filled circles) and centre of the body (crosses) during the twist manoeuvre shown in A. Bars represent the apical segment of the tail fin. The curved broken outlines plot the motion of a ring vortex shed from the tail at the end of the manoeuvre. (C) Successive outlines of a ring vortex shed from the tail at the end of a twist manoeuvre. On the far right, the fin has just completed its extension (corresponding approximately to the 120 ms stage in A) and is shedding the vortex. The first indication of the vortex follows 20 ms later. Small, broken circles within the vortex outline represent the vortex core.

 


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Fig. 7. (A,B) Kinematic and hydrodynamic variables measured during the twist manoeuvre. Panel A shows the motion of the head (open circles) and tail tip (filled circles) during the manoeuvre. Panel B shows the initial orientation of the body, direction of exit of the head at the end of the extension phase and vortex propagation axis, all as straight arrows. V and Vjet, the head velocity and jet velocity of the vortex as measured at the ring plane, respectively; {phi}, angle between the vortex axis and a line projected dead-aft of the line of motion of the head, measured in the horizontal plane; {theta}, turning angle of the head and the anterior part of the body during the manoeuvre. (C) Scale drawing of the ring vortex. R, ring radius; Ra, external radius orthogonal to the ring plane; Rp, external radius parallel to the ring plane.

 


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Fig. 4. Kinematics of a twist manoeuvre in larva of Enallagma cyathigerum. (A) Consecutive 20 ms profiles seen from in front as the larva reacts to a stimulus presented to the left anterior part of the body. Curved arrows represent the rolling motion of the body onto its side. (B) Consecutive profiles seen from the right side of the larva as it reacts to a stimulus presented to its left side. (C) Superimposed line representations of the longitudinal body axis corresponding to the profiles shown in B. Open circles represent the head. Broken lines plot the motion of the head and tail tip.

 

The duration of flexion phase, measured to the point where the tail fin makes contact with the side of the head, was 77±20 ms (N=20). The duration of the extension phase, measured to the point where the tail fin reaches its maximum excursion to the opposite side of the body to the initial flexure, was 79±12 ms (N=20).

In contrast with the simple flex manoeuvre, in which all three constituent lobes of the tail fin bend uniformly in response to largely unidirectional side forces applied to the fin, a degree of independence of movement between the plates is manifest during the twist and flex. At rest, the lateral plates diverge to the sides of the body with little indication of any flexion between apical and basal segments (Fig. 5, 0 ms stage). Tail elevation (Fig. 5, 20 ms and 40 ms stages) leaves the median plates unaffected but flexes the apical segment of the lateral plates outwards (i.e. in the direction of abduction) relative to the basal segments. During the twist (Fig. 5, 60-100 ms stages), lateral forces flex all the apical segments in one direction relative to the base but are evidently too weak to force the plates together in the median plane. Finally, during the flex and extension (Fig. 5, 120-180 ms stages), strong lateral forces, similar to those experienced during steady swimming, result in compression of the plates together and identical bending at the base and the flexion line.



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Fig. 5. Kinematics of the tail fin during a twist manoeuvre. (A) Successive series of images of the tail fin viewed from above. In the resting insect (0 ms stage), the tracheal plates are seen in edge-on view and there is little indication of any flexure of the apical segments relative to the basal segments. Successive stages show various degrees of movement of the tracheal plates in response to the forces experienced during elevation and twist (20-100 ms stages), flexion (120-140 ms stages) and extension (160-180 ms stages). Arrows indicate flexion of the apical segments relative to the basal segments of the tracheal plates. See text for further details. (B) Schematic representation of tracheal plate kinematics shown in A. The drawings represent the view seen in tail-fixed co-ordinates, i.e. the view seen from immediately above the tail assuming that the viewer travels with the tail.

 

Hydrodynamics
Within 20-40 ms of the completion of the extension phase of both manoeuvres, a thrust jet could be seen impinging on the bottom layer of the tracer and propagating away from the body (Fig. 6). Quantitative data were collected for the twist manoeuvre only, which was the commoner of the two responses (Fig. 7A,B). The momentum angle of the jet in the horizontal plane was 24±16.5° (N=20) measured relative to dead-aft. The jet was associated with a single, discrete ring vortex, the opposite cores of which could often be identified (Fig. 3C) although images were not detailed enough to allow accurate measurement of the core radius. The measured ring radius R, the external radius orthogonal to the ring plane Ra, and the external radius parallel to the ring plane Rp (Fig. 7) were 0.0025±0.0003 m (N=14), 0.0028±0.0003 m (N=14) and 0.004±0.001 m (N=14), respectively. The velocity of the axial jet (Vjet) measured at the ring plane within 20-40 ms of the shedding of the vortex was 13.1±2.0 cm s-1 (N=16; Fig. 7B). The velocity of the head (V) in the direction of escape measured over the same period was 21.6±5.4 cm s-1 (N=15; Fig. 7B). There were insufficient data to allow a velocity profile to be established along the vortex axis.



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Fig. 6. Visualisation of hydrodynamic events during a twist manoeuvre in which the larva receives a light touch to the left side of the head and executes an escape to its right. In the first frame (0 ms), the insect has just begun to react to the stimulus from the syringe needle tip shown in the lower right of the panel; the end of the abdomen is beginning to elevate and twist to the insects right. At 100 ms, the twist and elevation stages have been completed, the insect has been rolled onto its right side and the abdomen is beginning to flex to its left. By 160 ms, extension of the abdomen is completed, driving the insect directly to the left of the frame. The vortex being released from the tail has not yet made contact with the tracer on the bottom. In the 200 ms-stage image, a ring vortex is propagating along its axis, marked by the arrow, and leaving its impression in the tracer.

 


    Discussion
 TOP
 Summary
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
Morphology and kinematics
The functional morphology of the damsel-fly larval tail fin was discussed in a previous paper (Brackenbury, 2002Go). Each of the three tracheal plates (one median, two lateral) comprising the fin is divided by a transverse flexion line into a basal segment stiffened by ribs and a more flexible apical segment that sets the angle of attack of the fin. Lateral forces during steady swimming compress all three plates together in the median plane, although the individual elements can slide relative to one another in a fan-like manner within this plane, enabling the height of the fin to be varied throughout the tail-beat cycle. The three-lobed design of the fin, with each lobe being able to move independently from the base, confers a similar kind of radial mobility of fin elements to that found in some ray-finned fishes. Undulations of the soft dorsal fin of the sunfish Lepomis macrochirus produce vortices that contribute to thrust (Drucker and Lauder, 2001bGo), and, in the same species, the caudal fin is varied in height throughout the stroke as a result of asymmetric movements within the dorsal and ventral lobes regulated by intrinsic fin muscles (Lauder, 2000Go). The dorsal lobe also undergoes a greater lateral excursion than the ventral lobe and develops an upward force counteracting the weight of the body. Although damsel-fly larvae are negatively buoyant, there was no clear evidence in the previous study (Brackenbury, 2002Go) of any fish-like asymmetry in the lateral excursion of the fin lobes to provide the lifting force necessary to sustain level swimming.

It is clear from the present study that the behaviour of the tail fin during steady swimming represents only a fraction of the potential flexibility of this organ. The twist manoeuvre, in particular, highlights the degree of independence of the constituent lobes of the fin. Hinge-like movements of the plates in the transverse plane of the body can occur both at the base and along the flexion line. The simple flex manoeuvre is based on the same kind of sideways motion of the tail that occurs during steady swimming, which imposes mainly lateral forces on the fin elements and causes them to bend as a unity throughout their length. The twist manoeuvre, by contrast, subjects the tail to torque (during the twist) and tangential (during elevation) forces. Tangential forces, produced by movement of the tail fin within the median plane, tend to splay the lateral elements outwards from the base as well as along the flexion line (20 ms and 40 ms profiles in Fig. 5B), while torque imposes a combination of tangential and weak lateral forces resulting in the profiles depicted in the 40-100 ms stages shown in Fig. 5B. The strong lateral forces experienced during the final stages of the flex (120 ms and 140 ms stages) and during extension (160 ms and 180 ms stages) result in a grouping and bending regime similar to that shown during steady swimming. The above is a very simplified analysis of tail fin function based solely on kinematic data and without the benefit of detailed information about the flow field around the tail fin. Nor can the possibility of some degree of active control of the tracheal lobes from the base be discounted.

As Drucker and Lauder (2001aGo) have argued, animals probably spend much more time executing short-term manoeuvres such as stopping, starting, turning, braking and negotiating obstacles than they do in performing steady movement. Their investigations in the sunfish showed that turning is not simply a modification of steady swimming but involves specialised manoeuvres by the pectoral fins. A stimulus administered to one side of the body led to rapid abduction of the strong-side fin, which produced a rotation with little or no translation. The contralateral or weak-side fin produced a delayed thrust jet that accelerated the body away from the stimulus. The rapid C-start manoeuvre of fish, which often involves large turning angles (Domeninci and Blake, 1993, 1997; Blake et al., 1995Go), also involves a re-orientational stage (rapid flex) followed by a translational phase (extension), and parallels have already been drawn between this manoeuvre and the flex response of damsel-fly larvae (Brackenbury, 2002Go). Whilst in the sunfish these sequential movements are brought about by independent activity in the pectoral fins, in C-starting fish and rapid-flexing damsel-fly larvae re-orientation and translation represent a continuum in the movements of caudal fin and body. Although nothing can be said directly in the present study concerning the neuromotor programmes responsible for executing rapid evasion manoeuvres, significant questions arise from a simple comparison of kinematic events. The common factor linking C-starting fish and rapid-flexing damsel-fly larvae is an initial weak-side response [the `away response' of Domenici and Blake (1997Go)]: contraction of the weak-side flexors produces the C-shaped cavity into which a thrust jet is drawn and eventually shed `into the face' of the threatening stimulus. Analysing the hydrodynamics of the C-start, Wolfgang et al. (1999Go) have shown how fluid is drawn into the concavity as two oppositely signed vortices form simultaneously around the head and tail ends of the body. Rapid straightening then massages the vortices caudally until they are shed into the wake as a ring vortex with a powerful central jet (Fig. 8). Although the translational phases of the rapid flex and twist responses of damsel-fly larvae appear to be functionally equivalent, this cannot be said about the preparatory re-orientational phases, which involve different muscle-activation patterns driven by independent neuromotor programmes: the C-shaped cavity of the twisting larvae at the functionally equivalent stage (Fig. 8, stage 2) has been formed via an initial strong-side, not weak-side, flexure. The cavity faces forward in the direction of escape only because the body has rolled and yawed away from the stimulus. The twist is self-evidently a much more complex manoeuvre than the rapid flex, involving what is tantamount to a helical contraction of the body to bring about the required re-orientation.



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Fig. 8. Schematic representation of the mechanism of thrust vortex generation during a simple flex manoeuvre. The larva is viewed from above. The head and tail ends of the C-flexing body (stage 2) generate mutual starting vortices; the body vortex is then propagated down the body during the extension phase (stages 3-5) and finally released, along with the tail-generated vortex, as a ring vortex. The inset below shows the corresponding configuration of the body, at the end of the flexion phase, during the twist. The two configurations are functionally equivalent, although in the latter case the body has rolled onto its left side and the C-shaped cavity into which water will be drawn and thrust caudally has been formed by a right-side body flexure rather than a left-side flexure.

 

Any biomechanical advantages of the twist over the simple flex are not clear because, as will be shown in the following section, the impulse provided by the thrust jet during a rapid twist escape is only approximately 50% more than that produced during a half-stroke of normal steady swimming. Nor is the twist capable of producing an appreciably faster response, or a greater turning angle, than the rapid flex. The real difference may lie in a more subtle area of the insect's biology viz. behaviour. For example, in some situations, it might benefit the insect to present its ventral side, including its legs, to the potential enemy as it makes its escape, rather than its flank. In these circumstances, the insect would choose to initiate the twist and not the simple flex. For the moment, this is merely speculation, but such ideas may be useful in framing the questions to be posed in any future behavioural study of escape responses in these insects.

A study on rapid C-start behaviour in larval Chinook salmon (Oncorhynchus tschawytscha; Hale, 1996Go) makes it possible to compare the kinematics of a virtually identical manoeuvre in a vertebrate and invertebrate of similar body length (2-3 cm). With such a complex movement, it is not possible to assign a single, whole-body Reynolds number. In the case of the final-stage damsel-fly larva (body length approximately 2 cm), an upper estimate can be arrived at during the extension phase at the end of which the head velocity reaches 0.22 m s-1. Assuming a characteristic length of 0.02 m, the resultant Reynolds number is approximately 4.5x103. This is somewhat higher than Hale's estimate for juvenile salmon, although both animals clearly lie in the zone of `intermediate' Reynolds numbers. In other respects, C-start performance is remarkably similar between the insect and the fish. The total duration of the manoeuvre (stage 1 plus stage 2) was approximately 150-200 ms in each case, although stage 1 in the fish (60 ms) was shorter than in the insect (77 ms). The C-start in the fish is technically equivalent to the flex, described in the present study, as opposed to the `flex and twist', although, as was shown earlier, these are very similar. One of the most interesting findings of Hale's study was that the relationship between fast-start performance parameters and body length differs between adult and juvenile fish. Experimental studies have shown that high-acceleration manoeuvres are important for predator avoidance in both young (Eaton et al., 1977Go) and mature (Webb, 1982Go; Fuiman, 1993Go) fish. However, in adults, C-start duration increases with body length when comparisons are made both within and between species (Webb, 1976Go, 1978Go), whereas in larval Chinook salmon C-start duration decreases with age and size. Hale (1996Go) suggests that the transition from the larval to the adult relationship probably coincides with the point where the yolk sac reserves have become depleted and the larval fish begins active foraging, exposing it to heightened predator threat. According to this analysis, C-start performance peaks during early larval development. Whether or not the relative speed of escape response varies throughout the development of larval damsel-flies is not known, as the present study deals only with the final instar. Clearly, the ontogeny of rapid escape manoeuvres would be an important area to address in further studies on this insect.

Hydrodynamics
Although the bottom-layer technique is suitable for visualising flow events associated with an organism in close proximity to the substrate, its main weaknesses are that it presents only a two-dimensional impression of a three-dimensional wake structure and it is difficult to quantify with accuracy. These deficiencies were addressed in a previous study where wake modelling from bottom-layer and open-water dye-streamer techniques was compared during steady swimming (Brackenbury, 2002Go). Both were consistent with the picture of a wake consisting of single, discrete ring vortices shed alternately to the left and right side of the swimming path with consecutive half-strokes. The momentum angle of the vortex jets was approximately 70° relative to dead-aft, implying considerable side-forces generated by the body and tail. Wake momentum and thrust estimates were consistent with values predicted from kinematic data using a standard bulk-momentum model for large-amplitude, elongated-body fish locomotion (Lighthill, 1971Go). The ring vortices produced during steady swimming, as visualised by the bottom-layer and open-water techniques, were slightly smaller and had a jet velocity slightly lower than the thrust vortex identified at the end of the twist manoeuvre in the present study.

These comparisons are important in view of the lack of open-water data in the present study against which to check the results of the bottom-layer technique. The larva exits from the twist manoeuvre with its body held within 0.5 cm of the bottom, making it almost inevitable that the wake will impinge on the bottom: after all, that is the basis of the technique and, regardless of possible ground effects on the wake, this is the normal wake pattern produced by the larva in these circumstances. In some cases, the measured external diameter of the vortex was based on direct impressions within the milk layer; in others, such as that illustrated in Fig. 3C, the geometry of the vortex was clearly shown as milk was drawn into its trailing edge. In the latter instances, the lower edge of the vortex was just (approximately 1 mm) clear of the bottom. This kind of variability precludes any precise quantification of ground effects on the shape, size, velocity and symmetry of the wake, but comparison with the previous study (Brackenbury, 2002Go) suggests that the error in the measurement of the dimensions of the vortex is probably less than 25%. The momentum M of an axi-symmetric ring vortex can be estimated as:

(1)
where {Gamma} is the circulation given by the line integral of the tangential velocity component v about a curve enclosing the vortex core (Spedding et al., 1984Go), and {rho} is the density of water. From Spedding et al. (1984Go), {Gamma} can be obtained by integrating v normal to the ring plane down the centre line of the vortex. Equation 1 assumes that the vortex meets the appropriate geometric criteria, i.e. that it is a small-cored ring vortex with a core radius to ring radius ratio of 0.25 or less. In the present study, the only velocity that could be measured was the jet velocity at the ring plane Vjet, and images were not detailed enough to provide a profile of v along the vortex axis. However, in similar discrete ring vortices identified in the wakes of swimming culicid pupae, the jet velocity was seen to regress in a uniform manner from its maximum value at the ring plane, Vjet, to zero at the leading and trailing edges of the vortex (Brackenbury, 2001Go): this is approximately what would be expected in a classic ring vortex. In the present study, it is assumed that a similar velocity profile exists down the central axis of the ring vortex. By knowing Vjet, it is then possible to estimate {Gamma} as follows:

(2)
Using the measured values for R, Ra and Vjet in the present study (Fig. 7C) yields a momentum value for the thrust vortex of 0.8x10-5 kg m s-1, which is approximately 50% greater than the figure of 0.5x10-5 kg m s-1 obtained for individual vortices during steady swimming. If the thrust vortex is the sole source of wake momentum, and there are no additional `hidden' wake structures contributing to it, the measured thrust vortex momentum should balance the momentum imparted to the body as it is accelerated in the direction of escape. The changing shape of the body as it extends during the thrust phase makes it difficult to establish the position of the centre of mass. Assuming, to a first approximation, that the motion of the head is reasonably representative of the motion of the centre of mass, Fig. 7B shows that the generation of the vortex accelerates the insect to a velocity of 0.22 m s-1, imparting a momentum of approximately 0.5x10-5 kg m s-1 to a body weighing approximately 22 mg (Brackenbury, 2002Go). In view of the many simplifications made in the calculations, these figures of the estimated wake and body momentum must be viewed with caution but they are sufficiently close in value to lend reasonable confidence to the conclusion that the vortex is the dominant, if not sole, wake element associated with the manoeuvre.

The rapid flex and twist manoeuvres are single-stroke movements distinct from the rhythmical sinusoidal movements involved in steady swimming, but there are also clear dynamic and kinematic similarities. As in the individual half-strokes of steady swimming, the escape manoeuvre generates a single thrust vortex. In the former case, there was clear evidence of body as well as well as tail-generated flows that combined to produce the final vortex shed from the caudal fin. The very large lateral undulation of the body and the tail resulted in vortices being shed at nearly 70° away from dead-aft. The wake structure of continuously swimming damsel-fly larvae differed from the high-efficiency reverse Karman vortex sheet, with its caudally directed zigzagging jet, characteristic of some caudal fin swimming fish (Blickan et al., 1992Go; Muller et al., 1997Go; Wolfgang et al., 1999Go), and was much more like that of the intermittently swimming Zebra Danio Brachydanio rerio (McCutchen, 1977Go) and the continuously swimming eel Anguilla anguilla (Muller et al., 2001Go). The digital particle image velocimetry images of Muller et al. (2001Go) showed a double vortex shed to the side of the swimming path with each half-stroke, which was interpreted as a ring vortex formed by contributions from a body wave (termed the `protovortex' by these authors) and movements of the tail. As discussed by Brackenbury (2002Go), the rapid-flex manoeuvre of startled damsel-fly larvae can be modelled on the fast C-start of fish (Fig. 8). Flow visualisation studies by Wolfgang et al. (1999Go) show that rapid curvature of the backbone into a C-shape draws fluid into the C-shaped cavity as two oppositely signed vortices develop simultaneously around the head and tail ends of the body. Rapid straightening then leads to these vortices being shed into the wake as a thrust jet that drives the fish in the direction of the initial flexure. By forming the body into a C-shape, the damsel-fly larva ensures that the resultant thrust jet is directed approximately due aft of the realigned anterior part of the body.


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 Summary
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 Materials and methods
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 References
 

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