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The Vortex Wake of the Free-swimming Larva and Pupa of CULEX PIPIENS (Diptera)

John Brackenbury^*

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

View larger version (22K): [in a new window]   Fig. 1. Kinematic events at the start of a pupal mini-dive. (A) Body profiles at 10ms intervals from the start of diving (0ms). The dorsal surface of the insect is indicated, in this and the following figures, by the projecting respiratory siphon. The filled and open circles in the resting position indicate the centre of gravity of the body and the abdominal paddles, respectively. The dashed lines indicate the position of the radius vector from the base to the tip of the abdomen in the resting and full-down (end-downstroke) positions. Arrows with open or filled heads indicate the direction of rotation of the abdomen and head/thorax about the centre of gravity, respectively. (B) The motion of the centre of gravity and abdominal paddles at the stages corresponding to those shown in A. (C) Abdominal tip and paddles.

View larger version (23K): [in a new window]   Fig. 2. (A,B) Kinematic events during a complete cycle of continuous swimming in the pupa. The traces show motion of the centre of gravity (filled circles), the abdominal paddles (open circles) and the leading edge of the head/thorax capsule (stars). (C) Cartoon sequence of the stroke starting on the left with the abdomen curled above the head/thorax at the end of the preceding upstroke. Note how the mean path of the body tacks downwards through 26° during the downstroke and upwards through 26° during the upstroke relative to the mean forward swimming path. A, B and C are from different swimming events.

View larger version (36K): [in a new window]   Fig. 3. Kinematic variables during continuous swimming in the pupa. (A) Changes in the forward velocity of the centre of gravity relative to the water during a complete downstroke/upstroke cycle. The cartoons represent the configuration of the body at the corresponding points in the cycle. Open and filled arrowheads represent the motion of the abdomen and head/thorax, respectively, around the centre of gravity. (B) Changes in the forward velocity component of the centre of gravity (filled circles, also shown in A) and the abdominal paddles (open circles). The hatched parts of the graph represent the parts of the swimming cycle when the abdominal paddles are moving backwards with respect to the mean swimming path through the water. (C) Changes in the angular velocity of the abdominal paddles about the centre of gravity, relative to the longitudinal axis of the head/thorax: this motion is indicated by the open-headed arrow in the cartoon on the right. (D) Changes in the angular velocity of the longitudinal axis of the head/thorax about the centre of gravity, relative to the water. This motion is indicated by the filled arrow in the cartoon on the right. The vertical dotted lines in B–D indicate the point, in the middle of a half-stroke, when the forward velocity of the centre of gravity is at its peak. The dashed lines demarcate the half-strokes and pause periods.

View larger version (178K): [in a new window]   Fig. 4. Vortex production during a mini-dive by the pupa. (A) The pupa is floating towards the surface following its initial dive into a layer of dyed water on the bottom of the container. To the right can be seen a number of vortices associated with previous dives. (B) 1.4s later, the pupa has dived out of sight, leaving behind two ring vortices produced by the first upstroke (V1) and first downstroke (V2). The arrows show the convection axes of the vortices.

View larger version (21K): [in a new window]   Fig. 5. Simultaneous kinematic and hydrodynamic events during the first three half-strokes of a pupal mini-dive. Data points plot the motion of the centre of gravity (filled circles), the abdominal paddles (open circles) and the dye front moving along with the associated vortices (V1–V3) (open triangles, filled squares and filled triangles, respectively) at 20ms intervals. The data are from four individual dives, and the cartoon shows the starting orientation in each case (0ms position). Arrows show the directions of movement of the dye front along the propagation axis of the vortex and of the centre of gravity and abdominal paddles.

View larger version (21K): [in a new window]   Fig. 6. (A) Pooled data from 62 individual pupal dives. For each data point, the x,y coordinates were plotted relative to the starting (0ms) position of the centre of gravity. Points were measured at 20ms intervals and show the motion of the centre of gravity (filled circles) and the dye front associated with the vortices (V1–V3; open triangles, open squares and filled triangles, respectively). The three profiles represent (from top to bottom) the configuration of the body in the resting position (0ms) and in the middle of the second and third half-strokes (40ms and 80ms positions of the centre of gravity). The S.E.M. for each data point was similar to or smaller than the symbol width, so error bars are not shown. Open-headed arrows show the angular motion of the abdomen about the centre of gravity; arrows on the vortices indicate the motion of the dye front along the axis of the vortex. The dashed circle indicates the size and position of the spherical vortex at the time of the final data point. The cartoon, on the right, is a scheme of the movement of the dye front into the vortex. Initially, the dye is drawn into the trailing edge of the vortex (cartoon 1); it then moves along the axis to the centre of the ring (cartoon 2). At a later stage (cartoon 3), the dye has recirculated into the ring: the leading edge of the dye front is now coincident with the leading edge of the vortex and travels with the same velocity as the vortex. R and Re are the ring radius and external radius of the vortex, respectively. (B) The velocity of the dye front along the centre line of five individual ring vortices. It was difficult to obtain data over the trailing half of the vortex axis. The dashed line is drawn by hand. The cartoon on the right of B represents a median section through a vortex travelling in the direction of the straight arrow.

View larger version (108K): [in a new window]   Fig. 7. Vortex production in (A) a pupa and (B) a final-stage larva. In A, the top videograph shows two consecutive stages, at 20ms intervals, in the execution of a downstroke. The two images have been superimposed on the same frame and separated horizontally for clarity. A vortex has been produced by the end of the stroke and is travelling towards the dye streamer on the left in the direction of the arrow. After 80ms, the leading edge of the vortex hits the streamer, and after a further 140ms (middle videograph) it emerges from the other side of the dye streamer with its outline faintly showing through the dye, a plug of dye being drawn into the centre of the vortex. After a further 100ms (bottom videograph), the dye that entered the vortex is now recirculating back into the ring. In B, the top videograph shows two superimposed and horizontally separated images of the larva viewed from above flexing to its right side. 20ms later, the leading edge of the vortex produced by the body contraction has reached the streamer, and after a further 100ms has almost passed through the streamer (middle videograph). The outline of the leading edge of the vortex is faintly visible, and a plug of dye is being drawn into the centre of the vortex. 200ms later (bottom videograph), the dye that entered the vortex is now recirculating back into the ring.

View larger version (20K): [in a new window]   Fig. 8. Vortex production during continuous swimming in the pupa. The solid line traces the path of the tip of the abdominal paddle. Numbers 1–8 indicate half-strokes, and the jets of water associated with them are shown as stippled regions outlined by dashed lines. The open-headed arrows show the direction of the jets, which are orientated at ±26° from dead aft of the swimming path. The jets were traced directly from a video sequence. Each jet appeared in the second half of the stroke as the abdominal tip began to move forward relative to the water. The jets were usually only visible for approximately 50ms, but in this case between the fifth and sixth half-strokes the insect turns upwards; this was accompanied by the release of a persistent jet on the outside of the bend. This jet, labelled number 6 in the drawing, is crossed by a forwardly directed ‘stopping jet’ associated with the change in direction.

View larger version (115K): [in a new window]   Fig. 9. Composite videograph of vortex generation by a pupa during the performance of a turn. The vortex is produced by a downstroke that begins at the 0ms position and is complete by the 40ms position of the pupa. Its production is associated with a change in swimming direction of approximately 60° (the angle between the two smaller arrows). The vortex travels to the left in the direction of the large white arrow. The dye pattern corresponds to the position of the vortex 1s after its production, by which time it has travelled approximately 3cm from the 0ms position of the pupa. During the same period, the pupa disappeared from the lower right of the screen. Superimposed on the videograph are the images of the vortex 2s and 4s after its formation. Note that the vortex corresponds to the turning vortex shown in Fig.8; the stopping vortex also illustrated in that figure is not visible here because of the absence of dye in the relevant area. The dye pattern in the middle of the videograph is a streamer falling slowly from the surface of the water.

View larger version (21K): [in a new window]   Fig. 10. Kinematics of continuous swimming in the final-stage larva of Culex pipiens. (A) Schematic illustration of the larva resting at the surface of the water. Note the respiratory siphon and tracheal gills and associated hairs. (B) Cartoon sequence illustrating a single cycle of swimming movements. The cartoons represent body profiles seen from the dorsal side at 10ms intervals. The horizontal scale has been expanded to allow separation of the profiles. The dot on the animal in position 1 is the centre of the thorax, and the line intersecting it is the transverse axis of the thorax, changes in the orientation of which are illustrated in C. (C) The path of the centre of the thorax (dot) and the transverse axis of the thorax (line) through the water. Note how the axis of the thorax rotates through 132° throughout the half-stroke (compare profiles 1 and 5 in B) and the centre of the thorax tacks from side to side through 48°. The dashed line between B and C links corresponding stages (stage 6).

View larger version (26K): [in a new window]   Fig. 11. Kinematics of continuous swimming in a final-stage larva. (A) Semi-schematic depiction of the path followed by the centre of gravity (dashed line) and the abdominal tip (continuous line) during two swimming cycles. The centre of gravity is assumed to lie at the junction between the thorax and the abdomen. The superimposed profiles represent the configuration of the body just after the half-way points in the cycle when the body is beginning to flex rapidly and the abdominal tip travels backwards with respect to the mean swimming path through the water. (B) The path of the centre of gravity (filled circles) and the abdominal tip (open circles) at 10ms intervals. (C) The forward velocity of the centre of gravity (filled circles) and the abdominal tip (open circles). The hatched areas in C represent the period when the abdominal tip is travelling backwards through the water relative to the mean forward swimming direction. The numerals in C are the velocities calculated from the corresponding intervals between points shown in B.

View larger version (19K): [in a new window]   Fig. 12. Vortex production at the start of swimming in the final-stage larva. (A) The initially extended body contracts rapidly to one side, producing a vortex that propagates along an axis lying at right angles to the extended body and intersecting it approximately half-way along its length. The straight open-headed arrows indicate the direction of motion of the vortex and the centre of gravity (filled circle) of the body. (B) The outer diameters (2Re) of vortices measured at various times during the propagation of the vortex in 33 separate experiments.

View larger version (27K): [in a new window]   Fig. 13. Structure of the abdominal paddle and thoracic bristle tufts of the final-stage larva. (A) Abdominal tip showing details of the fan-like paddle. The inset shows an individual tuft of 12 bristles from the fan. (B) Details of thoracic bristle tufts. Each of the four tufts consists of 13 bristles: the inset shows two bristles at higher magnification. (C) Drawings from a video sequence showing three stages in the right-to-left swing of the abdomen of a swimming larva viewed from above. During the rapid flexural stage of the stroke (middle profile), the thoracic bristle tufts on the concave side of the body are bent forward in the direction of flow (dashed line). Open-headed arrows indicate the scissor-like motion of the anterior and posterior halves of the body. The filled circle at the junction of the thorax and abdomen indicates the position of the presumed centre of gravity of the larva.