Function of the heterocercal tail in sharks: quantitative wake dynamics during steady horizontal swimming and vertical maneuvering
1 Department of Biological Sciences, University of Rhode Island, 100 Flagg
Road, Kingston, RI 02881, USA
2 Museum of Comparative Zoology, Harvard University, Cambridge, MA 02138,
USA
* e-mail: cwilga{at}uri.edu
Accepted 25 May 2002
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Summary |
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We present a summary of forces on a swimming shark integrating data obtained here on the tail with previous data on pectoral fin and body function. Body orientation plays a critical role in the overall force balance and compensates for torques generated by the tail. The pectoral fins do not generate lift during steady horizontal locomotion, but play an important hydrodynamic role during vertical maneuvering.
Key words: swimming, heterocercal tail, flow visualization, hydrodynamics, digital particle image velocimetry, shark, Triakis semifasciata, Chiloscyllium punctatum
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Introduction |
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The second view of heterocercal tail function in sharks was proposed by
Thomson (1976; see also
Thomson and Simenak, 1977
). In
this model (summarized in Fig.
1B), the shark tail generates a reaction force directed through
the center of mass. No torque is generated by the action of the tail and,
hence, no counterbalancing forces need to be generated by the pectoral fins
and body.
No experimental hydrodynamic data currently exist to permit a quantitative
assessment of the function of the heterocercal tail in sharks during in
vivo locomotion. Some progress in understanding shark tail function has
been made using manipulative studies of isolated tails or tail models
(Grove and Newell, 1936;
Affleck, 1950
;
Alexander, 1965
;
Simons, 1970
). The
three-dimensional kinematic study of freely swimming sharks of Ferry and
Lauder (1996
) and the
dye-stream tracking in their study strongly supported the classical model,
while the drawings of tail position during swimming by Thomson
(1976
) supported the
alternative model.
To quantify the function of the heterocercal tail in sharks and resolve the
two alternative views discussed above, it is necessary to evaluate the forces
generated by the tail during both steady horizontal locomotion and vertical
maneuvering. The technique of DPIV has been used successfully to analyze the
hydrodynamic function of pectoral fins in both sharks and sturgeon
Acipenser transmontanus (Wilga and Lauder,
1999,
2000
,
2001
) and to examine the
function of the caudal fin of sturgeon
(Liao and Lauder, 2000
). DPIV
has the advantages of (i) allowing freely swimming animals to be studied in a
controlled laboratory setting, (ii) providing detailed quantitative data on
water flow in the wake of swimming fishes (see Drucker and Lauder,
1999
,
2000
,
2001
;
Lauder, 2000
;
Nauen and Lauder, 2001
) and
(iii) allowing the direction of force application by the tail to the water,
and hence the direction of the reaction force, to be calculated.
In this study, we use the technique of DPIV to address several questions.
First, does the heterocercal tail in sharks swimming horizontally generate a
jet flow that is oriented at a large posteroventral angle, as predicted by the
classical model (Ferry and Lauder,
1996), or is the tail vortex jet flow oriented so as to produce
reaction forces directed through the center of mass, as predicted by Thomson
(1976
)? Second, does the
hydrodynamic function of the shark tail change during vertical maneuvering?
Third, do sharks adjust vortex jet angle relative to their path of motion when
maneuvering vertically? Fourth, are tail hydrodynamics in sharks comparable
with that of the similarly shaped heterocercal tail in sturgeon, which can
alter jet angle relative to the path of motion of the body
(Liao and Lauder, 2000
)? We
address these questions using leopard sharks Triakis semifasciata, an
epibenthic species, as well as bamboo sharks Chiloscyllium punctatum,
a benthic species. These two species differ somewhat in heterocercal tail
morphology, allowing us to test the classical model with a moderate diversity
of shark tail shapes.
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Materials and methods |
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Digital particle image velocimetry with simultaneous high-speed
recording
Water flow in the wake of the caudal fin of sharks during steady horizontal
swimming and during vertical maneuvering was analyzed using digital particle
image velocimetry (DPIV) as in previous research (e.g. Drucker and Lauder,
1999,
2001
;
Lauder, 2000
;
Liao and Lauder, 2000
; Wilga
and Lauder, 2000
,
2001
). Briefly, water in the
flow tank was seeded with 6 g of near-neutrally buoyant 12 µm diameter
silver-coated hollow glass beads (density 1.3 g cm-3; Potters
Industries Inc.). A Coherent 5 W argon-ion laser was focused into a 1-2 mm
thick by 10 cm wide light sheet and oriented into vertical and horizontal
configurations in separate experiments using mirrors. Particle movement in the
water flow was visualized as light reflected by the beads and recorded using a
NAC HSV 500c3 two-camera synchronized high-speed video system at
250 frames s-1 (downloaded image resolution 640x480 pixels
for each camera). The working area of the flow tank was 82 cm long by 28 cm
wide by 28 cm high. Water flow and particle reflections in the wake of the
caudal fin in lateral (parasagittal) view were recorded by placing one camera
perpendicular to the side of the flow tank
(Fig. 2). The position of the
shark relative to the laser light sheet in lateral view was recorded by a
second (synchronized) camera aimed at the swimming shark and slightly
overlapping the laser sheet (Fig.
2). This method allowed us to visualize fluid flow and vortex
rings shed by the tail while simultaneously recording the orientation and
behavior of the swimming shark. This combination proved critical in accurately
assessing caudal fin function relative to body angle and in determining the
orientation of the reaction force relative to the center of mass.
|
Leopard sharks, Triakis semifasciata, and bamboo sharks, Chiloscyllium punctatum, were filmed while holding position (steady horizontal swimming) in the flow tank at 1.0 L s-1. Five different sequences for each of three individuals for each species were digitized, giving a total of 30 sequences. Rising and sinking (vertical maneuvering) locomotion in the water column were also studied to investigate whether the locomotor function of the tail is to change vertical position. Only leopard sharks were filmed during rising or sinking, and five different sequences for each of three individuals for each behavior were digitized, giving a total of 30 sequences. In total, 300 images were digitized for these measurements of body and caudal fin position during swimming: five fields equally spaced throughout a tailbeat for five tailbeats in four individuals for three behaviors. The vertical laser light sheet was positioned in the center of the tank for all experimental protocols to minimize potential boundary effects from the tank walls on the flow around the fish. Thus, all sequences in which the tail intersected the laser sheet occurred well away from the sides of the flow tank.
We define holding position as the fish maintaining a stationary (within 2 %
L s-1 deviation from a fixed reference point) horizontal
(anteroposterior) and vertical position in the water column. Rising and
sinking are defined as maintaining horizontal position in the water column
while actively increasing or decreasing vertical position by at least 4 cm
s-1 with minimal lateral deviation. These criteria follow previous
studies (Wilga and Lauder,
1999,
2000
). We analyzed only those
video sequences in which sharks maintained horizontal and vertical position
during holding or ascended or descended with near-constant velocity in the
water column (in all cases with minimal lateral, upstreamdownstream
pitching, except when initiating changes in vertical position or roll
motions). The initiation of rising and sinking behaviors necessarily involves
pitching movements, as described previously (Wilga and Lauder,
1999
,
2000
).
Several variables were used to quantify body and tail kinematics for swimming sharks during all behaviors (Fig. 3). Vertical velocity was calculated by digitizing a fixed point (the center of mass) at two points in time. Body angle was measured as the angle between the horizontal and a line drawn along the ventral surface of the body between the anterior base of the pectoral and pelvic fins. Tail angle was measured as the angle between a line representing the dorsal surface of the caudal peduncle and a line indicating the leading edge of the tail (Fig. 3). The path of motion was calculated as the angle between the horizontal and a line connecting a fixed point (the center of mass) at two moments in time (200 ms apart).
|
Sequences of particle images during station-holding, rising and sinking in
the water column during locomotion in sharks were identified using the
criteria described above for fin kinematics. Consecutive pairs of video images
(4 ms apart) of water flow just downstream of the caudal fin were digitized
and analyzed using two-frame cross correlation to produce a 20x20 matrix
of 400 velocity vectors, as for conventional DPIV methods used previously
(e.g. Raffel et al., 1998;
Drucker and Lauder, 1999
,
2000
,
2001
; Wilga and Lauder,
1999
,
2000
;
Lauder, 2000
). In total, 60
image pairs were analyzed using DPIV: five occurrences of pelagic
station-holding from each of three leopard and three bamboo sharks, and five
occurrences each of rising and sinking in the water column holding from three
leopard sharks.
Fluid flow patterns in the wake of the caudal fin were documented by
estimating flow structure using the magnitude and direction of velocity
vectors from plots of the 20x20 matrix of velocity vectors. Mean
downstream flow was subtracted from the matrix of velocity vectors to reveal
fluid structures in the wake. Fluid vorticity was calculated to quantify
rotational motion in the wake using the velocity vector matrix. Plots of
vorticity (e.g. Fig. 4) are
shown in order to visualize rotational fluid motion; in these plots, a
greenish color indicates low vorticity, a red/orange color is used for
counterclockwise fluid movement and a purple/blue color for clockwise motion
(Drucker and Lauder, 1999;
Wilga and Lauder, 1999
,
2000
,
2001
). Jet angle was
calculated by taking the mean angle of 10 high-velocity vectors located in the
center of the vortex ring. Ring axis angle was calculated as the angle between
the horizontal and a line connecting the centers of the two counter-rotating
vortices of the vortex ring (Fig.
3). Ring axis angle was measured directly from the DPIV-analyzed
images of the laser light sheet. These conventions correspond to those used by
Liao and Lauder (2000
) in
their study of sturgeon tail function, and the use of those conventions here
permits comparison with the sturgeon data.
|
Statistical analyses
Mean values of variables measured for each locomotor behavior are reported
in Table 1. These data reflect
the means from our a priori categorization of locomotor behavior into
holding position, rising or sinking in the water column based on the analysis
of the lateral whole-body video sequences. However, because there was
extensive variation among sequences in the rapidity of vertical maneuvering
and also modest variation in the body angle used during holding position, we
also treat the data as continuous without any attempt to categorize individual
sequences. In Table 2, we
present the means predicted from regression analyses for each variable; these
data take into account the entire range of natural variation without a
priori categorization and are thus the means used in the Discussion and
in the presentation of our overall model of shark locomotor dynamics in
Fig. 9. Presentation of both
analyses allows comparison with previous analyses of sturgeon locomotor
hydrodynamics (Liao and Lauder,
2000), which used the a priori categorization
analysis.
|
|
|
|
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|
Model I least-squares linear regressions with adjusted
r2 values were calculated using body angle, tail angle,
path angle, jet angle and ring axis angle. Slopes were first tested for
significance and then tested statistically against the slope of the expected
relationships based on a priori geometric relationships between body
angle, ring axis angle and vortex jet angle. Student's t-tests were
used to test the significance of the intercepts and slopes between data
regression lines and predicted lines according to Zar
(1996). The same variables
were used in analyses of locomotor behavior, which consisted of a mixed-model
two-way analysis of variance (ANOVA) using Type III sums of squares
(Hicks, 1982
;
SAS Institute, 1998
). Behavior
(rising, holding or sinking) was treated as a fixed main effect and individual
as a random main effect; consequently, behavior was tested over the behavior
x individual interaction term. If a significant difference was detected
by ANOVA, then a post-hoc StudentNewmanKeuls (SNK)
multiple-comparisons test was performed. Data were tested for homogeneous
variances using the Levene median test (P<0.05) and for normal
distribution using the KolmogorovSmirnov test (P<0.05).
Statistical tests were performed using statistical software (SAS v. 6.12 or
SigmaStat v. 2.01) or calculated using Zar
(1996
).
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Results |
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Analysis of vertical light sheet DPIV images of the wake behind the heterocercal tail of leopard and bamboo sharks reveals slices through discrete vortex rings containing a central high-velocity jet of water (Fig. 4). This vortex ring is shed after each tail beat (Fig. 4) and is linked with the vortex ring formed during the subsequent tail beat. Shark tail vortex rings are inclined significantly to the flow with the plane of the vortex ring relative to the horizontal, reaching a mean of 120° in leopard sharks and 125° in bamboo sharks during steady horizontal locomotion (Tables 1, 2). Plots of vortex jet angle versus body angle indicate that jet angles were, on average, nearly 30° below the horizontal during steady horizontal locomotion in both leopard and bamboo sharks (Fig. 5; Table 2). However, mean ring axis angle ranges from 55 to 160° during vertical maneuvering in leopard sharks (Fig. 7C).
Leopard sharks do not alter their tail angle with changes in body angle, as shown by the lack of difference in the slope of the regression line from the predicted 180° linear relationships between tail and body angles (Fig. 7A). Thus, the tail maintains a consistent angular relationship with the body regardless of locomotor behavior. Ring axis angle also retains a consistent relationship to body angle, as shown by the lack of significant difference between the slope of the regression line from that of the 90° perpendicular predicted relationship (Fig. 7C). In fact, ring axis angle averages 18° greater than the predicted 90° relationship, indicating that vortex rings are produced at an angle of approximately 108° to the shark body. Jet angle decreases with increasing body angle at the same rate as to be expected if a parallel relationship were predicted (shown by the lack of a significant difference between the slope of the regression line from that of the 180° parallel predicted relationship; Fig. 7B).
Leopard sharks do not alter their jet angle with their path of motion angle, as shown by the lack of significant difference between the slopes of the regression line from that of the 180° parallel predicted relationship (Fig. 8A). The data regression line is approximately 28° lower than that predicted; therefore, the tail vortex jet is produced at an angle of 152° to the path of motion followed by the shark. However, a plot of ring axis angle versus jet angle shows a significant departure from the 90° predicted relationship (Fig. 8B). Jet angle decreases with increasing ring axis angle at a slower rate than to be expected if a perpendicular relationship were to exist. Thus, jet angle remains closer to the horizontal than expected as ring axis angle changes.
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Discussion |
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If the shark tail functions to generate a reaction force that passes
through the center of mass, as suggested by Thomson
(1976), then vortex jet angles
must be equal and opposite to the body angle, even when the body angle is
altered during vertical maneuvering. Mean jet angles were nearly 30° below
the horizontal in leopard and bamboo shark tails during steady horizontal
locomotion, as revealed by plotting vortex jet angle versus body
angle (Fig. 5). The reaction
force from the tail vortex rings of both leopard and bamboo sharks must be
directed anterodorsally, as predicted by the classical model of heterocercal
tail function in sharks (Alexander,
1965
; Ferry and Lauder,
1996
), since a mean positive 11° body tilt is adopted during
steady horizontal swimming (Fig.
9; holding). Furthermore, leopard sharks maintain a consistent
relationship between jet and body angle during unsteady maneuvering
locomotion, as indicated by the linear relationship paralleling the 180°
predicted line. The direction of vortex ring jets is not altered by leopard
sharks while maneuvering vertically and, thus, the heterocercal tail generates
a jet force that is constant in direction relative to the longitudinal body
axis. In notable contrast to this result, white sturgeon Acipenser
transmontanus are capable of actively altering the angle of jet flow
produced by the heterocercal tail by up to 10°, as shown by Liao and
Lauder (2000
). The basis for
this difference in ability between sturgeon and the two shark species studied
here to modulate vortex jet direction is unknown, but might reflect their
differing abilities to recruit dorsal and ventral myotomal musculature
differentially to change tail shape and flexibility and, hence, to alter the
direction of thrust from the tail.
Vortex rings in the wake of the shark tail are inclined relative to the
flow with the plane of the vortex ring averaging 120° during steady
horizontal locomotion and ranging from 55 to 160° while maneuvering. Shark
tail vortex rings are inclined significantly more towards the horizontal
compared with the more nearly vertical vortex rings produced by the homocercal
tail of bluegill sunfish Lepomis macrochirus
(Lauder, 2000) and mackerel
Scomber japonicus (Nauen and
Lauder, 2002
). Indeed, compared with those of a ray-finned fish
with a heterocercal tail (the sturgeon), shark vortex rings are inclined
approximately 15° more towards the horizontal
(Liao and Lauder, 2000
) during
steady horizontal locomotion. The heterocercal tail of sturgeon generates
reaction forces directed through the center of mass of the body, while the
heterocercal tail of sharks results in reaction forces directed dorsal to the
center of mass (Fig. 9).
Why heterocercal tails produce vortex rings that are more inclined relative to body angle than homocercal tails has yet to be investigated. It may simply be an effect of the inclined posterior edge of the caudal fin. If the vortex ring is shed simultaneously from the dorsal and ventral lobes, then it would tend to maintain a tilted axis as it rolls off the edge of the dorsal and ventral fin lobes into the wake. As sharks rise in the water column, the trailing edge of the tail is more horizontally oriented, generating vortex rings that tend to be inclined more horizontally (Fig. 6A; Tables 1, 2). As sharks sink in the water column, the posterior edge of their tail is more vertical, generating vortex rings that have a more vertical axis (Fig. 6B). This, together with the constant angle of the tail during all behaviors (holding, rising, sinking), is consistent with the idea that tilted rings are an effect of tail trailing edge shape and movement.
|
Comparative studies show, however, that vortex ring angle is not
necessarily directly related to the morphological angle formed by the trailing
edge of the tail; the kinematics of the tail also plays a major role in
determining vortex ring orientation. For example, in sturgeon
(Liao and Lauder, 2000),
vortex rings shed during steady locomotion are more vertically oriented than
would be predicted from trailing edge angle as a result of the complex
three-dimensional motion of the tail tips
(Lauder, 2000
). In homocercal
tails, which have a primarily vertical trailing edge, shed vortex rings may be
inclined significantly to the vertical or have non-horizontal jet flow as a
result of asymmetrical movement of the dorsal and ventral tail tips
(Lauder, 2000
;
Nauen and Lauder, 2002
).
Differences between shark and sturgeon tail function may be due to
significant differences in kinematics. Lauder
(2000) described sturgeon tail
kinematics and noted that the dorsal and ventral lobes are often significantly
out of phase with each other and that oscillation of surface elements of
sturgeon tails occurs around the vertical plane. During locomotion, sturgeon
tails show remarkable flexibility, and portions of the dorsal lobe move in the
opposite direction to the ventral tail lobe for much of the tailbeat cycle.
This is in sharp contrast to the kinematic pattern described for shark tails
by Ferry and Lauder (1996
).
Shark tails possess considerable internal stiffness compared with sturgeon
tails and move at an inclined angle to the horizontal much in the manner
proposed by the classical model (Fig.
1A). Phase differences among parts of the tail in sharks never
approach those seen for sturgeon (Lauder,
2000
). Differences in tail kinematics between sharks and sturgeon
thus appear to correlate with observed hydrodynamic differences in vortex jet
angle relative to the center of mass.
Although our hydrodynamic data support the classical model of heterocercal
tail function in sharks, our previous analyses of the hydrodynamic function of
the pectoral fins in sharks contradicts the classical view that the pectoral
fins generate lift forces during steady horizontal locomotion (Wilga and
Lauder, 2000,
2001
). Three-dimensional
kinematic analyses of the pectoral fins of leopard and bamboo sharks show that
these fins are held in a concave-down orientation at a mean chord angle of
-5° to the flow. Thus, leopard shark pectoral fins are not held at a
positive angle of attack to the flow during steady horizontal locomotion and
should not be expected to generate lift. In addition, DPIV analyses of the
pectoral fin wake reveal that the pectoral fins generate no lift forces during
steady horizontal swimming (Wilga and Lauder,
2000
,
2001
).
Combining the hydrodynamic and kinematic data on pectoral fin, body posture and caudal fin function in leopard and bamboo sharks during steady horizontal swimming with that for leopard sharks during vertical maneuvering suggests a new force balance for shark locomotion (Fig. 9). Vertical forces (F) generated by swimming sharks are separated into the head and branchial region (Fhead) and pectoral fins (Fpectoral), which are anterior to the center of mass, and the body (Fbody) and tail (Ftail), which are posterior to the center of mass. The body weight (Fweight) of the shark acts at the center of mass. The vortex jet force (Fjet) produced by the tail is equivalent and opposite in direction to the reaction force on the tail (Freaction). Our new force balance proposes that the torque produced by the heterocercal tail during steady horizontal swimming by leopard sharks is balanced by the torque generated by the relatively large positive body angle to the flow, which generates lift forces both fore and aft of the center of mass, and not by the pectoral fins (Fig. 9).
Although our hydrodynamic and kinematic data on shark pectoral fins
indicate that the pectoral fins generate no lift during steady horizontal
locomotion, the pectoral fins of leopard sharks are used actively to initiate
rising and sinking maneuvers, during which positive and negative lift forces,
respectively, are actively generated by the pectoral fins (Wilga and Lauder,
2000,
2001
). During rising, the
pectoral fins shed a vortex that generates positive lift and acts to increase
the body angle of the shark, which increases the lift generated by the tilted
body. During sinking, the pectoral fins generate a vortex with negative lift
that acts to tilt the body angle to a more negative angle relative to the
flow.
The experimental hydrodynamic and three-dimensional kinematic analyses of shark locomotion show that body forces are balanced in an unexpected manner. Although the classical model of heterocercal tail function in sharks is supported, the locomotor roles of the pectoral fins and body posture have not been previously recognized. The advent of experimental hydrodynamic techniques allows long-standing hypotheses of fin function in fishes to be tested, and such approaches will play a key role in elucidating the functional significance of variation in fin morphology among the considerable diversity of shark species and locomotor modes.
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Acknowledgments |
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