Hydrodynamics of caudal fin locomotion by chub mackerel, Scomber japonicus (Scombridae)
Department of Organismic and Evolutionary Biology, Harvard University, 26 Oxford Street, Cambridge, MA 02138, USA
* e-mail: jnauen{at}oeb.harvard.edu
Accepted 13 March 2002
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Summary |
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Patterns of flow indicated that the wake consisted of a series of linked elliptical vortex rings, each with central jet flow. The length of the minor axis (height) of the vortex rings was approximately equal to caudal fin span; the length of the major ring axis was dependent on swimming speed and was up to twice the magnitude of ring height. Profiles of wake velocity components were similar to theoretical profiles of vortex rings.
Lift, thrust and lateral forces were calculated from DPIV measurements. At 1.2FLs-1, lift forces measured relative to the X axis were low in magnitude (-1±1mN, mean ± S.D., N=20) but oriented at a mean angle of 6° to the body axis. Reaction forces tend to rotate the fish about its center of mass, tipping the head down. Thus, the homocercal caudal fin of S. japonicus functions asymmetrically in the vertical plane. Pitching moments may be balanced anteriorly via lift generation by the pectoral fins. Thrust estimates for the two smallest fish based on DPIV analysis were not significantly different from drag measurements made by towing those same animals. At a speed of 1.2FLs-1, thrust magnitude was 11±6mN (mean ± S.D, N=40). Lateral force magnitudes were approximately double thrust magnitudes (22±6mN, mean ± S.D., N=20), resulting in a mean mechanical performance ratio (thrust/total force) of 0.32 at 1.2FLs-1. An increase in speed by a factor of 1.8 resulted in a mean increase in thrust by a factor of 4.4, a mean increase in lateral forces by a factor of 3, no change in the magnitude of lift produced and an increase in mean mechanical performance to 0.42. The relatively high lateral forces generated during swimming may be a necessary consequence of force production via propagated waves of bending.
Key words: hydrodynamics, locomotion, swimming, scombrid, fish, force balance, mackerel, Scomber japonicus
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Introduction |
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In the present study, we use DPIV to describe the wake morphology and force
balance for chub mackerel Scomber japonicus (Teleostei: Scombridae).
S. japonicus is a basal member of the family Scombridae, a group that
includes the high-performance bonitos and tunas and is characterized by a
streamlined body and an externally symmetrical or homocercal caudal fin.
Steady swimming kinematic patterns of mackerel are typically classified as
characteristic of the carangiform swimming mode
(Lindsey, 1978), in which
lateral body oscillations are largely restricted to the posterior third of the
body, with large lateral oscillation amplitudes by the caudal peduncle and fin
(see, for example, Gibb et al.,
1999
; Donley and Dickson,
2000
; Nauen and Lauder,
2001a
). The anterior body segments of S. japonicus
undergo small lateral oscillations (amplitudes <2.5 % of total body length)
during steady swimming, and oscillation amplitude increases approximately
exponentially over the posterior third of the body (see Fig. 6A in
Donley and Dickson, 2000
).
Thus, in contrast with anguilliform locomotion, where much of the body
undergoes large lateral oscillations
(Lindsey, 1978
;
Gillis, 1998
) and produces
hydrodynamic force during steady swimming,
(Müller et al., 2001
),
the primary site of hydrodynamic force production for S. japonicus is
the posterior third of the body, including the caudal peduncle and
particularly the caudal fin.
As scombrid fishes are noted for their high-performance steady locomotion
(see, for example, Fierstine and Walters,
1968; Magnuson,
1978
; Wardle and He,
1988
), one goal of this project was to describe the wake produced
by a scombrid fish during steady swimming. These data can be compared with
previous data on wakes produced during caudal fin locomotion by mullet
(Müller et al., 1997
),
eel (Müller et al.,
2001
), giant danio (Anderson,
1996
; Wolfgang et al.,
1999
), sturgeon (Liao and
Lauder, 2000
) and bluegill sunfish
(Drucker and Lauder, 2001b
).
Since all previous quantitative data on caudal fin wake structure have been
obtained from an analysis of either the horizontal (frontal, XZ) or
vertical (parasagittal, XY; Fig.
1) plane at a single swimming speed, a second goal of the project
was to determine the effect of speed on wake characteristics. We collected
data at both relatively slow and fast steady cruising speeds (1.2 and 2.2 fork
lengths s-1, respectively, where FL is fork length).
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Wake morphology measurements were made in both the horizontal (XZ) and vertical (XY) planes (Fig. 1) to provide two separate measurements of wake morphology (and thus thrust production) from orthogonal light-sheet orientations. By inducing fish to swim steadily at different heights in the water, we altered the position of the caudal fin relative to the horizontal light sheet and were thus able to characterize the wake shed by different areas of the caudal fin. DPIV thrust measurements at a steady swimming speed of 1.2 FL s-1 were compared with drag measurements made by towing the same individuals (post mortem) at that speed. To establish the mechanical performance of the homocercal mackerel tail in the horizontal plane, we determined the ratio of thrust to total force produced during steady swimming.
Characterizing the wake of Scomber japonicus also allowed us to
address questions concerning the magnitude and orientation of hydrodynamic
forces produced by a homocercal caudal fin of a teleost fish. The symmetrical
morphology of the homocercal tail has led to the assumption that, during
steady swimming, forces are generated only in the horizontal plane and that no
is lift produced (for a review, see
Lauder, 2000). Mackerel have
negatively buoyant bodies (Magnuson,
1973
) that require lift production for steady horizontal swimming.
Three sources of lift traditionally identified for scombrids are the pectoral
fins, body and caudal keels (summarized by
Magnuson, 1978
). However, a
recent kinematic study of steady swimming by S. japonicus showed that
the caudal fin is tilted at an angle of up to 10° relative to the vertical
and its movement is thus asymmetrical
(Gibb et al., 1999
),
suggesting that the caudal fin of S. japonicus may produce lift
during steady swimming. To address this question, we used DPIV data from the
vertical plane to measure the angle of the reaction force on the body relative
to the center of mass.
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Materials and methods |
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Flow visualization
Experiments were conducted using a 6001 recirculating saltwater flow tank
at 19±°C. The flow tank has a working area 82cm long by 28cm wide
by 28cm high; flow speed in the tank was controlled using a variable-speed
motor. Details of the flow tank and flow speed calibration have been presented
previously (Jayne et al.,
1996; Gibb et al.,
1999
). We used a flow tank, rather than have mackerel swim across
the field of view of the cameras in still water conditions, to control the
speed of the fish and use a relatively small field of view (approximately
10cmx12cm) to provide a high-resolution view of the wake.
As in previous studies of flow visualization from our laboratory (Drucker
and Lauder, 1999,
2000
; Wilga and Lauder,
1999
,
2000
;
Lauder, 2000
;
Nauen and Lauder, 2001a
), flow
was visualized by seeding the water with near-neutrally buoyant silver-coated
glass beads 12µm in diameter (density 1.3 g cm-3; Potters
Industries, USA) that reflected light from a 5W argon-ion laser
(Fig. 1). Examples of particle
density are shown in Fig. 1A,B.
The laser light sheet was approximately 2mm thick and 10cm wide. It was
positioned in the center of the working section of the flow tank and oriented
in either the vertical (parasagittal, XY,
Fig. 1) or horizontal (frontal,
XZ) plane. The vertical light sheet was projected from below the tank
(Fig. 1). The horizontal sheet
was projected from the left side of the tank; a ventral view of the horizontal
light sheet (Fig. 1B) was
recorded with a camera that viewed a front-surface mirror set at 45°
beneath the tank.
Images of the fish were recorded at 250 Hz using one camera of a two-camera synchronized NAC high-speed video system; these images were used to determine the fish's position relative to the light sheet and the angle of the body to the X axis (defined in Fig. 1). A second camera viewed the movement of particles illuminated by the light sheet. The cameras' fields of view were calibrated by recording images of a ruler at the beginning of each experiment. Note that as the caudal fin moved across the field of view it blocked portions of the light sheet (which resulted in dark areas in the images; e.g. Fig. 1A,B).
Three Scomber japonicus (fork length 22 cm, 24 cm and 26 cm) were
used for both horizontal and vertical light-sheet experiments. One other
individual (23 cm fork length) was used for horizontal light-sheet experiments
only. A final individual (20 cm fork length) was used for vertical light-sheet
experiments only. Fish swam at speeds of 1.2 FLs-1 (the
lowest speed at which steady swimming was observed) and 2.2
FLs-1. These speeds are within the range of swimming
speeds Atlantic mackerel can sustain for longer than 200 min (0.4-3.5 total
lengths s-1, where TL is total length;
Wardle and He, 1988), are well
below the maximum sustainable swimming speeds of 4-5 FLs-1
for S. japonicus of this size
(Sepulveda and Dickson, 2000
)
and match speeds used in a previous study of S. japonicus caudal fin
kinematics (Gibb et al.,
1999
).
To obtain accurate force measurements for steady swimming from the DPIV data (see below), video sequences were analyzed only when mackerel were holding position for several strokes and not drifting either vertically or laterally because even small deviations from steady swimming produced markedly different flow patterns in the wake. Measurements of body angle to the X axis were obtained at the time the vortex of interest was shed from the caudal fin by analyzing video images of mackerel body position obtained by the second video camera synchronized with the DPIV recordings (Fig. 1). Stroke duration was determined as the time between maximum excursions of the caudal fin in the XZ plane.
Digital particle image velocimetry (DPIV)
DPIV methods have been described in detail previously
(Willert and Gharib, 1991;
Anderson, 1996
;
Raffel et al., 1998
); the
specific methods used in the present study are based on previous studies on
the wakes of fish conducted in our laboratory (e.g.
Drucker and Lauder, 1999
;
Lauder, 2000
;
Liao and Lauder, 2000
;
Wilga and Lauder, 2000
). Video
images were imported into a PC computer using DT-Acquire software with a Data
Translation video card (Data Translation, Inc., USA). Using Insight software
(v. 3; TSI, Inc., USA), selected areas (e.g.
Fig. 1A,B) of sequential pairs
of video images (4 ms apart in time) were analyzed by subdividing the analysis
area of interest into a series of interrogation windows and comparing these
data subsets using two-frame cross-correlation analysis. The areas of flow
analyzed here were typically rectangular in shape and were thus analyzed with
a grid of 40x30 vectors. The cross-correlation analysis used a
fast-Fourier transform correlation process with a Gaussian peak search
algorithm, a spot size of 64 pixels and a peak signal-to-noise ratio of
1.5.
Vector trajectories and mean velocities were calculated trigonometrically from orthogonal velocity components using Transform (v. 3.3; Fortner Research LLC, USA). To determine vortex geometry, average free-stream velocity was subtracted from each vector to reveal vortical structures (e.g. Fig. 2). Velocity gradients across the wake were examined to compare vortex morphology with theoretical patterns.
|
More than 200 pairs of images were analyzed using DPIV (at least 12 pairs for each fish at each speed for each of the XY and XZ views of the wake). At the relatively slow speed of 1.2 FLs-1 (absolute speeds of 26.4-31.2 cm s-1), background turbulence was low and flow data were of high quality, resulting in 10 (five for each light sheet) very good DPIV analyses for each fish (see Table 1). This sample size was sufficient for statistical analysis. At the speed of 2.2 FLs-1 (48.4-57.2 cm s-1), high background turbulence obscured many images of the wake. Thus, only 12 horizontal light-sheet and seven vertical light-sheet images of good quality were obtained from the more than 100 pairs of images analyzed. The 2.2 FLs-1 data set is presented in Table 1 and Figs 4, 6 and 7, but the data set was not large enough for statistical comparison with 1.2 FLs-1 data.
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DPIV measurements and force calculations
Circulation of vortices in the wake was used to infer propulsive forces on
the caudal fin that arise from circulation about the fin. This inference is
justified by equivalence in the absolute magnitude of bound and shed
circulation during the impulsive start of a hydrofoil (according to Kelvin's
theorem; Milne-Thompson, 1966;
Dickinson, 1996
), such as that
observed during caudal fin acceleration, which occurs during the first half of
each stroke by Scomber japonicus
(Nauen and Lauder, 2000
). The
methodology applied here was used successfully to estimate the force produced
during pectoral fin locomotion by the bluegill sunfish Lepomis
macrochirus (Drucker and Lauder,
1999
).
Assuming that all the momentum added to the fluid by the fish is contained
in vortices in the wake, the time-averaged locomotor force F can be
calculated as:
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The distance between the centers of the vortices (representing ring width
in the horizontal plane and ring height in the vertical plane), and the angle
between the X axis of the vector map (defined in
Fig. 1) and the ring axis or
the jet, were measured from the vector plots using Scion Image (Scion Corp,
USA). A mean value of ring area (calculated as the area of an ellipse) was
calculated for each swimming speed and used in the force calculation described
above because ring height and ring width could only be measured from either
the vertical and horizontal light sheets, respectively, and the distance
between vortex centers was independent of individual (see
Table 2). Stroke duration was
defined as the time between points of maximum stroke amplitude and was
determined from video images of the ventral aspect of the mackerel (horizontal
light-sheet data only). A mean value of stroke duration was calculated for
each speed and used in the force calculation described above because stroke
duration was independent of individual (analysis of variance, F=2.0,
P=0.15).
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Drag measurements
The total drag of post-mortem Scomber japonicus was measured using
a force transducer to compare with estimates of thrust calculated from the
DPIV measurements. The technique used was similar to that of Drucker and
Lauder (1999). A flexible
vertical rod secured from above was placed so that the fish was suspended in
the center of the tank. Individuals were attached to the rod via
suture line threaded through the jaws and skull; the mouth was fixed in place
slightly open to ensure a flow of water through the branchial cavity. All the
fish used in the study were tested at flow speeds equal to swimming speeds of
1.2 and 2.2 FLs-1; however, the fish were only stable at
relatively low flow speeds. At higher flow speeds, excessive flutter of the
fish body on the line precluded accurate drag estimates, and the data were
discarded. Thus, the drag measurements presented here are for the two smallest
fish (fork length 20 and 22 cm) at the speed of 1.2
FLs-1.
Rod bending (measured as displacement at the rod tip) due to the drag of the fish was recorded using high-speed digital video (Redlake Corp.) and measured using the Scion Image digitizing program. Bending of the unloaded rod in flow was also recorded, measured and subtracted from that of the loaded rod to account for the small amount of drag due to the transducer in the flow. Three independent tests were conducted for all the measurements. Rod displacement was recorded for 10 s at 60 Hz. More than 40 images from that series were randomly selected, rod displacement was measured from those images and a mean displacement value was calculated.
The transducer was calibrated before and after the experiment by clamping the rod horizontally and hanging a range of masses (0.4-10 g, corresponding to 3.9-98 mN) from it so that the masses pulled on the bar in the same manner as the drag from the fish. The transducer showed a linear response in the range of loads measured and no change in response due to the load of the fish. Because of the averaged nature of the rod displacement measurements, all force measurements were rounded to the nearest mN.
Statistical analyses
Statistical analyses were performed using SuperANOVA (v. 1.11) on kinematic
and flow data for five strokes from each of four fish (N=20) swimming
at 1.2 FL s-1. As stroke duration and lateral forces were
determined from the horizontal light-sheet data only, and the angle of the
body to the X axis and vertical forces were determined from the
vertical light-sheet data only, single-factor analysis-of-variance (ANOVA)
tests were performed to determine the effect of individual on these variables.
All other wake variables (see Table
1) were determined from data collected with both light sheets, so
two-factor ANOVAs were performed in which light-sheet orientation was a fixed
factor and individual was a random factor (see
Table 2). All F values
were calculated as described by Zar
(1984). To correct for
performing multiple tests on the data set, the Bonferroni correction of
P=0.05/k, where k is the number of variables
analyzed (Rice, 1989
), was
applied (as previously; see Nauen and
Lauder, 2001b
). Regression relationships were calculated using
Statgraphics (v. 3; Manguistics Corp.). Force values calculated from DPIV data
showed significant differences in variance from force data measured with the
transducer (Bartlett's test; P=0.003 for the 20 cm fish and
P=0.007 for the 22 cm fish). Therefore, median values of force were
compared using the KruskalWallis comparison of median values test
(Zar, 1984
).
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Results |
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General wake structure
Viewed in either the horizontal or vertical plane, the wake consisted of a
series of strong counter-rotating vortices
(Fig. 2) typical of the
structure of a series of linked vortex rings. Between each pair of
counter-rotating vortices, a jet of high-velocity flow was formed. Correlating
movement of the caudal fin along the Z axis with patterns of flow in
the wake (the time series in Fig.
2) indicates that a vortex was shed from the caudal fin during the
first quarter of each stroke.
As a test of vortex ring height, horizontal (XZ) light-sheet data were collected at the dorsal tip of the caudal fin, at the middle of the dorsal lobe of the fin and at the midpoint or `V' of the fin (Fig. 3). At the dorsal tip of the fin (Fig. 3A), essentially no vorticity was seen. When the middle of the caudal fin's upper lobe (Fig. 3B) and the midpoint of the caudal fin (Fig. 3C) beat through the light sheet, a series of vortices was seen (Fig. 2). Thus, vortex ring height was approximately equal to caudal fin span. The jet formed between the pairs of counter-rotating vortices showed some continuity between vortex pairs (see Fig. 3C) but had a strong lateral component (e.g. Fig. 2C).
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Analysis of flow in the vertical (XY) plane showed a series of counter-rotating vortex pairs (Fig. 4), each with a central jet of flow in the wake. At both slow (1.2FLs-1, Fig. 4A) and relatively fast (2.2FLs-1, Fig. 4B) cruising speeds, the main axis connecting the centers of the counter-rotating vortices (see Fig. 4B) was approximately perpendicular to the X axis, and jet trajectory was approximately horizontal. Note that the relatively strong lateral component of the jet seen in the XZ plane images of Figs 2 and 3 is not present in the vertical light-sheet images because that flow is out of the plane of the vertical light sheet.
Profiles of wake velocity components were very similar to theoretical profiles for isolated vortex rings (Fig. 5). The left panels of Fig. 5 show three theoretical velocity profiles across XY planar sections of the wake. The right panels contain raw empirical data from this study calculated from a high-resolution 50x50 vector field. X' is the longitudinal axis of the ring; Y' is perpendicular to X' (see Fig. 4B for an illustration of the axes described here). The components of velocity parallel to X' and Y' are u' and v', respectively. Fig. 5A is a longitudinal velocity profile of the wake at the midpoint of the vortex cores. Fig. 5B is a velocity profile across the ring's central axis or jet; Fig. 5C is a velocity profile across a single vortex core. In all the profiles, velocity is high at the edges of a vortex core or at the midpoint between the two vortices. The peak in velocity at the midpoint between two vortices reflects the strength of the central jet. In general, the empirical data and theoretical profiles agree, indicating that the vortices viewed are part of vortex rings. The fact that velocity is greater than zero at the jet margins (rather than decreasing to zero as in the theoretical profile in Fig. 5B) indicates that these rings are part of a vortex chain (depicted in Fig. 8) rather than single, isolated rings. Similarly, the experimental data in Fig. 5C do not reach the zero point at the vortex margins because of the velocity imparted by upstream and downstream linked rings.
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Vortex orientation and geometry
On average, vortex core radii were slightly less than 1 cm
(Table 1) at both the slow and
fast speeds. As vortex radius was independent of light-sheet orientation
(P=0.381, Table 2), as
well as individual (P=0.519, Table
2) and interaction (P=0.499,
Table 2) effects, the vortices
were symmetrical at 1.2 FLs-1. Vortex circulation and
momentum were also independent of individual (P=0.087 and
P=0.130, respectively; Table
2) and the interaction effect of individualxlight-sheet
orientation (P=0.593 and P=0.559, respectively,
Table 2). Vortex circulation
and momentum values determined from the horizontal light-sheet data were
approximately twice the magnitude of those determined from the vertical
light-sheet data (Table 1)
because the strong lateral flow visible with the horizontal sheet (see, for
example, Figs 2 and
3) was out of the plane of the
vertical light sheet and was thus not viewed in the vertical light-sheet
images. Despite these differences, the effect of light-sheet orientation was
not statistically significant for vortex circulation or momentum
(P=0.018 and P=0.019, respectively,
Table 2) because a low
P value was used to determine significance in order to correct for
multiple comparisons.
The distance between vortex centers was independent of individual (P=0.043, Table 2) and the interaction of individualxlight-sheet orientation (P=0.029, Table 2). Although the effect of lightsheet orientation on the distance between vortex centers was not statistically significant (P=0.033), ring width was on average 1.7 times ring height at the speed of 1.2 FLs-1 (Table 1), suggesting that the rings were elliptical instead of circular. This ratio increased to 1.9 at a speed of 2.2 FLs-1 (Table 1), indicating that the long axis of the ellipse increased in length with increased speed.
Ring axis angle relative to the X axis was independent of the effects of individual and individualxlight-sheet orientation (P=0.013 and 0.367, respectively; Table 2). Light-sheet orientation had a significant effect on ring axis angle (P=0.006, Table 2). Jet angle to the X axis was also independent of the effects of individual and individualxlight-sheet orientation (P=0.689 and P=0.413, respectively, Table 2), but was dependent on light-sheet orientation (P=0.001, Table 2). The dependence of these variables on light-sheet orientation reflects the fact that the vertical and horizontal light sheets showed perpendicular views of the obliquely oriented vortex rings.
Wake views obtained using the vertical light sheet (Fig. 4) suggested that the vertical ring axis was approximately perpendicular to the X axis. Values of ring axis angle to the X axis were close to 90° for both speeds (Table 1) although a range of values were seen, with some rings tilted by up to 30° from vertical (Fig. 6). Vertical light-sheet views of the wake also suggested that the angle of the jet to the X axis was nearly zero. Overall, jets were angled slightly negative to the X axis at both speeds (Table 1). The mean value of body angle at the swimming speed of 1.2 FLs-1 (-3±4°, mean ± S.D., N=20, Table 1) was significantly different from zero (t=test, P=0.02). In the vertical plane, jet angle was independent of ring axis angle at the speed of 1.2 FLs-1 because the slope of a linear regression model fitted to the data was not significantly different from zero (ANOVA, P=0.57; Fig. 6). Jet angles at the speed of 2.2 FLs-1 showed a similar range and relationship to ring axis angle to those at the lower speed (Fig. 6).
Wake views obtained using the horizontal light sheet (e.g. Figs 2, 3) indicated that the ring axis was at an oblique angle to the horizontal and that the jet was approximately perpendicular to the ring axis angle. On average, values of ring axis angle to the X axis from the 40 rings analyzed were approximately 30° (Table 1). Values of jet angle relative to the X axis were always less than 90° and tended to be lower at the speed of 2.2 FL s-1 (Table 1; Fig. 6). In the horizontal plane, jet angle was independent of ring axis angle because the slope of a regression model fitted to the data was not significantly different from zero (ANOVA, P=0.22; Fig. 6).
As discussed above, S. japonicus tended to swim with a slightly negative body angle (Table 1). Body angles (determined at the time each vortex was shed) ranged from -10 to +2° (Fig. 7). Both ring angle and jet angle values were independent of body angle at 1.2 FL s-1 (Fig. 7) because the slopes of regression models fitted to the data were not significantly different from zero (ANOVA, P=0.08 for ring angle and P=0.61 for jet angle). The data were similar at 2.2 FL s-1.
Force magnitudes and balance
Three factors determine the magnitude of force produced (equation 1):
stroke duration, vortex area and vortex circulation. Jet angle in the
horizontal plane determines the ratio of thrust to lateral force produced. As
discussed above, mean values of vortex area and stroke duration and individual
values of vortex circulation, momentum and jet angle were used to calculate
force. Estimates of downstream force were independent of individual
(P=0.172; Table 2),
light-sheet orientation (P=0.107;
Table 2) and the interaction
effect of individualxlight-sheet orientation (P=0.750;
Table 2). Thus, there were no
significant differences between estimates of downstream force from the
separate measurements of force production made using the vertical and
horizontal light sheets.
At the swimming speed of 1.2 FL s-1, the magnitude of
mean downstream force was 11±6 mN (mean ± S.D., N=40).
Lateral forces, calculated from horizontal light-sheet data, were independent
of individual (ANOVA, F=1.577, P=0.234) and high in
magnitude (22±6 mN, mean ± S.D., N=20). Vertical forces
(calculated from vertical light-sheet data) were also independent of
individual (ANOVA, F=1.975, P=0.158) and were low in
magnitude (-1±1 mN, mean ± S.D., N=20;
Table 1). Thus, lateral forces
dominated the wake, resulting in a mean mechanical performance (, equal
to thrust/total force) of 0.32 at 1.2 FL s-1.
At the swimming speed of 2.2 FL s-1, downstream forces
calculated from the vertical (N=7) and horizontal (N=12)
light-sheet images were not significantly different (ANOVA, F=0.494,
P=0.491). At the speed of 2.2 FL s-1, downstream
force magnitude was 48±16 mN (mean ± S.D., N=19). Thus,
on average, an increase in speed by a factor of 1.8 resulted in an increase in
downstream force by a factor of 4.4. Mean lateral force at 2.2 FL
s-1 increased by a factor of 3.0 to 65±14 mN (mean ±
S.D., N=12). Mean vertical forces of -1±2 mN (mean ±
S.D., N=7) at 2.2 FL s-1 were essentially
identical to those seen at the lower speed. On average, increased to
0.42 at 2.2 FL s-1.
Measurements of drag made using a force transducer with the two smallest fish used in the DPIV experiments (post mortem) indicated that at the speed of 1.2 FL s-1 total drag was 9±0 mN (mean ± S.D., N=3) for the 20 cm fish and 11±1 mN (mean ± S.D., N=3) for the 22 cm fish. In comparison, thrust estimates made using DPIV analysis were 9±3 mN (mean ± S.D., N=5) for the 20 cm fish and 14±7 mN (mean ± S.D., N=5) for the 22 cm fish. In both cases, estimates of drag using the transducer and DPIV analysis were not significantly different based on a comparison of median values using the KruskalWallis test (P=0.18 for the 20 cm fish and P=0.35 for 22 cm fish).
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Discussion |
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This pattern of flow is termed a reverse von Kármán (or
thrust) wake (von Kármán and
Burgers, 1935; Lighthill,
1975
); it is produced by an oscillating, thrust-producing foil
moving steadily forwards (Triantafyllou et al.,
1991
,
1993
,
2000
;
Anderson, 1996
;
Anderson et al., 1998
). Reverse
von Kármán wakes are produced during caudal fin locomotion by
bluegill sunfish Lepomis macrochirus
(Lauder, 2000
;
Drucker and Lauder, 2001b
),
giant danio Danio malabaricus
(Anderson, 1996
;
Wolfgang et al., 1999
), mullet
Chelon labrosus (Müller et
al., 1997
; Videler et al.,
1999
), trout Oncorhynchus mykiss
(Blickhan et al., 1992
) and
white sturgeon Acipenser transmontanus
(Liao and Lauder, 2000
). The
wake morphology of a double row of pairs of vortices, reported for caudal fin
locomotion by eel Anguilla anguilla
(Müller et al., 2001
) and
danio Brachydanio albolineatus
(Rosen, 1959
), was not created
by S. japonicus. In addition, the wake of a single large vortex ring
modeled for caudal fin locomotion by eel
(Carling et al., 1998
) and the
model of `wakeless' caudal fin locomotion due to the sequential creation and
destruction of vortices modeled for a forked caudal fin by Ahlborn et al.
(1991
) were not supported by
the present data. The timing of vortex shedding during the first quarter of
each stroke in S. japonicus is similar to that described for the
danio Brachydanio rerio
(McCutchen, 1976
) and the
giant danio (Wolfgang et al.,
1999
).
Vortex geometry
Vortex ring height was approximately equal to caudal fin height, indicating
that caudal fin size determines one parameter of vortex size (as noted by
Blickhan et al., 1992;
Müller et al., 2000
). The
magnitude of caudal fin excursion in the Z dimension determined the
distance between the vortices in the XZ plane and, thus, the length
of the vortex ring. These data suggest that the vortex rings were elliptical
rather than round in shape (Fig.
8), as was inferred for the vortex rings in the wake of the mullet
Chelon labrosus (Müller et
al., 1997
). As the length of the ellipsoid was dependent on speed
and was approximately double the height of the ellipse at the speed of 2.2
FL s-1, the data indicate that accurate measurements of
ring geometry (which are necessary for force calculations) require
measurements of vortex ring geometry in both the XY and XZ
planes.
The elliptical shape of the vortex rings seen here is a departure from the
axisymmetrical shape of an ideal vortex ring (according to Helmholtz's
theorem; see Milne-Thompson,
1966). A second departure of the present data from the
characteristics of an ideal vortex ring is seen in the geometric relationship
between the vertical ring axis and the central jet. The central jet flow of an
ideal vortex ring (such as that created by ejection of fluid from a circular
nozzle by a piston, see Webster and
Longmire, 1997
; Raffel et al.,
1998
) extends perpendicular to the plane of the vortex ring. In
the wake of Scomber japonicus, however, the angle of the jet to the
X axis was typically close to 0°, although the ring axis angle to
the X axis varied from 60 to 110° (with 90° being vertical).
Variability in the angle between the vertical ring axis and the central jet
has been seen in wakes created during pectoral fin locomotion by bluegill
sunfish Lepomis macrochirus
(Drucker and Lauder, 1999
) and
during caudal fin locomotion by sturgeon Acipenser transmontanus
(Liao and Lauder, 2000
) and
L. macrochirus (Lauder,
2000
). The described differences between the wake structures seen
here and those of ideal vortex rings have been attributed to the fact that
these wakes are produced by reciprocating hydrofoils that are flexible, deform
in a complex manner under load and are undergoing unsteady motions [see, for
example, bluegill pectoral fin kinematics
(Gibb et al., 1994
) and
mackerel caudal fin kinematics (Gibb et
al., 1999
)]. Given the differences in shape and jet orientation
between ideal vortex rings and the wake described here, the wake of
Scomber japonicus may be most appropriately described as a series of
linked vortex `loops' rather than rings
(Dickinson and Götz,
1996
).
Force magnitudes and balance
Estimates of thrust calculated from separate DPIV measurements in the
vertical and horizontal planes were not significantly different. In addition,
for the two smallest animals that could be tested (20 and 22 cm fork length),
there was no significant difference between estimates of thrust based on DPIV
measurements and measurements of total body drag obtained by towing those
animals at the same flow speed.
Note that the present force data based on DPIV measurements were calculated
using the full values of vortex circulation obtained for both the horizontal
and vertical planes. In the only previous study of caudal fin locomotion in
which forces were calculated from DPIV data and compared with independent
force estimates (in that case, force estimates calculated from a kinematic
model; Müller et al.,
1997), wake vortices were visualized in the horizontal plane only,
and the value of half the measured circulation was used to calculate fluid
forces on the basis of the premise that the vortices viewed in the horizontal
plane are linked and that the circulation visible in that plane is equivalent
to the added circulation of two rings. In the present study, the magnitude of
vortex circulation viewed using the horizontal light sheet was approximately
twice that of the vortices viewed using the vertical light sheet
(Table 1) because the vertical
light sheet showed fluid movement in the vertical plane only and thus missed
the strong lateral flow component. The full value of vortex circulation was
used here to calculate forces from data collected in both planes, and the good
agreement between present estimates of thrust from the vertical and horizontal
light-sheet data together with the lack of significant difference between the
thrust estimates and the drag measurements support this methodology and the
force balance presented in Fig.
8.
A balance between thrust and drag is predicted for an animal moving at a
steady speed; however, such force balances have been difficult to demonstrate
empirically. The present study demonstrates such a balance with the lack of
significant difference between drag measurements obtained by towing dead
animals and thrust estimates obtained from DPIV measurements by the same
animals swimming freely at the same speed. For one animal, the measured body
drag measurements were lower (although not significantly so) than the thrust
estimates, which may be attributable to the fact that oscillation of the
caudal peduncle and fin by a swimming fish will increase its drag
(Webb, 1975). Drag is
proportional to the square of velocity, so one would predict increases in drag
by a factor of 3.4 as swimming speed increased from 1.2 to 2.2 FL
s-1 (assuming no change in drag due to transitions from laminar to
turbulent flow in the boundary layer). On the basis of the DPIV measurements,
thrust increased, on average, by a factor of 4.4.
Measurements of whole-body drag in fishes are notoriously difficult to
perform, and a host of experimental and theoretical issues potentially
confound estimates of whole-body drag (for reviews, see
Webb, 1975;
Dickinson, 1996
). We also
experienced considerable difficulty in obtaining repeatable measurements of
whole-body drag, and our estimates do not take into account changes in drag
that might result from locomotor movements. Nonetheless, the general
quantitative agreement obtained here between estimates of thrust from DPIV and
drag obtained from towing fish at the same speed suggests that the DPIV force
estimates are at least reasonable estimates of the thrust needed to overcome
drag at the swimming speeds studied. Indeed, given recent advances in DPIV
methodology, DPIV measurements are in some ways more reliable and repeatable
than data obtained from towing fish. One possible objection to the DPIV
approach is that during caudal fin locomotion momentum is removed from fluid
passing over the body. This same fluid is then reaccelerated by the caudal
fin, making it difficult to determine the total momentum added to the fluid
and, thus, absolute values of thrust. While this is a valid theoretical issue,
in practice, the mackerel caudal fin encounters nearly free-stream flow (Nauen
and Lauder, 2000a) because of its lateral oscillation and the vertical extent
of the fin well above and below the caudal peduncle. This suggests that the
caudal-fin-generated vortex rings in mackerel measured here probably capture
the majority of momentum imparted to the water by the mackerel and, hence,
that the present measurements reflect the thrust needed to overcome drag
during steady swimming.
The thrust of the order of 11 mN determined here for caudal fin locomotion
by Scomber japonicus at 1.2 FL s-1
(Table 1) is approximately a
quarter of the 40 mN produced by both pectoral fins of bluegill sunfish,
Lepomis macrochirus, of slightly smaller size (approximately 20 cm
TL) swimming at 1 TL s-1
(Drucker and Lauder, 1999) but
similar to the mean thrust force of 14 mN produced by the caudal fin of L.
macrochirus (approximately 21 cm TL) swimming at 1.1 FL
s-1 (Drucker and Lauder,
2001b
, p. 2949). At 1.1 TL s-1, L.
macrochirus also uses its dorsal fin and pectoral fins to swim, however,
so that the total thrust produced by a bluegill (56 mN) is approximately five
times that of S. japonicus at a similar speed. The large discrepancy
in thrust force magnitudes produced by the two species at the relatively slow
cruising speed of approximately 1 TL s-1 probably reflects
the high drag of the relatively deep and globose body of L.
macrochirus compared with the streamlined body of S.
japonicus.
Force production
Vortex central jet flow orientation relative to the fish's path of motion
determines the proportion of the total reaction force that is thrust and,
thus, the mechanical performance () of the stroke. A jet oriented
opposite to the direction of travel of the fish generates a reaction force
composed completely of thrust, with
values of 1. Jets oriented at an
angle to the direction of travel result in a reaction force that is a
combination of thrust and lateral forces. It has been predicted that the wake
of a well-streamlined fish (such as a scombrid) swimming steadily forwards
without accelerating would produce only a weak `thrust' wake without strong
lateral flows that may be difficult to visualize
(Rayner, 1995
). The wakes
generated by Scomber japonicus were easily visualized, however, and
contained lateral flows up to approximately twice the magnitude of downstream
flows, so that values of
(0.32 at the swimming speed of 1.2
FLs-1 and 0.42 at the swimming speed of 2.2
FLs-1) were relatively low.
The high magnitude of lateral forces seen here was somewhat surprising
given that the chub mackerel Scomber japonicus is a member of the
family Scombridae, a family of fish that includes bonitos and tunas. These
fishes are noted for high-performance locomotion in terms of high burst speeds
[from 18 TLs-1 for mackerel
(Wardle and He, 1988) to up to
27 TLs-1 for tuna
(Fierstine and Walters, 1968
;
see also Magnuson, 1978
)],
high cruising speeds (3.5 to greater than 5 TLs-1 for
mackerel, Wardle and He, 1988
;
Sepulveda and Dickson, 2000
)
and 6-10 TLs-1 for tuna
(Yuen, 1970
; summarized in
Beamish, 1978
) and long
migration distances (as far as 9700 km for the trans-Pacific crossing of the
bluefin tuna; Lindsey, 1978
).
Morphological adaptations thought to increase locomotor performance include a
streamlined body that tapers to a caudal peduncle with finlets and a forked
(mackerel), semi-lunate (bonito) or lunate (tuna) caudal fin shape.
The suite of morphological characters described above forms the basis of
the prediction that scombrid fish would generate only a weak `thrust' wake of
high efficiency (Rayner,
1995). In addition, the data cited above suggest that more derived
members of the scombrid clade show greater locomotory performance. Specific
differences in steady swimming kinematics have been identified between
juvenile kawakawa tuna (Euthynnus affinis) and juvenile S.
japonicus (Donley and Dickson,
2000
). At a given steady swimming speed, E. affinis shows
significantly less lateral body displacement than S. japonicus
(Donley and Dickson, 2000
);
such decreased axial flexion is characteristic of thunniform locomotion and
has been previously documented for tunas
(Fierstine and Walters, 1968
;
Dewar and Graham, 1994
).
However, lateral movement at the tip of the snout, or yaw (which contributes
to drag), was not significantly different between the two species, and E.
affinis showed higher tailbeat frequencies than S. japonicus at
the same swimming speeds (Donley and
Dickson, 2000
).
More direct measurements of locomotor performance also indicate
surprisingly little difference between juvenile tuna and mackerel. Sepulveda
and Dickson (2000) determined
that maximum sustainable speeds and net cost of transport (and therefore
swimming efficiency) are not significantly different between juvenile E.
affinis and juvenile S. japonicus. Thus, detailed studies of
swimming kinematics (Donley and Dickson,
2000
) and cost of transport
(Sepulveda and Dickson, 2000
)
indicate that juvenile tuna are not more efficient propulsors than mackerel of
the same size.
On the basis of the previous kinematic and physiological data, we predict
that the wake flow patterns and thrust and drag measurements made here are
generally applicable to more derived scombrid species of similar size swimming
at the speeds studied here. Note that this comparison is facilitated by the
fact that mean tailbeat frequencies seen here for Scomber japonicus,
2.5 Hz and 4.2 Hz at swimming speeds of 1.2 and 2.2 FLs-1,
respectively, are similar to the values of 2.9 Hz and 4.0 Hz seen previously
(tailbeat frequencies calculated for those speeds from
Table 1 of
Donley and Dickson, 2000).
Mean tailbeat frequencies for S. japonicus of Gibb et al.
(1999
) were very similar at
1.2 TLs-1 (2.4 Hz) but lower (3.0 Hz) at 2.2
TLs-1 than those measured here.
The present data also indicate a surprising lack of difference in
mechanical performance between a scombrid and a more basal perciform fish, the
bluegill sunfish Lepomis macrochirus. Mean mechanical performance for
Scomber japonicus swimming steadily at 1.2 FLs-1
is 0.32, which is slightly less than the values of 0.39 for labriform
swimming by the bluegill sunfish Lepomis macrochirus
(Drucker and Lauder, 1999
) and
0.38 for caudal fin locomotion by Lepomis macrochirus
(Drucker and Lauder, 2001b
)
for similarly sized fish swimming at nearly identical speeds. Note that all
the previous
values are much lower than the value of 0.7 calculated for
trout (Blickhan et al., 1992
)
and the value of 0.97 calculated for the mullet
(Müller et al., 1997
),
although few specifics of those data are available for direct comparison. The
similarity of mechanical performance of caudal fin locomotion for fishes as
disparate in morphology and locomotor habit as chub mackerel and bluegill
suggests that undulatory carangiform propulsion in fishes with homocercal
tails is relatively inefficient from a mechanical perspective.
A different measure of the caudal fin performance is the Strouhal number
(St):
![]() | (2) |
The present data indicate that high lateral force production is a feature
of caudal fin locomotion by chub mackerel. Combined with the study of Drucker
and Lauder (2001b), it appears
that high lateral forces and relatively low mechanical performance are a
general feature of caudal fin locomotion by teleost fishes at speeds of
approximately 1 FLs-1 and not a limitation of pectoral fin
locomotion or of fishes with relatively low locomotor capacity (such as
bluegill sunfish). Low mechanical performance for caudal fin locomotion might
reflect the nature of undulatory propulsion as a posteriorly propagated wave
of lateral bending, which may necessitate the generation of relatively large
lateral forces. Supporting this hypothesis is the finding of Triantafyllou et
al. (1991
) of optimum
mechanical performance values of approximately 0.2 at Strouhal numbers of
0.2-0.3 for foils oscillating transversely through uniform oncoming flow. Such
foils are physical models of caudal fin locomotion at a steady forward
speed.
Lift production by a homocercal tail
A second feature of vortex jet orientation important to force production is
the orientation of the jet relative to the X axis (defined in
Fig. 1). An orientation of
0° indicates that the jet is horizontal and that the caudal fin is not
producing lift. Lift is an important factor in the force balance of animals
moving through water as it is necessary for maneuverability and to counteract
negative buoyancy. Lift may be produced by the interaction between virtually
any fin or body surface and the fluid. For example, on the basis of a
kinematic study of body angle as a function of swimming speed for the Atlantic
mackerel Scomber scombrus, He and Wardle
(1986) suggested that
negatively buoyant fishes produce lift by swimming at a positive body angle.
Hydrodynamic evidence of such lift production during steady swimming has been
provided for leopard shark Triakis semifasciata
(Wilga and Lauder, 2000
) and
white sturgeon Acipenser transmontanus
(Wilga and Lauder, 1999
). Lift
production by the caudal fin has been demonstrated for T.
semifasciata (Ferry and Lauder,
1996
) and A. transmontanus
(Liao and Lauder, 2000
); lift
production by pectoral fins has been demonstrated for bluegill sunfish
Lepomis macrochirus (Drucker and Lauder,
1999
,
2000
) and black surfperch
Embiotoca jacksoni (Drucker and
Lauder, 2000
).
The caudal fin of Scomber japonicus is externally symmetrical, or
homocercal, in shape. Homocercal caudal fins are classically viewed as moving
symmetrically in the lateral plane (as a homogeneous, stiff, flat plate) and
generating only lateral forces and thrust but not lift (for a review, see
Lauder, 2000). Recent
kinematic data on the homocercal caudal fin of bluegill sunfish indicate,
however, that the fin moves at an acute angle to the horizontal plane with
asymmetrical movement of the fin's dorsal and ventral lobes that would
generate lift (Lauder, 2000
).
This hypothesis was confirmed with DPIV analysis of the wake, which consisted
of a chain of linked vortex rings with a jet of flow that was somewhat
ventrally inclined (Lauder,
2000
).
Analysis of caudal fin movement by Scomber japonicus
(Aleev, 1969;
Gibb et al., 1999
) indicated
that, like the bluegill sunfish, the homocercal caudal fin is at an acute
angle relative to the vertical axis during lateral movement. On the basis of
these kinematic data, one would predict that the caudal fin of S.
japonicus generates lift that can be visualized as a ventrally oriented
central jet of flow in each vortex ring. As predicted from the kinematic data,
the vortex jet was oriented at a slightly negative angle relative to the
X axis [-3°, which is in the same direction but at a
substantially smaller angle than that demonstrated for sharks
(Ferry and Lauder, 1996
) and
sturgeon (Liao and Lauder,
2000
)]. This posteroventral orientation resulted in the generation
of small negative lift forces (approximately -1 mN).
S. japonicus swam with their bodies tilted slightly head-downward,
however (on average, also 3° below horizontal), as has been found
previously (Gibb et al.,
1999). In comparison, their sister species S. scombrus
tend to swim with a body angle of approximately 0° at their preferred
swimming speeds of 0.9-1.2 TLs-1
(He and Wardle, 1986
); S.
scombrus tilts its head up and reaches body angles as high as 20°
when swimming speeds decrease to 0.4-0.8 TLs-1
(He and Wardle, 1986
). The
slightly negative body angle of S. japonicus seen here resulted in a
net 6° difference between the orientation of the body and the jet
(Fig. 8). Reaction forces
generated at the caudal fin would be oriented at +3° above the horizontal,
thus generating a small but probably significant lift force tending to rotate
the animal about its center of mass by inducing a torque.
Lift generated by orientation of the body or pectoral fins to oncoming flow
could counteract lift generation at the caudal fin (Magnuson,
1973,
1978
). The body orientation of
Scomber japonicus probably does not generate high magnitudes of lift
at the low orientation angles seen here and previously
(Gibb et al., 1999
). The
pectoral fins, a prominent feature in the more derived scombrid species, are a
second potential source of lift (Magnuson,
1970
,
1978
). The pectoral fins of
S. japonicus are frequently abducted during steady swimming at the
speeds studied here (Gibb et al.,
1999
), and any lift forces generated would act at the base of the
fin, which is anterior to the center of mass
(Fig. 8). To test this
hypothesis would require visualization of the wake of S. japonicus
pectoral fins, as has been performed for other fishes (Drucker and Lauder,
1999
,
2000
; Wilga and Lauder,
1999
,
2000
) and calculation of a
whole-body vertical force balance.
The whole-body vertical force balance for Scomber japonicus, and
for the genus Scomber, is complicated by morphological variation
within the genus and among scombrids in general. Swimbladder presence and size
are variable among scombrids and are not a diagnostic feature of the group
(Collette, 1978). The
swimbladder of S. japonicus in the size range studied here has an
elongate oval shape; its center is positioned approximately at the center of
mass of the animal (J. C. N. and G. V. L., personal observation). Thus, the
swimbladder is unlikely to compensate for lift forces produced by the caudal
fin. Of the remaining two Scomber species, S. australasicus
also has a swimbladder, but the organ is lacking from S. scombrus
(Collette and Nauen, 1983
).
With regard to the more derived scombrids, Thunnus tonggol also lacks
a swimbladder (Collette,
1978
), and other members of Thunnini have a swimbladder as
juveniles, but the structure degenerates with growth (e.g. Auxis and
Euthynnus; Richards and Dove,
1971
).
Pectoral fin size, another potential factor in lift production, is also
variable, although the relatively large pectoral fin surface area and the
presence of a swimbladder are found more often in scombrid species of larger
body size (Magnuson, 1973).
Median bony caudal keels present on the caudal peduncle of derived scombrids
(but not externally on S. japonicus;
Nauen and Lauder, 2000
) have
also been proposed as lift generators (Magnuson,
1970
,
1978
). Variability in the
presence of a swimbladder and a central caudal keel, as well as changes in
pectoral fin size and factors such as body fat content and distribution (and
thus fish density) over ontogeny and among species, suggests that there will
be considerable differences between the vertical force balances of different
scombrid fishes swimming under different conditions. The scombrid homocercal
caudal fin may show interesting differences in function under these variable
conditions.
![]() |
Acknowledgments |
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Footnotes |
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References |
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