Locomotor function of the dorsal fin in rainbow trout: kinematic patterns and hydrodynamic forces
1 Washington Trout, PO Box 402, Duvall, WA 98019, USA
2 Museum of Comparative Zoology, Harvard University, 26 Oxford Street,
Cambridge, MA 02138, USA
* Author for correspondence (e-mail: glauder{at}oeb.harvard.edu)
Accepted 4 October 2005
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Summary |
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Key words: swimming, maneuvering, locomotion, dorsal fin, adipose fin, vortex wake, flow visualization, digital particle image velocimetry, rainbow trout, Oncorhynchus mykiss
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Introduction |
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In spite of these contributions, data on dorsal fin function in swimming
fishes remain scarce in three important areas. First, there is little
information about patterns of dorsal fin use during steady locomotion at
different speeds and during unsteady maneuvering locomotion
(Drucker and Lauder, 2001a;
Standen and Lauder, 2005
), and
synchronized kinematic and electromyographic data are available for only one
teleost species (Jayne et al.,
1996
). Second, we lack empirical hydrodynamic analyses of dorsal
fin function based on experimental investigation of wake momentum flows. Such
an approach is critical to understanding the functional significance of dorsal
fin design in fishes. Third, our knowledge of dorsal fin mechanics in basal
teleost fishes with soft dorsal fins is extremely limited. Previous work on
these clades has focused on morphologically specialized taxa with highly
elongate dorsal fins and with other fins absent or much reduced, such as
certain osteoglossomorph, elopomorph and anguilliform fishes
(Blake, 1980
;
Lindsey, 1978
;
Lissmann, 1961
). We are aware
of no prior empirical study of dorsal fin hydrodynamic function in a teleost
fish possessing generalized soft dorsal fin anatomy.
In this paper, we conduct an experimental hydrodynamic analysis of dorsal
fin function in a representative teleost with a soft dorsal fin, the rainbow
trout (Oncorhynchus mykiss), through the use of quantitative wake
flow visualization. Salmoniform fishes, including trout and salmon, are well
known for high-speed, long-distance swimming powered by body and caudal fin
(BCF) undulation (Webb, 1984),
yet little is known about the role of non-BCF propulsion in this major
taxonomic group. The function of the paired pectoral fins during locomotion in
O. mykiss was examined recently by Drucker and Lauder
(2003
); median fins other than
the tail have been studied in salmonids primarily in the context of
non-locomotor function such as territorial display
(Kalleberg, 1958
;
Keenleyside and Yamamoto,
1962
). The primary goal of the present paper is to characterize
how the dorsal fin in trout is recruited as an ancillary propulsor during
axial locomotion and the extent to which the fin generates propulsive fluid
forces. Specifically, we first describe the kinematics and wake dynamics of
the dorsal fin during steady swimming over a range of speeds and during
unsteady turning maneuvers. Second, we evaluate a previously untested
hypothesis in the literature concerning the functional role of the basal
teleost soft dorsal fin in generating thrust and lateral stabilizing forces.
Finally, we examine hydrodynamic interactions between the tail and the wake
shed by the dorsal fin to assess the possibility that multiple median fins
oscillating in tandem can affect overall propulsive efficiency.
We interpret our results from trout in the light of an earlier study
(Drucker and Lauder, 2001a)
that initiated experimental hydrodynamic study of dorsal fin function in
bluegill sunfish (Lepomis macrochirus) and a previous
three-dimensional kinematic analysis of median fin function in sunfish
(Standen and Lauder, 2005
).
Through a comparison of representative basal and derived teleosts, we seek to
document variation in function of the soft-rayed dorsal fin, the plesiomorphic
portion of the fin retained throughout teleost fish evolution.
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Materials and methods |
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Behavioral observations and wake visualization
Trout swam individually in the center of the working area (28 cmx28
cmx80 cm) of a temperature-controlled variable-speed freshwater flow
tank (600 liters) under conditions similar to those described in our previous
research on salmonids (Drucker and Lauder,
2003; Liao et al.,
2003a
,b
;
Nauen and Lauder, 2002b
). The
swimming behaviors induced were directly comparable with those characterized
in our previous work on sunfish dorsal fins
(Drucker and Lauder, 2001a
).
Steady rectilinear locomotion in trout was elicited at three speeds: 0.5, 1.0
and 2.0 L s1 (range, 942 cm
s1). In addition, fish performed yawing turns in response to
a visual and auditory stimulus as in previous work on sunfish
(Drucker and Lauder, 2001b
).
While trout swam steadily at 0.5 L s1, a
small-diameter wooden dowel was directed into the water approximately 20 cm
lateral to the head to induce yawing maneuvers. The fish's immediate response
to this stimulus and the lateral location of the dowel precluded any
interaction between the dorsal fin wake and the wake shed by the dowel. To
characterize patterns of movement of the dorsal fin during both steady
swimming and maneuvering, fish were imaged simultaneously in lateral and
dorsal aspect using synchronized digital high-speed video cameras (Redlake
Motion Scope PCI 500; San Diego, CA, USA) operating at 250 frames
s1 (1/250 s shutter speed). Review of these light video
recordings revealed general patterns of activity- and speed-dependence of fin
kinematics.
In separate swimming trials, the wake of the dorsal fin was visualized
using digital particle image velocimetry (DPIV). We employed this technique to
obtain empirical, quantitative information about momentum flow in
two-dimensional sections of the fluid moved by the fish's propulsors (as
described in detail by Drucker and Lauder,
1999,
2001b
;
Lauder, 2000
;
Willert and Gharib, 1991
). An
8 W continuous-wave argon-ion laser (Coherent Inc., Santa Clara, CA, USA) was
focused into a thin light sheet (12 mm thick, 16 cm wide) that
illuminated reflective microparticles suspended in the water. Particle motion
induced by fin activity was recorded by imaging the laser sheet with one of
the Redlake video cameras (250 frames s1, 1/1000 s shutter
speed). Wake flow was observed in the frontal (horizontal) plane from a dorsal
perspective by means of a mirror inclined at 45° above the working area. A
second camera synchronously recorded a perpendicular (lateral) reference view,
showing the position of the fish and its fins relative to the visualized
transection of the wake. The horizontal laser plane was positioned at three
heights along the dorsoventral body axis of the fish
(Fig. 1A). This variable
positioning of the laser plane allowed measurement of the structure and
strength of vortices shed by the soft dorsal fin alone during steady swimming
and turning (Fig. 1A, plane 1)
and observation of the tail's interaction with the dorsal fin's wake
(Fig. 1A, plane 2). Trout
occasionally swam with the adipose fin also within the light sheet at plane 2,
providing a simultaneous view of all three dorsal median fins. In its lowest
position (Fig. 1A, plane 3),
the laser plane intersected the tail at mid-fork. Flow patterns within this
plane were used to characterize the structure of the tail's wake and to
estimate caudal-fin swimming forces, which provided a context for interpreting
calculated dorsal fin forces.
Kinematic and hydrodynamic measurements
To quantify temporal and spatial patterns of median fin motion during
steady swimming, selected video frames were analyzed using ImageJ software.
For each of three fish, we measured the mediolateral excursions of all median
fins visible in dorsal aspect within the horizontal laser plane
(Fig. 1A, plane 2).
Specifically, over the course of five consecutive fin beats performed at each
swimming speed, we tracked the position of the trailing edges of the dorsal
and adipose fins, and the position of the leading edge of the caudal fin, in
alternate video frames (i.e. at 8 ms intervals). Tracking movement of the
leading edge of the caudal fin, as opposed to the trailing edge, enabled
assessment of potential hydrodynamic interactions between the anterior portion
of the tail and the dorsal fin wake produced upstream. Body reference points
(pigment spots) at longitudinal positions corresponding to the tips of the
dorsal and adipose fins were also digitized. These data collectively allowed
(1) graphical representation of fin-tip trajectories in excursiontime
plots, with each fin beat cycle comprised of approximately 3050 points;
(2) analysis of the speed dependence of kinematic parameters such as fin beat
frequency and mediolateral fin sweep amplitude; (3) measurement of the phase
lag of oscillatory motion between more anteriorly and posteriorly situated
median fins; and (4) calculation of the Strouhal number, the product of fin
beat frequency and peak-to-peak sweep amplitude divided by swimming speed,
which serves as a theoretical predictor of propulsive efficiency
(Anderson et al., 1998;
Triantafyllou et al.,
1993
).
From DPIV video sequences, 130 swimming events performed by six fish were
reviewed to establish general patterns of water flow in the wake. Of these,
detailed quantitative analysis was restricted to scenes in which fish swam at
a constant speed either during prolonged rectilinear locomotion
(N=933 fin beats per behavior) or immediately before turning
maneuvers (N=14). For the purpose of calculating stroke-averaged
locomotor force, the duration of propulsive fin movement, , was measured
from each swimming sequence. For steady swimming,
was defined as the
stroke period of median fin oscillation (i.e. the interval in ms separating
the position of maximal left or right excursion of the fin tip and the
analogous position in the immediately following stride). For turning, during
which vortical wake structures were generated over the course of a single
half-stroke,
was taken as the duration of dorsal fin abduction and
following adduction to the midline.
Two-dimensional water velocity fields in the wake of trout were calculated
from consecutive digital video images (480 pixelsx420 pixels, 8-bit
grayscale) by means of spatial cross-correlation
(Willert and Gharib, 1991), as
in our previous research (e.g. Drucker and Lauder,
1999
,
2000
,
2001b
;
Lauder and Drucker, 2002
). The
relatively weak wake flows generated by the trout dorsal fin were resolved
using a recursive local-correlation image-processing algorithm
(Hart, 1998
) implemented by
Insight Ultra software (TSI Inc., St Paul, MN, USA; also see
Lauder et al., 2002
). We
measured frontal-plane flow fields that were 710 cm on each side and
comprised nearly 2300 uniformly distributed velocity vectors (i.e. 52
horizontal x 44 vertical, or 30 vectors cm2). Vectors
falling within regions of shadow cast by the fish, or overlying the body
within laser planes close to the illuminated skin surface (e.g.
Fig. 1A, plane 2), were
misrepresentative of actual water flow and were deleted manually from flow
fields. For all swimming behaviors, the mean free-stream flow velocity of the
flume was subtracted from each vector matrix to reveal vortical structures in
the wake and to allow measurement of jet flow structure and strength (for
details, see Drucker and Lauder,
1999
). Vortex circulation was calculated using a custom-designed
computer program. Jet flow velocity was taken as the mean magnitude of vectors
(N=247 on average) comprising the central region of accelerated flow
within the frontal plane. For both steady swimming and turning, jet angle was
defined as the mean orientation of these vectors, measured relative to the
upstream heading of the fish at the onset of the fin stroke. Both jet
measurements were made at the end of median fin adduction, at which time
vortices and associated jet flow were fully developed.
In previous DPIV studies of fish locomotion, we have examined wake flow in
multiple, perpendicular orientations of the laser light sheet (e.g. Drucker
and Lauder, 1999,
2000
), allowing
three-dimensional reconstruction of wake geometry. In the present study,
visualization of the wake was restricted to the horizontal plane; vertically
oriented laser sheets (i.e. in the parasagittal and transverse planes)
projected from below are obstructed by the body of the fish itself and were
therefore not employed. However, earlier DPIV work examining flow within
orthogonally oriented laser planes supports a three-dimensional vortex-ring
wake structure for the median fins of fishes
(Lauder, 2000
;
Liao and Lauder, 2000
;
Nauen and Lauder, 2002a
;
Wolfgang et al., 1999
). On
this basis, we used flow measurements from frontal-plane transections of the
dorsal and caudal fin wakes to estimate vortex-ring morphology and associated
fluid forces generated during locomotion. We assumed that paired vortices
observed in the frontal plane represent approximately mid-line sections of a
toroidal vortex ring. Ring momentum was calculated as the product of water
density, mean vortex circulation and ring area (the latter two measurements
made at the end of the fin stroke). Ring area was taken as
R2, where R is half the distance between
paired vortex centers. Following earlier work
(Milne-Thomson, 1966
),
time-averaged wake force was then computed as the momentum added to the wake
divided by the period of propulsive fin motion. Total force exerted by each
median fin was resolved geometrically into perpendicular components within the
frontal plane (thrust and lateral force) according to the mean jet angle.
Further details of the calculation of wake force magnitude and orientation by
this method can be found in earlier studies
(Dickinson, 1996
;
Dickinson and Götz, 1996
;
Drucker and Lauder, 1999
,
2001a
,
2003
;
Lauder and Drucker, 2002
;
Spedding et al., 1984
).
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Results |
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In contrast to the dorsal fin, the adipose fin of trout exhibits negligible motion independent of the body during steady swimming. Adipose fin height does not change measurably during slow and fast locomotion, and although adipose fin-beat frequency and peak-to-peak fin beat amplitude increase with speed (Fig. 3B,D,F), these kinematic parameters are not significantly different from those of the body at the same longitudinal position (paired t-tests at 0.5, 1.0 and 2.0 L s1; d.f.=4; P=0.21.0). Corrected adipose stroke amplitude remains near zero (<0.1 cm) at all swimming speeds examined (Table 1). Mean trailing-edge amplitude of the caudal fin (uncorrected) measured from 0.52.0 L s1 exceeds that of the dorsal and adipose fins anteriorly by 0.292.15 and 1.341.81 cm, respectively. For all three dorsal median fins, the frequency of mediolateral oscillation shows a direct dependence on swimming speed, and at each speed this frequency shows no significant difference among fins (two-way analysis of variance; speed effect, F2,72=202.89; P<0.001; fin effect, F2,72=0.45; P=0.64; also see Fig. 3; Table 1).
Unlike steady swimming, low-speed turning maneuvers elicited from trout are
characterized by non-periodic dorsal fin activity. At the onset of a turn,
trout erect the dorsal fin and unilaterally abduct it to the side of the body
towards which the experimental stimulus is directed
(Fig. 2E,F). This fin motion is
accompanied by ipsilateral abduction of the pectoral and pelvic fins (also see
fig. 3 in Drucker and Lauder,
2003). Relatively rapid fin adduction follows; for the dorsal fin,
the total duration of propulsive fin motion is considerably less than that
during steady swimming (Table
2). Together with low-amplitude bending of the trunk, these median
and paired fin motions cause both yawing rotation (mean, 13 deg.
s1; Drucker and Lauder,
2003
) and translation of the body away from the source of the
stimulus.
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Wake dynamics
The structure and strength of the wake produced by the dorsal fin of trout
vary markedly with swimming behavior. During steady, straight-ahead locomotion
at low speed (0.5 L s1), each complete stroke of
the dorsal fin generates a distinct wake visible within the frontal plane as
paired counter-rotating vortices with interposed jet flow (e.g. structure 2 in
Fig. 4). The development of
this wake morphology involves (1) excursion of the dorsal fin from a maximally
abducted position to a corresponding contralateral position, which entrains
jet flow from one side of the body to the other (structure 3,
Fig. 4A) and generates a free
vortex at the downstream edge of the jet (partially obscured by body
reflection in Fig. 4A; cf.
Drucker and Lauder, 2001a);
(2) rapid stroke reversal and return of the fin to its original position,
during which a second free vortex of opposite-sign rotation is shed and the
jet is strengthened (structure 3, Fig.
4B). This subsequent fin motion additionally initiates the jet
flow of the next half-stroke (structure 4,
Fig. 4B). During continuous
dorsal fin oscillation at 0.5 L s1, multiple vortex
pairs persist within the horizontal laser plane, with their associated fluid
jets alternating to the left and right sides of the body. Over time, these
structures migrate laterally, pass through the laser plane and ultimately lose
their paired-vortex appearance (structure 1,
Fig. 4).
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During steady swimming at higher speed (1.0 L
s1), the dorsal fin continues to shed a wake comprised of
both vortical and linear (i.e. jet) flows
(Fig. 5). The mean velocity and
orientation of the wake jet do not change significantly between 0.5 and 1.0
L s1 (unpaired t-tests; d.f.=21;
P=0.70 and 0.99, respectively;
Table 2). However, the dorsal
fin stroke is performed more rapidly at 1.0 L s1
(mean difference in stroke duration, 86 ms), leading to a marked increase in
fluid force production (Table
2). In addition, there is a notable difference in the geometry of
the wake generated during slow and fast swimming. At 1.0 L
s1, the vortex shed at the end of each half-stroke coalesces
with the same-sign vortex produced at the onset of the next half-stroke
(forming a `stoppingstarting' vortex; cf.
Drucker and Lauder, 2001a).
The wake at this speed is therefore comprised of a continuous, nearly linear
trail of counter-rotating vortices aligned with the body axis
(Fig. 5), as opposed to
discrete vortex pairs on opposite sides of the body (cf.
Fig. 4). Trout wake flow
patterns at 0.5 and 1.0 L s1 are schematically
summarized and compared in Fig.
8A,B.
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Lateral oscillations of the trailing edge of the dorsal fin and the leading edge of the caudal fin are approximately one-quarter cycle out of phase with each other during steady rectilinear locomotion at 1.0 L s1 (phase lag=99±4 ms, 114±3°, means ± S.E.M.; Fig. 9AE). As a result, the leading edge of the caudal fin traces a path directly through the centers of the vortices shed by the dorsal fin and passes through the developing lateral jet flows formed between vortex centers (Fig. 9F).
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Discussion |
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A second notable pattern in dorsal fin recruitment by trout is evident in
the gait transition that occurs between low- and higher-speed swimming. The
range of locomotor behaviors exhibited by aquatic vertebrates can be
partitioned into functional categories according to the anatomy and kinematics
of the propulsors involved. Webb
(1984) proposed several such
categories for fishes including `median and paired fin' (MPF) propulsion and
`body and caudal fin' (BCF) locomotion. The idealized gait progression
expressed with increasing swimming speed is MPF
BCF
(Webb, 1994
, p. 11;
Webb and Gerstner, 2000
). This
influential scheme has inspired much research on swimmers at the extremes of
the gait continuum, but only relatively recently has close attention been
given to swimming modes involving a combination of the MPF and BCF gaits.
In this paper, we document, in trout swimming steadily at low to
intermediate speeds, the combined use of dorsal fin oscillation and axial
undulation (Figs 3A,C,
9F) without continuous
concomitant pectoral fin motion. Simultaneous recruitment of anterior median
fin propulsion together with body and caudal fin locomotion define an aquatic
gait we term MBCF. A similar fin-use pattern has been observed for
balistiform swimmers at high speed
(Korsmeyer et al., 2002;
Wright, 2000
). This gait is
distinct from the MPFBCF swimming mode described for certain
ostariophysan fishes, in which pectoral, dorsal and anal fin beating occurs
together with `small-amplitude' caudal fin undulation during forward swimming
(Webb and Gardiner Fairchild,
2001
). For trout, the range of steady swimming speeds over which
the pectoral fins are recruited is compressed (00.5 L
s1), such that MPF locomotion is restricted largely to
hovering in still water (Drucker and
Lauder, 2003
), and forward swimming is characterized by the gait
transition from MBCF to BCF propulsion (which occurs just below 2.0
L s1 for fish 20 cm in length). Detailed study of
paired and median fin motion in other clades lacking specialized swimming
modes will contribute further to our understanding of the diversity of
locomotor behaviors employed by teleost fishes.
The observation of periodic dorsal fin oscillation in trout raises an
important functional question: does the fin move actively and independently
from the body to which it is attached? The soft dorsal fin of teleost fishes
is invested with segmentally arranged muscles, distinct from the myomeric
muscle mass, that are capable of controlling mediolateral motion of the
propulsive fin surface. On both sides of the body, dorsal inclinator muscles
arise from the fascia overlying the epaxial myomeres and insert onto the
lateral base of each flexible dorsal fin ray, thereby enabling fin abduction
(Geerlink and Videler, 1974;
Jayne et al., 1996
;
Winterbottom, 1974
).
Electromyographic recordings from the dorsal inclinator muscles of bluegill
sunfish reveal discrete activity patterns during both steady and unsteady
swimming behaviors (Jayne et al.,
1996
). Although the recording of such activity has not yet been
attempted for other species, we expect that the dorsal fin of trout also has
the capacity to serve as an active control surface during locomotion. On the
basis of observed locomotor kinematics, we may infer the extent to which the
dorsal fin indeed moves as a result of independent muscular control. If the
dorsal inclinator muscles were inactive during steady forward swimming, then
lateral movement of the body would cause passive deflection of the dorsal fin
in the opposite direction (Jayne et al.,
1996
). In this scenario, one would expect a substantial phase lag
in the oscillatory motion of the dorsal fin and body (i.e. the maximal lateral
excursion of the dorsal fin tip during each half-stroke would be delayed
relative to that of the body at the same longitudinal position). Since this
phase lag is negligible in trout (Fig.
3A,C,E), we predict that the dorsal inclinator muscles are active
during rectilinear locomotion, functioning minimally to stiffen the dorsal fin
and resist its tendency to bend passively as the body sweeps laterally through
the water. If the inclinators served only to stiffen the dorsal fin, however,
one would expect that the amplitude of side-to-side motion of the fin and body
would be nearly identical. Although this pattern is seen for the adipose fin
(Fig. 3B,D,F), which lacks
intrinsic musculature, the dorsal fin's stroke amplitude exceeds that of the
body at all but the highest speed studied
(Fig. 3A,C,E). In addition,
during turning maneuvers, the dorsal fin is capable of extreme flexion (Figs
2F,
7) at any point during the
body's undulatory period. We predict therefore that the dorsal fin of trout is
under active muscular control during both steady and unsteady swimming, which
allows the fin to act as a propulsor independent of the underlying body. This
prediction may be tested in future work through electromyographic recording
from the dorsal inclinators and observation of locomotor kinematics following
chronic paralyzation of fin musculature.
Hydrodynamic function of the trout dorsal fin
Functions traditionally ascribed to the dorsal fin of basal teleost fishes
have been largely non-propulsive. In the sister group to Teleostei, the highly
elongate, undulatory dorsal fin of amiiform fishes plays a definitive role in
thrust production during locomotion
(Breder, 1926). However, the
plesiomorphic teleostean dorsal fin, which has a short base of attachment to
the body, has been regarded as serving more hydrodynamically passive roles,
such as acting as a static keel or body stabilizer during rectilinear swimming
and as a fixed pivot point for body rotation during turning maneuvers
(Aleev, 1969
;
Harris, 1936
). These proposed
functions have persisted in the literature
(Helfman et al., 1997
, p. 168)
in the absence of experimental data. Using kinematic analysis together with
quantitative flow visualization, we test the hypothesis that the basal teleost
dorsal fin morphology typified by trout plays a non-propulsive role in steady
and unsteady locomotion.
The impact of an oscillating body on wake structure and associated fluid
force is predicted by the Strouhal number, St (defined in Materials
and methods). Experimental studies of foils in steady forward motion and a
combination of heaving and pitching motion
(Anderson, 1996;
Anderson et al., 1998
) reveal
that when St<0.2, a loosely organized wake forms that generates
very low or negative thrust. In this case, one observes either a `wavy wake'
with no distinct vortex formation or a drag-producing Kármán
street characterized by staggered, counter-rotating vortices and a central
region of jet flow oriented upstream that reduces the momentum of the incident
flow. As St rises to within the range of 0.20.5, wake
structure and force change dramatically: a reverse Kármán street
develops that generates a strong thrust force
(Anderson et al., 1998
). This
wake trail is comprised of paired vortices with opposite-sign rotation and a
downstream-directed momentum jet between each vortex pair
(Lighthill, 1975
;
Triantafyllou et al., 1993
,
2000
;
von Kármán and Burgers,
1935
; Weihs,
1972
). Aside from a recent study of dorsal fin function in sunfish
(Drucker and Lauder, 2001a
),
only the tail has been considered previously in calculations of median-fin
Strouhal number. For rainbow trout, tail St shows a general decline
with increasing swimming speed
(Triantafyllou et al., 1993
;
based on calculations from Webb et al.,
1984
); similar results have been obtained for eels
(Tytell, 2004
). In the present
study, we find a reduction in mean St for the oscillating dorsal fin
of trout from 0.37 to 0.21 as speed increases from 0.5 L
s1 (mean 9.8 cm s1) to 1.0 L
s1 (mean 19.6 cm s1)
(Table 2). This reduction in
St to the lower limit of the range of predicted peak propulsive
efficiency is reflected by a decrease in dorsal fin beat amplitude as speed
increases to 1.0 L s1
(Fig. 3A,C). On the basis of
these kinematic results, we reject the hypothesis presented above and predict
that dorsal fin oscillation in trout over low to intermediate swimming speeds
contributes to overall fluid force production for locomotion.
Further evidence to support this prediction comes from analysis of dorsal
fin wake patterns in trout, which show a small but significant downstream
(thrust) component of the central vortex jets
(Table 2; Figs
4,
5). The dorsal fin of trout
generates approximately 7.7% of the thrust generated by the tail at a swimming
speed of 1.0 L s1. However, the most remarkable
aspect of trout dorsal-fin hydrodynamic function is the large lateral forces
generated by the dorsal fin at all swimming speeds at which a significant wake
is observed. The trout dorsal fin generates five to six times as much
laterally directed force as thrust, and the central vortex jet is directed at
a mean angle of 75° to the body (Table
2). Comparative studies of the hydrodynamic function of fish fins
have shown that the existence of a large lateral component of fin forces
appears to be a general phenomenon (Drucker and Lauder,
1999,
2002b
;
Lauder and Drucker, 2002
;
Lauder et al., 2003
). But no
other median fin in any behavior studied to date has shown the extreme lateral
force orientation exhibited by the trout dorsal fin. The occurrence of such
lateral forces during routine rectilinear swimming clearly indicates that
locomotion previously considered to be controlled exclusively by the body and
caudal fin also involves significant anterior median fin activity. The
possible impact that dorsal fin forces have on the overall force balance
during locomotion is considered further below.
Comparisons to sunfish dorsal fin function
We have previously analyzed the dorsal fin wake in sunfish using techniques
and swimming speeds directly comparable to those of this study
(Drucker and Lauder, 2001a).
Sunfish, unlike trout, possess an anterior spiny portion of the dorsal fin
that supports the posterior soft-rayed section
(Fig. 1). During steady
swimming at approximately 1 L s1, the sunfish soft
dorsal fin contributes 12.1% of the total thrust force generated by the median
and paired fins. At this speed, the lateral component of dorsal fin force is
twice the thrust force component, and the mean jet angle is 62°. In both
trout and sunfish, then, the soft dorsal fin plays a significant role in
steady propulsion and generates a large lateral force with each fin beat
(Fig. 8B,D). However, in trout,
this lateral force is approximately three times greater, relative to thrust
force, than in sunfish. This proportionately greater lateral force generated
by trout dorsal fins may be a function of the elongate, roughly cylindrical
body shape of trout, a morphology with a greater susceptibility to roll than
the gibbose and laterally flattened shape of sunfish. The soft dorsal fin must
thus be viewed as an integral part of routine swimming in teleost fishes,
generating both thrust and lateral (stabilizing) forces with each locomotor
stroke cycle. Steady locomotion, at least in the species studied to date,
necessarily involves force generation both by the dorsal fin and by the body
and caudal fin.
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The roll moment induced by dorsal fin activity in trout leads to a
prediction about the function of the anal fin that is amenable to experimental
test. Since the attachment of the anal fin is ventral to the body's center of
mass, anal fin wake flow is expected to contain vortex structures that produce
lateral jet flows to the same side of the body as those of the dorsal
fin. Same-side jet flows would result in opposing torques and
contribute to a balance of roll forces. Based on the results of this study, we
suggest that the distinction between MPF propulsion and BCF propulsion in
fishes obscures the important role of multiple propulsors, including the tail
and other median fins, which act in a coordinated fashion to stabilize the
body during steady rectilinear locomotion (also see
Lauder, 2005).
In sunfish, we demonstrated previously that the tail passes through the
wake of the dorsal fin and experiences an altered hydrodynamic environment
relative to free-stream flow (Drucker and
Lauder, 2001a). Depending on the structure of this wake, the
kinematic phase lag between caudal and dorsal fins and the relative amplitudes
of lateral motion, the caudal fin could experience enhanced thrust as a result
of intercepting dorsal fin vortices. During steady swimming at low speed, the
tail of sunfish moves through a staggered array of dorsal fin vortices whose
rotational flow is hypothesized to increase incident velocity over the tail
and to enhance same-sign vorticity bound to the tail (see figs 7, 10 in
Drucker and Lauder, 2001a
). In
trout, the dorsal fin wake trail at 1 L s1 is
generally similar to that of sunfish, taking the form of a reverse
Kármán street (Fig.
8B,D). Vortices within the trout dorsal fin wake, however, are
more linearly arranged than in the wake of sunfish; hence, sinusoidal
excursions of the trout tail cut through the vortex centers left behind the
dorsal fin (Fig. 9F). During
steady swimming at 1 L s1, the tail encounters a
dorsal fin wake flow with a downstream component increased over free-stream
flow velocity by an average of 35% and 3%, respectively, in sunfish and trout.
This increased velocity could theoretically augment drag forces but, depending
on the phase and angle of tail motion relative to the incident flow, may
instead reinforce developing circulation around the tail or enhance attached
separation of the tail's leading-edge vortex (cf.
Akhtar and Mittal, 2005
;
Mittal, 2004
) and thereby
enhance overall tail thrust production.
A number of recent experimental studies of foils heaving and pitching in a
variety of wake flow patterns have addressed the effect of foilflow
interactions on foil thrust and efficiency
(Anderson, 1996;
Beal, 2003
;
Lewin and Haj-Hariri, 2003
;
Read et al., 2003
;
Triantafyllou et al., 1993
,
2000
). Although most of these
studies have focused on foils encountering drag wakes, several important
conclusions have emerged that are relevant to understanding possible
hydrodynamic interactions between the caudal and dorsal fins. Thrust generated
by foils encountering an oscillating incident flow is maximized when there is
a phase lag of
100° between the foil and the flow. At this phase
difference, lateral motion of the foil's leading edge is opposed by lateral
motion of the oncoming fluid (Beal,
2003
). This increases the effective angle of attack of the foil.
In addition, motion of the foil's leading edge in opposition to oncoming flow
may increase the duration of leading-edge vortex attachment to the tail fin,
delaying stall and hence increasing mean lift force over the duration of a
tail beat. Enhancement of mean circulation could also occur as a result of
increased flow velocity over the tail. Fig.
9E,F shows that the tail of trout undergoes lateral motions that
are phase-delayed relative to, and directly opposed by, lateral flows
generated by the dorsal fin in the manner described by Beal
(2003
) for foils generating
peak thrust. Understanding the precise effect of incident wake structure on
tail thrust magnitude awaits detailed visualizations of fluid motion on the
tail surface and computational studies of thrust calculated from flow
structure and tail and dorsal fin kinematics. But existing experimental data
from both trout and sunfish demonstrate that the caudal fin, when oscillating
in tandem with the dorsal fin, experiences a flow environment that is markedly
different from the free-stream flow lateral to the fish body.
Comparison of dorsal fin function in sunfish and trout additionally reveals
that the species differ considerably in the magnitude of locomotor force
generated per unit dorsal fin area, with trout generating substantially
smaller relative forces. During steady swimming at 1 L
s1, the sunfish soft dorsal fin generates 6.3 times more
thrust and 2.4 times more lateral force per unit fin area than the trout
dorsal fin. During slow turning, sunfish exert 65 times more thrust per area
and 3.6 times more lateral force per area than trout
(Table 2; fig. 20 in
Lauder and Drucker, 2004).
Functional design of fish median fins
Significant evolutionary changes in median fin structure within ray-finned
fishes have resulted in a diversity of dorsal, anal and caudal fin
configurations (Drucker and Lauder,
2001a; Lauder and Liem,
1983
; Rosen,
1982
). Five key areas of diversity in median fin design are (1)
the presence or absence of an anterior spiny dorsal fin, (2) the extent of
separation of the spiny and soft dorsal fins (the two can be widely separated
or attached, as in sunfish), (3) the distance between the trailing dorsal fin
margin and the leading edge of the caudal fin, (4) the size and kinematic
versatility of the anal fin and (5) the presence or absence of an adipose fin
on the dorsal midline. Empirical quantitative data on dorsal fin hydrodynamic
function are only available for two species to date (trout and sunfish), and
it is thus premature to speculate on broader functional patterns. But current
wake visualization data do lead to a number of hypotheses regarding the
functional design of median fins that could be tested through future
experimental and computational hydrodynamic studies in a broader array of
species.
First, the propulsive force generated by the dorsal fin per unit fin area is expected to be greater in species with a dorsal fin design like that of sunfish as opposed to that of trout. Stabilization of the leading edge of the soft dorsal fin by anterior spiny elements (Fig. 1B) may permit more rapid lateral fin motion around the soft dorsal fin's leading edge and larger momentum transfers to the water. Without leading-edge stabilization, soft dorsal fin musculature may be required to stiffen the fin substantially in addition to providing force for lateral oscillation. Coactivation of right- and left-side inclinator muscles for soft dorsal fin stiffening may greatly reduce the magnitude of fin force per unit area that can be generated for propulsion.
Second, constructive hydrodynamic interactions among median fins may be
more prevalent in species with more closely apposed fins. Vortices shed by the
soft dorsal fin carry fluid energy downstream, which may be absorbed by the
tail to augment thrust according to the tail's proximity to and phase
relationship with the upstream propulsor. When the distance between the
trailing edge of the soft dorsal fin and the leading edge of the tail is
relatively small, as in short-bodied species like sunfish
(Fig. 1B), dorsal fin vortices
encountered by the tail can enhance circulation around the tail and
potentially augment caudal fin thrust
(Drucker and Lauder, 2001a).
By contrast, when this inter-fin distance is relatively large, as in elongate
fishes like trout (Fig. 1A),
the energy of dorsal fin vortices may be reduced by the time these wake
structures are intercepted by the tail so that constructive hydrodynamic
interactions are much less likely.
Third, the anal fin should exhibit in-phase movement with the dorsal fin
(i.e. simultaneous ipsilateral excursion) in species subject to roll moments
around the body's center of mass resulting from laterally directed dorsal fin
forces (Fig. 10). A recent
kinematic analysis of dorsal and anal fin motion in sunfish
(Standen and Lauder, 2005)
supports this hypothesis. Experiments simultaneously quantifying the wake of
dorsal and anal fins in a variety of species would further clarify functional
interdependencies between these median fins.
Finally, the enigmatic adipose fin present in many euteleostean fishes
(Fig. 1A) remains of uncertain
function. Data presented here confirm that it shows negligible movement
independent of the body, but wake visualization does clearly reveal a narrow,
sinusoidal drag wake downstream of the adipose fin that is intercepted by the
tail. The hydrodynamic function of such a drag wake remains incompletely
understood, particularly in regard to its effect on flow at the tail surface.
On the basis of computational studies of tandem flapping foils
(Akhtar and Mittal, 2005;
Mittal, 2004
), we speculate
that the adipose fin's drag wake influences the flow environment around the
caudal fin, causing an augmentation of thrust through enhancement of the
tail's leading-edge vortex. This hypothesis is probably best addressed
via a combination of computational fluid dynamic simulations of flow
over the tail and direct measurement of forces on a tandem pair of
computer-controlled heaving and pitching foils undergoing realistic median fin
motions. Reimchen and Temple
(2004
) have recently shown
that in some trout the tail beat amplitude increases (mean 8%) when the
adipose fin is removed. This apparent functional compensation by the tail
points towards a definitive role of the adipose fin in locomotor force
production. The adipose fin, present in so many euteleostean fishes, remains
an intriguing aspect of median fin design deserving of additional study.
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