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Locomotor function of the dorsal fin in teleost fishes: experimental analysis of wake forces in sunfish

Eliot G. Drucker^1,* and George V. Lauder²

¹ Department of Ecology and Evolutionary Biology, University of California, Irvine, CA 92697, USA and
² Museum of Comparative Zoology, Harvard University, 26 Oxford Street, Cambridge, MA 02138, USA

View larger version (18K): [in a new window]   Fig. 1. Interrelationships among selected orders of teleost fishes to illustrate variation in dorsal fin design (see Lauder and Liem, 1983). Basal teleosts (e.g. Clupeiformes and Salmoniformes) typically possess a single, soft-rayed dorsal fin (shown in red). Most acanthopterygian fishes have, in addition, a spiny dorsal fin (shown in blue) positioned anterior to the soft-rayed portion. The two fins may be either contiguous (e.g. Perciformes) or separated by a gap (e.g. Atheriniformes). In this study, we investigate the wake generated by the soft dorsal fin of Lepomis macrochirus, a representative perciform fish, to explore the functional role of this conserved feature of teleostean locomotor anatomy. Fish images modified from Nelson (Nelson, 1994).

View larger version (35K): [in a new window]   Fig. 2. Experimental approach for visualizing the median fin wake. (A) Within the region bound by the rectangle, lateral video images of bluegill sunfish were recorded during steady swimming at both low and high speed and during unsteady turning maneuvers. (B) Representative lateral-view reference image showing the dorsal lobe of the tail and the trailing edge of the soft dorsal fin intercepted by a horizontal (frontal-plane) laser sheet seen on edge as a white stripe. (C) Synchronized dorsal-view video of this laser sheet allowed analysis of wake flow using digital particle image velocimetry (see Materials and methods). (D) To study the wake structures and fluid forces generated by the soft dorsal and caudal fins, flow was analyzed within laser planes at three heights (1–3). Fin movements and the resulting fluid flow within these planes are illustrated in Figs3–8 and Fig.10.

View larger version (39K): [in a new window]   Fig. 3. Frontal-plane water velocity vector fields in the vicinity of the dorsal fin during swimming by sunfish at 0.5Ls-1 (10.5cms-1), where L is total body length. (A) Laser plane slightly above position 1 (see Fig.2D) to illuminate the leading edge of the spiny dorsal fin (several fin spines are visible, each of which casts a discrete shadow) and the anterior portion of the soft dorsal fin (at right). (B) Laser plane at position 1 intersecting the trailing edge of the soft dorsal fin. At this low swimming speed, propulsion is achieved solely by oscillation of the paired pectoral fins (anterior to the field of view); the dorsal fin is not observed to oscillate. At a gross level, incident flow encountering the spiny dorsal fin (A) remains unchanged in orientation and velocity when measured downstream of the soft dorsal fin (B). Scales: arrow, 20cms-1; bar, 1cm.

View larger version (91K): [in a new window]   Fig. 4. Representative flow fields in the wake of the oscillating soft dorsal fin of sunfish during steady swimming at 1.1Ls-1, where L is total body length. A–D show wake flow patterns within the frontal-plane laser sheet intersecting the middle of the soft dorsal fin (Fig.2D, position 1) for two consecutive fin half-strokes. The direction of fin motion is indicated by large solid-line arrows. Free-stream velocity (23.1cms-1) from left to right has been subtracted from each velocity vector to reveal vortical wake structures. Schematic illustrations of these structures are given in E–H (observed vortices and fluid jets are represented by dashed-line arrows). At this relatively high swimming speed, the soft dorsal fin’s activity causes substantial deflection and acceleration of the incident flow (cf. Fig.3). (A) As the fin sweeps medially (here at the beginning of a half-stroke), a strong center of vorticity is generated at the fin’s trailing edge, while opposite-sign vorticity bound to the fin develops upstream. These two rotational flows can be seen converging on the concave surface of the dorsal fin. Note that the jet and clockwise vortex at the right side of this panel were developed during the previous half-stroke in the opposite direction. (B) At the end of the half-stroke, vorticity is released from the trailing edge of the fin and shed into the wake as a free vortex (see counterclockwise flow). Vorticity previously attached to the anterior portion of the fin migrates downstream to contribute to new trailing edge vorticity (clockwise flow). (C) On the return half-stroke, trailing edge vorticity is strengthened and contributes to developing jet flow. (D) By the end of the return stroke, a second vortex has been shed into the wake (see clockwise flow), while opposite-sign, bound vorticity develops at the fin’s trailing edge. Each complete fin stroke therefore creates a pair of free counterrotating vortices (I and II+III) with a central region of jet flow. Over repeated cycles of soft dorsal fin oscillation, a staggered trail of linked vortices is formed, with downstream jets alternating on the left and right sides of the body. From the momentum of this reverse von Kármán vortex street, stroke-averaged wake forces for propulsion can be calculated. Note that the vortices labeled I–IV in E–H are directly comparable with those illustrated for turning (see Fig.5F,G). I, starting vortex of half-stroke 1; II, stopping vortex of half-stroke 1; II+III, stopping vortex of half-stroke 1 combined with same-sign starting vortex of half-stroke 2; IV, stopping vortex of half-stroke 2. Scales for A–D: arrow, 10cms-1; bar, 1cm.

View larger version (103K): [in a new window]   Fig. 5. A low-speed turning maneuver by a sunfish illustrating the propulsive roles of the paired and median fins. In light-video images (A–C), arrows signify the average orientation of jet flow developed by each fin sequentially during the turn. (A) In response to a stimulus issued on the left side of the fish (i.e. at the bottom of the panel), the ipsilateral or ‘strong-side’ pectoral fin abducts, generating a strong laterally oriented wake flow that rotates the body around the center of mass. (B) The contralateral ‘weak-side’ pectoral fin subsequently adducts, creating a posteriorly directed fluid jet that initiates forward translation of the body. Details of wake flow produced by the pectoral fins were presented in an earlier study (Drucker and Lauder, 2001). Near the end of the turn (B,C), the soft dorsal fin abducts independently of body bending and generates an obliquely oriented fluid jet. Flow fields in the wake of the soft dorsal fin during turning are presented in D and E for a frontal-plane laser sheet in position 1 (see Fig.2D). Large solid-line arrows indicate the direction of fin motion. Free-stream velocity of 0.5Ls-1, where L is total body length, or 10.5cms-1, from left to right has been subtracted from each vector. Schematic representations of observed wake structures are shown in F and G. (D) During abduction of the dorsal fin, a free vortex is shed from the trailing edge (shown as counterclockwise flow), while opposite-sign vorticity develops at the fin tip (cf. Fig.4B). (E) Upon return of the fin towards the body midline, bound vorticity is shed into the wake to form a second free vortex (cf. Fig.4C). The momentum of these paired vortices and associated jet flow on the strong side of the body is not balanced by subsequent fin abduction to the opposite side of the body as during steady swimming (Fig.4). The reaction force acting on the soft dorsal fin posterior to the center of mass of the body serves the dual function of slowing initial pectoral-fin-induced body rotation and helping to propel the animal forward away from the stimulus. CM, center of mass of the body (located at 0.36L posterior to the snout) (after Webb and Weihs, 1994). Light-video images in A–C are modified from previous work (Drucker and Lauder, 2001). Scales for D and E: arrow, 10cms-1; bar, 1cm. Vortex labels in F and G are defined in Fig.4.

View larger version (56K): [in a new window]   Fig. 6. Kinematic patterns for the soft dorsal fin (D) and tail fin (T) oscillating in tandem during steady swimming at 1.1Ls-1, where L is total body length. A–D show video images of the two fins moving within a frontal-plane laser sheet (Fig.2D, position 2) over the course of one complete stroke cycle. Digitizing such images allowed measurement of temporal and spatial patterns of fin tip excursion. In E, left–right movements of the trailing edges of the soft dorsal fin and the dorsal lobe of the tail are plotted against time for two consecutive stroke cycles. Although both fins oscillate at a frequency of 2.5Hz, motion of the tail lags behind that of the dorsal fin by an average of 121ms, or 30% of the stroke cycle. The abduction amplitude of the tail on each side of the body exceeds that of the dorsal fin by 0.51cm on average, a difference corresponding to 19% of the tail’s total sweep amplitude.

View larger version (65K): [in a new window]   Fig. 7. Sinusoidal paths described by the soft dorsal fin and dorsal lobe of the tail within the horizontal plane (Fig.2D, position 2) during steady swimming at 1.1Ls-1, where L is total body length. Flow fields generated separately by each fin are illustrated in Fig.4 and Fig.8. Vortices shed by the trailing edge of the soft dorsal fin are represented schematically, but are located in positions determined by analysis of DPIV videos. By virtue of phase-delayed motion and a larger sweep amplitude (Fig.6), the caudal fin is positioned to intercept wake vortices generated by the dorsal fin.

View larger version (72K): [in a new window]   Fig. 8. Representative flow fields in the wake of the oscillating caudal fin of sunfish during steady swimming at 1.1Ls-1, where L is total body length. Flow patterns within the frontal-plane laser sheet intersecting the tail at mid-fork (Fig.2D, position 3) are shown for the early stages of two consecutive fin half-strokes. The direction of tail fin motion is indicated by large white arrows. Free-stream velocity (24.7cms-1) from left to right has been subtracted from each velocity vector to reveal vortical wake structures. In general, the wake generated by the tail closely resembles that produced separately by the soft dorsal fin upstream (cf. Fig.4A,C). Each half-stroke generates vorticity at the trailing edge of the fin that is ultimately released into the wake (counterclockwise flow in A and B). Opposite-sign vorticity attached to the fin (in the upper left-hand corner of A) migrates to the trailing edge over the course of the stroke period (visible at the tip of the fin in B). Repeated cycles of caudal fin oscillation generate a reverse von Kármán vortex street. Scales: arrow, 10cms-1; bar, 1cm.

View larger version (25K): [in a new window]   Fig. 9. Summary of stroke-averaged locomotor forces generated by three fin systems in sunfish. Each force is reported as mean ± S.E.M. (N=6–11 fin beats) with the corresponding percentage of total force generated by all fins given in parentheses. (A) Thrust produced during steady swimming at 1.1Ls-1, where L is total body length. Dorsal and caudal fin forces are calculated from the momentum of three frontal-plane vortices developed during each complete fin stroke period (see Discussion; cf. Table1). Pectoral fin force is the mean reaction force experienced by both left and right paired fins together over the downstroke–upstroke period (from Drucker and Lauder, 1999). (B) Lateral force generated during turning following steady swimming at 0.5Ls-1. Since turning involves non-periodic fin motion, mean forces are calculated over the duration of the half-stroke. Pectoral force is for the strong-side fin (from Drucker and Lauder, 2001). The substantial contribution of the soft dorsal fin to locomotor force (12% thrust and 35% lateral force) supports an active role for this fin in propulsion. In general, the observed partitioning of force among fins highlights the ability of teleost fishes to use multiple fins simultaneously and independently during locomotion. CM, center of mass of the body (positioned according to Webb and Weihs, 1994).

View larger version (11K): [in a new window]   Fig. 10. Constructive wake interaction between the soft dorsal fin (D) and the dorsal lobe of the tail (T) during steady swimming at 1.1Ls-1, where L is total body length. Silhouettes of the two fins within a frontal-plane laser sheet (Fig.2D, position 2) are shown moving over the course of one stroke cycle. The direction of fin movement is indicated by solid-line arrows. Vortices observed in the raw DPIV video recording are indicated by dashed lines. Vortex a is shed as the soft dorsal fin sweeps laterally (A,B) and migrates downstream during the development of an analogous tail vortex b (C). As the tail completes its stroke, the two counterclockwise-rotating vortices coalesce, forming a single larger downstream vortex c (D). The process illustrated in A–D is repeated on both sides of the body to yield the tail’s reverse von Kármán street wake (cf. Fig.8). Reinforcement of developing circulation around the tail through interception of the dorsal fin’s vortices is proposed as a mechanism for enhancing thrust.