© 2002 by The Society for Integrative and Comparative Biology
Experimental Hydrodynamics of Fish Locomotion: Functional Insights from Wake Visualization1
1 Department of Ecology and Evolutionary Biology, University of California, Irvine, California 92697
2 Museum of Comparative Zoology, Harvard University, 26 Oxford St., Cambridge, Massachusetts 02138
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Despite enormous progress during the last twenty years in understanding the mechanistic basis of aquatic animal propulsion—a task involving the construction of a substantial data base on patterns of fin and body kinematics and locomotor muscle function—there remains a key area in which biologists have little information: the relationship between propulsor activity and water movement in the wake. How is internal muscular force translated into external force exerted on the water? What is the pattern of fluid force production by different fish fins (e.g., pectoral, caudal, dorsal) and how does swimming force vary with speed and among species? These types of questions have received considerable attention in analyses of terrestrial locomotion where force output by limbs can be measured directly with force plates. But how can forces exerted by animals moving through fluid be measured? The advent of digital particle image velocimetry (DPIV) has provided an experimental hydrodynamic approach for quantifying the locomotor forces of freely moving animals in fluids, and has resulted in significant new insights into the mechanisms of fish propulsion. In this paper we present ten "lessons learned" from the application of DPIV to problems of fish locomotion over the last five years. (1) Three-dimensional DPIV analysis is critical for reconstructing wake geometry. (2) DPIV analysis reveals the orientation of locomotor reaction forces. (3) DPIV analysis allows calculation of the magnitude of locomotor forces. (4) Swimming speed can have a major impact on wake structure. (5) DPIV can reveal interspecific differences in vortex wake morphology. (6) DPIV analysis can provide new insights into the limits to locomotor performance. (7) DPIV demonstrates the functional versatility of fish fins. (8) DPIV reveals hydrodynamic force partitioning among fins. (9) DPIV shows that wake interaction among fins may enhance thrust production. (10) Experimental hydrodynamic analysis can provide insight into the functional significance of evolutionary variation in fin design.
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The study of animal functional morphology has as a central objective to clarify the physical mechanisms underlying organismal behavior. For most animals, stabilization and propulsion of the body during locomotion are behaviors with critical importance throughout life, playing a central role in prey capture, predator avoidance, reproduction and migration. A biomechanical approach to the study of locomotor function is ultimately concerned with the question of how propulsive forces are generated. For terrestrial animals, devices such as force plates have been used successfully to measure the forces applied by the limbs directly to the ground during locomotion (e.g., Cavagna, 1975
; Biewener and Full, 1992; Roberts et al., 1998). For animals that move through fluids, however, such force transducers are not readily applicable, and alternative approaches are required for investigating locomotor function.
In studying the mechanics of locomotion by animals in fluids, two levels of analysis are required: musculoskeletal and hydrodynamic. At the first level, one asks how a propulsor is built and how it moves during locomotion. For swimming animals, there has been extensive study of the anatomy and kinematics of aquatic propulsors (recent work includes Geerlink, 1983; Videler, 1993; Gibb et al., 1994; Drucker and Jensen, 1996; Gillis, 1996; Domenici and Blake, 1997; Long et al., 1997; Walker and Westneat, 1997; Fish, 1998), as well as description of their neuromuscular control (Grillner and Wallen, 1984; Eaton et al., 1988; Jayne and Lauder, 1995; Wardle et al., 1995; Westneat and Walker, 1997). These data provide important information about the internal mechanisms by which swimming force may be generated. In addition, in vitro study of muscle physiology allows direct measurement of the mechanical forces available for propulsion (Altringham and Johnston, 1990; Luiker and Stevens, 1993; Rome et al., 1993; Coughlin, 2000). Indeed, most experimental work on the question of how animals swim has employed an approach focusing on musculoskeletal mechanics.
At the second level of analysis, one asks how the propulsor influences fluid in its wake. Although analysis of internal muscular forces contributes to an overall understanding of the locomotor mechanism, ultimately these mechanical forces must be transmitted to the fluid surrounding the animal for propulsion to occur. By examining the morphology and momentum of the wake shed by swimming organisms, it is possible to estimate the external forces produced during aquatic locomotion. The complexity of unsteady fluid flow around freely swimming animals has required that hydrodynamic analyses of locomotion be largely theoretical, focusing on mathematical or computational modeling (Weihs, 1972a; Lighthill, 1975; Blake, 1981; Lighthill and Blake, 1990; Fauci, 1996; Liu et al., 1997; Carling et al., 1998; Walker and Westneat, 2000).
A complimentary, experimental approach to understanding locomotor hydrodynamics, however, now exists which involves direct measurement of fluid flow around swimming organisms (Stamhuis and Videler, 1995; Müller et al., 1997; Drucker and Lauder, 1999; Lauder, 2000; Wilga and Lauder, 2000). Although gathering experimental data on wake flow behind live, swimming fishes can be technically challenging, such information permits the calculation of forces exerted by propulsive surfaces on the fluid and allows one to avoid simplifying assumptions about patterns of fin motion, as often required for theoretical modeling. Over the last several years a number of technical advances have facilitated the application of experimental hydrodynamic methods for studying locomotion in fishes, and have resulted in new insights into mechanisms of aquatic propulsion. In this paper we review a key new experimental approach to the study of locomotor hydrodynamics, digital particle image velocimetry (DPIV), and provide an overview of the significant functional insights into the biomechanics of swimming gained from recent DPIV studies. These insights are presented as ten "lessons learned" from experimental wake visualization that have general significance for the study of animal locomotion through fluids.
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FUNCTIONAL INSIGHTS FROM WAKE VISUALIZATION |
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The importance of understanding how propulsive surfaces of fishes effect motion of water and the significance of being able to quantify flow in the wake of propulsors has long been recognized (Gray, 1953
; Webb, 1975), but the desire for wake visualization data has, until recently, not been matched by our technical ability to acquire such data. In a discussion of conflicting hypotheses of function proposed for fish fins, Harris (1938, p. 33) concluded that "many of the problems concerning the use of these ...fins by the fishes can only be solved by a series of accurate and laborious hydrodynamical experiments." Writing in 1988, Webb noted (p. 710) that "ideally, momentum changes would be determined from direct observations of flow patterns or pressure fields around a swimming animal," but that "adequate techniques are rarely available to do this." More recently, in an analysis of the state of research on aquatic animal propulsion, Dickinson (1996, p. 553) argued similarly that in order to make significant progress we need to acquire "more elaborate flow visualizations and force measurements from swimming animals."
In an effort to obtain at least qualitative data on the wake of swimming fishes, researchers have employed a wide variety of approaches, including the tracking of streams of dye in the wake of the body and fins, and observing fish swimming in shallow layers of milk or in thermally stratified water so that disturbances in the fluid resulting from movement of the animal can be visualized (Rosen, 1959; Strickler, 1975; McCutchen, 1977; Ferry and Lauder, 1996). None of these approaches, however, provide the type of quantitative data needed to calculate locomotor forces and to understand the hydrodynamic significance of fin design.
Within the last five years biologists have begun to apply a technique originally developed for examining man-made flows in engineering applications: digital particle image velocimetry (DPIV) (Willert and Gharib, 1991; Krothapalli et al., 1997; Raffel et al., 1998; Stanislas et al., 2000). The DPIV technique involves seeding a moving fluid with small reflective particles and using a powerful laser to illuminate a thin slice of this flow. The laser is focused using a series of lenses into a light sheet that is 1–2 mm thick and about 10 cm wide. Light scattered by the particles within the flow is imaged using a high-speed video recording system to provide a time series of images showing particle displacement. By performing a cross-correlation analysis (Willert and Gharib, 1991) to compare the pattern of particle images in consecutively recorded video fields, a two-dimensional matrix of velocity vectors can be calculated that describes the average magnitude and orientation of flow over the course of the video framing period 
t (typically 4–33 msec). High video frame rates are required to avoid out-of-plane loss of particle images over t. As opposed to tracking the movement of individual particles within the laser plane, DPIV analysis relies on changes in grayscale pixel intensity from one digitized video frame to the next to provide a uniform distribution of velocity vectors across the entire flow field. Further details of engineering aspects of this technique are available in Adrian (1991) and Raffel et al. (1998), and the application of DPIV to problems of fish locomotion is discussed in Anderson (1996), Müller et al. (1997), Drucker and Lauder (1999), Wilga and Lauder (1999), Wolfgang et al. (1999), and Lauder (2000).
For our research on the hydrodynamics of locomotion in fishes we have used the experimental arrangement diagrammed in Figure 1. Fish swim in the center of a recirculating flow tank with one or more fins intersecting the laser light sheet, thereby allowing visualization of the wake. A high-speed video camera (250 frames sec–1) is used to image the pattern of particle movement within the light sheet (Fig. 1: Camera 1). A second synchronized camera provides a perpendicular reference view, monitoring the position of the fish relative to the light sheet via a small angled mirror in the flow (Fig. 1: Camera 2). Sample images of flow patterns in the wake, represented by matrices of velocity vectors calculated from DPIV analysis, are shown in Figure 2B. These velocity vectors provide the raw data needed for subsequent reconstruction of the three-dimensional geometry of the wake and calculation of both the orientation and magnitude of locomotor force as described below.
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DPIV permits, for the first time, quantitative, empirical study of the wake of swimming fishes and, in spite of the relatively short time that such experimental data have been available, has resulted in significant new insights into the biomechanics of aquatic animal locomotion. Below we present ten major findings about the mechanisms of fish locomotion that have resulted from recent experimental hydrodynamic analyses. Some of these findings are primarily technical and reflect recent knowledge gained about how effectively to conduct DPIV analyses in fishes, while other functional insights take the form of new biological information about locomotor mechanics. The final point we present addresses the issue of hydrodynamics and evolution, and represents a broader level of analysis for future study.
1. Three-dimensional DPIV analysis is critical for reconstructing wake geometry
The DPIV technique can provide quantitative information about the velocity of water moving in the wake of a swimming animal. For any single orientation of the laser light sheet, a two-dimensional velocity field can be calculated that describes flow patterns in the vicinity of the propulsor. In analyzing wake structure, however, it is critical to reorient the light sheet in separate experiments so that it illuminates flow in perpendicular sections of the animal's wake (Fig. 2A). Representative flow fields for three orthogonal planes of analysis are given in Figure 2B. In this example, flow produced by the pectoral fin of a bluegill sunfish (Lepomis macrochirus) is shown during steady labriform locomotion. Study of flow in three dimensions is essential for reconstructing both the gross morphology of the wake as well as its spatial orientation with respect to the animal. The appearance of paired, counterrotating vortices in the wake of the pectoral fin (Fig. 2B) is reflected in plots of fluid vorticity, which provides a measure of local rotation within the flow fields (Fig. 2C). Analysis of the relative positions of paired vortices in perpendicular planes allows a schematic three-dimensional reconstruction of the pectoral fin wake. The patterns of Figure 2C are consistent with slices through an enclosed, toroidal vortex filament, or vortex ring. With each complete fin stroke, the pectoral fin of sunfish generates a single obliquely oriented vortex ring with a central region of jet flow (Fig. 2D). During slow swimming (0.5 body length sec–1), vortex ring radius is approximately 2 cm in each of the three perpendicular planes of analysis, indicating a roughly symmetrical, near-circular loop. Vortices observed in transections of this loop are of comparable strength in each of the three planes. Specifically, average wake circulation does not differ significantly across planes (range = 43–61 g-cm sec–1; one-way analysis of variance: df among planes = 2, df within planes = 7, P = 0.65), a result matching the theoretical expectation for a symmetrical vortex ring under Helmholtz's theorem (Fung, 1990).
2. DPIV analysis reveals the orientation of locomotor reaction forces
In certain specific cases, hypotheses of function can be tested by flow visualization in a single plane, and by an analysis of the direction of force application alone. One such case concerns the function of the heterocercal tail in fishes. Ray-finned fishes such as sturgeon possess a heterocercal tail morphology which is asymmetrical with respect to the horizontal axis: the dorsal lobe is longer than the ventral lobe and contains the caudal extension of the vertebral column. This caudal fin structure contrasts with the externally symmetrical homocercal morphology present in most teleost fishes such as bluegill sunfish (Lauder, 1989, 2000). One hypothesis current in the literature is that, as a result of their asymmetrical structure, heterocercal tails should generate a lift force posteriorly that induces a rotational moment around the center of mass of the body tending to pitch the head ventrally (Aleev, 1969). Liao and Lauder (2000) conducted a DPIV analysis to test this hypothesis in freely swimming ray-finned fish. The authors measured the orientation of fluid force produced by the tail in white sturgeon (Acipenser transmontanus) relative to the angle of the body during both steady horizontal locomotion and vertical maneuvering. Since locomotor forces directed laterally (i.e., to the right and left) by steadily swimming fish cancel on average over the course of each stride, it was necessary only to resolve wake forces in the vertical (XY) plane. However, because sturgeon swim steadily with their body at a significant angle to the horizontal and because this angle changes during vertical maneuvering (Wilga and Lauder, 1999), it was essential to measure both body angle and wake jet orientation simultaneously in this XY plane in order to evaluate the rotational moments exerted by the heterocercal tail.
Plotting the orientation of the tail jet versus body angle for swimming sturgeon reveals two key features of heterocercal tail function (Fig. 3). First, during steady horizontal locomotion sturgeon maintain an average body angle of approximately 7° to the horizontal, and produce a vortex jet with an average inclination of –6°. This result indicates that during horizontal locomotion the reaction force acting on the sturgeon's heterocercal tail effectively intersects the center of mass of the body and therefore does not induce a substantial pitching moment as has been previously hypothesized (Aleev, 1969). Second, while rising and sinking in the water column, white sturgeon are capable of actively varying the direction of force produced by the tail through an angle of 10° on average. The slope of the jet angle–body angle relationship is significantly different from that of a hypothetical 180° line representing the condition in which heterocercal tail force is always directed opposite to the angle of the body (Fig. 3). Since the regression line intersects the 180° line, sturgeon must be adjusting the angle of the tail jet: tail force is directed at a greater angle than expected during locomotion at high body angles (e.g., during rising in the water column), and at a lower angle than predicted when body angle is negative as during sinking behavior (Liao and Lauder, 2000).
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3. DPIV analysis allows calculation of the magnitude of locomotor forces
In addition to revealing the orientation of locomotor reaction forces, DPIV analysis can also provide quantitative information about the magnitude of forces applied to the fluid during swimming. Locomotor forces experienced by aquatic propulsors can be calculated as the reaction to the time rate of change in wake momentum (Milne-Thomson, 1966
; Ellington, 1984; Dickinson and Götz, 1996). In our DPIV studies, the total stroke-averaged fluid force generated by a fish's fin is taken as the momentum of vortex ring structures shed into the wake divided by the time period over which the wake is produced (Drucker and Lauder, 1999, 2000, 2001a, b). Vortex ring momentum is estimated separately in each of the three perpendicular planes at the end of each fin stroke as the product of water density, mean circulation magnitude of paired vortices in midline sections of the ring, and the projected area of the vortex ring onto the plane of analysis. According to the average orientation of velocity vectors comprising the central fluid jet, the total force can be resolved into three perpendicular components: thrust, lift, and medially directed (parallel to the X, Y and Z reference axes, respectively; Fig. 2A).
The accuracy of DPIV in estimating wake forces is supported by an experimental analysis of the hydrodynamic force balance on freely swimming fish. Drucker and Lauder (1999) compared stroke-averaged forces calculated from DPIV wake measurements to empirically determined counter-forces during slow labriform swimming by bluegill sunfish. Lift and thrust forces derived from wake velocity fields were not significantly different from the resistive forces of body weight and total body drag, respectively (t-tests: df = 16, 18, P = 0.56, 0.73; Fig. 4). On opposite sides of the animal, medially directed forces on each pectoral fin arising in reaction to lateral wake force are presumed to balance, since sunfish show negligible sideslip during the course of the stroke cycle. Such a force equilibrium obviously matches the theoretical expectation for animals moving straight-ahead at constant speed, yet previous attempts to determine such a force balance experimentally have rarely been successful (see Spedding, 1987 for an exception). Empirically determining the force balance on a freely swimming fish indicates that DPIV can successfully detect the major vortical structures shed by swimming animals, and validates the technique for measuring locomotor forces from the wake.
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4. Swimming speed can have a major impact on wake structure
Experimental studies of fluid flow generated by swimming fishes have revealed two factors having a consistent, important influence on the structure of the wake. The first of these is swimming speed. Figure 5 shows three-dimensional reconstructions of the pectoral fin wake of bluegill sunfish swimming at 50% and 100% of the maximum labriform swimming speed. The major difference in wake structure observed relates to the number of vortex rings shed during the stroke. At low speed each fin downstroke produces a single vortex ring (Fig. 5A), whereas at high speed both the downstroke and upstroke are hydrodynamically active, together resulting in a pair of linked vortex rings, each with a central fluid jet (Fig. 5B). The overall effect of swimming speed is to increase the size of the vortex wake, a pattern reflecting the injection of additional momentum into the fluid behind the animal. Such a momentum addition is necessary for swimming animals to match the increased drag forces experienced at higher speeds.
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5. DPIV can reveal interspecific differences in vortex wake morphology
A second factor influencing wake morphology is related to taxonomic variation. Different fish species can show markedly different vortex wake structures, even when swimming at comparable speeds. Our interspecific DPIV studies compare wake dynamics of fishes swimming at equal fractions of their respective maximal swimming speeds within a gait. (The concept of the gait transition as representing an equivalent level of exercise for different swimming animals is reviewed by Drucker, 1996
.) The wakes of two representative perciform teleost fishes, the bluegill sunfish and the black surfperch (Embiotoca jacksoni), are illustrated in Figure 6. At 50% of each species' top labriform swimming speed, vortex structures shed by the pectoral fin show clear variation. With each complete downstroke–upstroke cycle, the sunfish sheds a single ring, while the surfperch sheds two linked rings. Further, the sunfish's ring is rotated so that its central fluid jet has a large lateral component of velocity (Fig. 6A). In contrast, the surfperch generates rings oriented so that both the downstroke and upstroke jets have strong downstream components of velocity (Fig. 6B). Such differences in wake structure provide critical information for interpreting interspecific variation in swimming performance.
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6. DPIV analysis can provide new insights into the limits to locomotor performance
Despite their close phylogenetic relationship and similar adult sizes and body shapes, sunfish and surfperch exhibit a pronounced difference in steady swimming ability. Comparably sized animals (i.e., approximately 20 cm in total length L) show a two-fold difference in maximal labriform swimming speed. Sunfish exhibit a pectoral-to-caudal-fin gait transition speed (Up–c) of 1.0 L sec–1, whereas surfperch can swim twice as fast as with the pectoral fins before recruiting the caudal fin to augment thrust. For both species, thrust calculated from the pectoral fin wake plateaus at Up–c as axial undulation begins, but surfperch are able to generate significantly greater wake force than sunfish at high swimming speed (Fig. 7). Underlying this interspecific difference in speed and thrust may be physiological variation between the two species, including differences in cardiovascular, respiratory or muscular performance.
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However, DPIV analysis reveals that there is an additional important hydrodynamic factor that may help explain the upper limit of pectoral-fin swimming speed. Observed interspecific variation in the orientation of the wake jet (e.g., Fig. 6) becomes increasingly pronounced as swimming speed increases. Figure 8 depicts the mean orientation of jet flow associated with vortex rings produced by sunfish and surfperch at swimming speeds up to and above Up–c. In surfperch, the average downstroke jet angle, as measured in the horizontal plane, decreases with speed from 67° to 1° on average, indicating an increasing contribution of the pectoral fins to forward thrust. Surfperch, in other words, can redirect their vortex jet increasingly downstream as swimming speed increases (Fig. 8). In contrast, sunfish progressively reorient this jet laterally. The downstroke jet angle in sunfish shows an unexpected increase with swimming speed to nearly a 90-degree angle to the body, reflecting the production of a large lateral component of force and a proportional reduction in thrust (Fig. 8). We conclude that swimming performance, as measured by maximal swimming speed within a gait (e.g., Fig. 7), may be limited by a species' ability to direct wake momentum downstream. With wake flow oriented essentially perpendicular to the axis of progression, as in sunfish nearing top speed, no variation in pectoral fin shape or increase in pectoral muscle power output can raise the observed speed limit.
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), as measured in the frontal (XZ) plane, is defined as 0° when velocity vectors within the jet are oriented on average directly downstream. Positive values for this angle reflect a lateral component of velocity within the jet. B. For both species, mean 7. DPIV demonstrates the functional versatility of fish fins
Insights into locomotor mechanisms provided by DPIV analysis are not limited to steady swimming behavior. The technique can also provide valuable information about the mechanics of unsteady maneuvering, a behavior likely comprising the largest portion of a swimming animal's locomotor time budget (Fuiman and Webb, 1988
; Webb, 1991; Boisclair and Tang, 1993; Krohn and Boisclair, 1994). Investigation of the wakes of fish performing a range of swimming tasks has exposed the breadth of the locomotor repertoire of fish fins—propulsors whose great functional versatility was not apparent from analyses of steady swimming alone.
In studies of steady swimming, the plateauing of thrust from the pectoral fins at the gait transition (Fig. 7) suggested a potential upper limit to the rate at which these fins can add momentum to the wake. However, study of maneuvering in the same species has revealed that steady swimming forces do not accurately represent the pectoral fin's complete range of function. Drucker and Lauder (2001b) compared wake dynamics during steady swimming and turning in bluegill sunfish. Fish performing rectilinear labriform locomotion were exposed to a visual and auditory stimulus, which induced an evasive maneuver involving both pectoral fins. Unlike "fast-start" escape turning driven by Mauthner-cell-mediated body flexion (Eaton et al., 1977, 1988; Eaton and DiDomenico, 1986), pectoral fin turning is a relatively slow behavior, involving an initial body rotation (up to 32 degrees sec–1) and a subsequent period of body translation (2–8 cm sec–1).
Examples of velocity fields in the wake of the pectoral fin during steady swimming and turning behavior are given in Figure 9. As observed previously for sunfish (Drucker and Lauder, 1999, 2000), planar visualizations of the pectoral fin wake generated during steady swimming reveal paired counterrotating vortices with central fluid jets (Fig. 9A, C). Subsequent turning results in a dramatic reorganization of wake structure. For the pectoral fin closer to the stimulus (termed the "strong-side" fin), each downstroke–upstroke cycle results in vortices that are considerably larger and stronger than those generated during steady swimming. In addition, the wake jet has a predominantly lateral, rather than downstream, orientation (Fig. 9B). The wake of the contralateral, or "weak-side," fin is also radically reoriented such that the thrust jet falls roughly in line with the longitudinal axis of the body at the onset of body translation (Fig. 9D).
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The impressive functional versatility of the pectoral fin is revealed through quantification of fin kinematics and wake dynamics during steady swimming and turning. Turning involves pectoral fin motions that are significantly shorter in duration than those observed during steady swimming (by up to a factor of five, Table 1). While the vortex ring's jet remains at nearly a 45-degree angle to the body on average during steady swimming (Table 1, Fig. 9A, C), momentum flows during turning are redirected by up to 50° (Table 1, Fig. 9B, D). During turning, the strong-side pectoral fin generates a wake jet whose average velocity is approximately twice as great as that produced during steady swimming (Table 1). In addition, the magnitude of wake force varies significantly between the two behaviors. The strong- and weak-side fins generate laterally and posteriorly directed components of force during turning that exceed those produced during rectilinear locomotion by 4- and 9-fold, respectively. Furthermore, the ratio of lateral to posterior force measured for the two behaviors spans almost two orders of magnitude (Table 1). These results emphasize the importance of examining a range of locomotor behaviors when defining the hydrodynamic repertoire of aquatic animal propulsors. Continued quantitative analysis of the wake of teleost fishes will improve our understanding of how fins serve different functions in the face of different locomotor demands.
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8. DPIV reveals hydrodynamic force partitioning among fins
In addition to being functionally versatile, fish fins are highly integrated components of the propulsive system. Fishes can employ multiple fins distributed over the body simultaneously both to produce and modulate swimming force. Three fins in particular are observed to work together in a coordinated way during swimming: the pectoral fin, the caudal fin and the dorsal fin (e.g., Arreola and Westneat, 1996
). For perciform fishes, the pectoral fin and tail are known to play important roles in propulsion and there is now a substantial literature on the function of these fins (e.g., Bainbridge, 1958; Aleev, 1969; Webb, 1973, 1975; Blake, 1979, 1983; Geerlink, 1983; Videler, 1993; Gibb et al., 1994; Drucker and Jensen, 1996; Lauder and Jayne, 1996; Walker and Westneat, 1997; Lauder, 2000). Functions traditionally assigned to the dorsal fin of perchlike fishes, however, have been mostly non-propulsive. For example, during steady swimming the dorsal fin has been described as a keel or body stabilizer (Aleev, 1969). During turning, the dorsal fin has been hypothesized to serve as a pivot point, again playing a largely passive, non-propulsive role (Helfman et al., 1997, p. 168).
DPIV can be used to test explicitly whether simultaneously recruited fish fins play active roles in generating propulsive force. Figure 10 illustrates two possible vortex flow patterns behind bodies within moving fluid. At intermediate Reynolds numbers (i.e., before flow separation), a bluff body sheds a trail of staggered, counterrotating vortices. Flow between each pair of vortices has a component of velocity oriented upstream, thereby reducing the momentum of the incident flow (Fig. 10A). This flow pattern is known as a von Kármán street and is a classic example of a drag-producing wake. In contrast, a heaving and pitching foil, like a fish's fin, can produce vortices with opposite rotation, so that a downstream-directed fluid jet is generated between each vortex pair (Fig. 10B). This is an actively produced thrust wake, or reverse von Kármán street (von Kármán and Burgess, 1935; Weihs, 1972b; Lighthill, 1975; Triantafyllou et al., 1993, 2000), which adds momentum to the fluid behind the fin.
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Analysis of the wake of sunfish during high-speed swimming reveals that the trailing edge of the dorsal fin clearly plays an active role in propulsion. At a steady swimming speed of 1.1 L sec–1 (i.e., slightly above Up–c for 20 cm-long fish), the soft dorsal fin is observed to undulate regularly and shed a reverse von Kármán street (Drucker and Lauder, 2001a
). Thus, at this speed, the dorsal fin supplements the thrust produced by the oscillating pectoral and caudal fins. The total thrust generated by all fins over the course of each stride is partitioned among the three fin systems as shown in Figure 11A; note that the soft dorsal fin contributes 12% of total thrust on average. During slow turning maneuvers in sunfish (described above), the soft dorsal fin is also active, shedding a laterally oriented momentum jet at the end of the body-rotation phase (Drucker and Lauder, 2001a). Both the pectoral and dorsal fins, therefore, exert laterally oriented wake forces during this unsteady swimming behavior, with the dorsal fin generating an average of 35% of the total (Fig. 11B). The fact that the soft dorsal fin produces approximately 10% of the total thrust generated by all fins during steady swimming, and more than one-third of the total lateral force during turning, underlines its active role in propulsion. The partitioning of swimming force among multiple fins is likely a widespread characteristic of the teleost locomotor system, but as yet has received very little experimental study.
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9. DPIV shows that wake interaction among fins may enhance thrust production
The observation that more than one fin can shed a vortex wake at the same time suggests the possibility of hydrodynamic interaction among nearby propulsors. Theoretical studies of fish locomotion have emphasized the potential for wake interaction among fish fins to increase propulsive efficiency (Lighthill, 1970
; Wu, 1971; Yates, 1983; Weihs, 1989). Experimental work in non-biological systems has demonstrated that vortex trails shed by upstream bodies can intercept and affect the strength of developing vortices generated by bodies downstream. Specifically, it has been shown that the drag wake of an upstream bluff body can interact in either a constructive or destructive way with the near-field thrust wake produced by a downstream oscillating foil (Gopalkrishnan et al., 1994; Anderson, 1996; Triantafyllou et al., 2000). The type of interaction observed depends on the sign of vortex rotation and the encounter phase of the foil with respect to the upstream vortices. For two adjacent foils shedding a thrust wake, as in a swimming fish, annihilation or reinforcement of vorticity will also depend on encounter kinematics.
Using DPIV, Drucker and Lauder (2001a) examined the dynamics of wake interaction between the soft dorsal fin and tail of bluegill sunfish. Given the proximity of these fins (see Fig. 11A), both constructive and destructive interactions among wake vortices are theoretically possible. During steady swimming slightly above the gait transition speed (1.1 L sec–1), both fins exhibit a sinusoidal pattern of motion with a mean phase lag of 120 msec. A horizontal laser light sheet was used to illuminate simultaneously the ventral portion of the soft dorsal fin and the dorsal lobe of the tail. Within this plane, the tail undergoes a lateral excursion 0.5 cm greater on average than that of the trailing edge of the dorsal fin, such that at the extremes of its left–right motion, the tail moves into the immediate vicinity of vortices cast by the soft dorsal fin.
Patterns of movement of the two fins and vortex shedding during the stroke cycle are illustrated in Figure 12. As the soft dorsal fin undulates laterally, it produces a trailing vortex (Fig. 12: vortex a) which represents part of the fin's reverse von Kármán street (cf., Fig. 10B). The DPIV video record reveals that the dorsal fin's vortex moves downstream and is consistently intercepted by the dorsal lobe of the tail. Vortex a is observed to follow the surface of the tail while the tail itself develops bound vorticity, which is ultimately shed as a distinct vortex (Fig. 12: vortex b). The two analogous vortices have the same rotational sense and correct timing of interaction to merge constructively immediately downstream of the tail, forming a larger, combined vortex (Fig. 12: vortex c). We hypothesize that, in the early stage of the tail's half-stroke, the presence of rotational flow from the dorsal fin's wake (vortex a) increases incident velocity over the tail and enhances same-sign vorticity bound to the tail (flow that enters the wake as vortex b). Such reinforcement of developing circulation is proposed as a mechanism for directing additional energy into the tail's wake and for increasing thrust production by the tail.
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10. Experimental hydrodynamic analysis can provide insight into the functional significance of evolutionary variation in fin design
To date, the focus of experimental hydrodynamic analyses of fish locomotion has been on the detailed mechanics of propulsor function as reflected in the functional insights presented above. However, new biomechanical tools such as DPIV can also be applied to examine the evolution of locomotor function over a broad phylogenetic scale. The fins of fishes have undergone a number of major historical transformations in design, yet, until now, we have not been equipped with an experimental technique for understanding the functional consequences of these evolutionary trends.
One example of such evolutionary variation in fin structure, long-recognized by vertebrate anatomists, is the suite of structural transformations that have occurred in pectoral fin morphology within ray-finned fishes (Schmalhausen, 1916; Breder, 1926; Harris, 1937, 1938; Greenwood et al., 1966; Gosline, 1971; Alexander, 1974; Rosen, 1982; Webb, 1982). In this group, clear trends exist in two aspects of fin design: anatomical position and fin base orientation. Basal taxa typically exhibit pectoral fins positioned low on the side of the body with horizontally inclined fin bases (e.g., sturgeon and gar). More derived taxa commonly possess fins located higher on the body, near the center of mass of the animal, with more vertically oriented insertions (e.g., perciform fishes). (Within the ray-finned fishes, there are, as expected, scattered exceptions to these anatomical trends. Among basal taxa, for instance, Polypterus exhibits nearly vertically inclined pectoral fins; among perciforms, some labroid fishes show more horizontal fin bases.) At present, the functional significance of these general patterns of evolutionary variation is poorly understood. One implication of these trends in pectoral fin design is that numerous differences may exist between basal and derived clades in the function of the fins during locomotion. For example, it is likely that the angle of inclination of the pectoral fin base constrains the range of directions in which force may be applied on the fluid during swimming. Specifically, taxa possessing horizontally inclined pectoral fins, with limited anteroposterior mobility, are expected to generate relatively low laterally directed force, as compared to taxa with more vertically inclined fin bases. In addition, fishes with ventrally positioned pectoral fins may exert greater rotational moments around the center of mass of the body than species with mid-dorsally positioned fins. In general, the observed variation in pectoral fin anatomy among ray-finned fishes is predicted to influence (a) the capacity for generating stabilizing and propulsive forces, (b) the balance of fluid forces acting on the body during steady swimming, and (c) the generation of pitching and yawing moments during unsteady maneuvering. Until recently, functional predictions of this kind could not be tested experimentally, as the tools for measuring the crucial data—locomotor force magnitudes and orientations—were not available. The use of experimental hydrodynamic methods, including quantitative wake visualization, will allow much-needed clarification of the functional significance of evolutionary trends in fin design in fishes.
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SYNOPSISINTRODUCTIONFUNCTIONAL INSIGHTS FROM WAKE...CONCLUSIONSReferences |
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The combination of traditional biomechanical tools, including kinematic analysis, measurement of muscle activity, and analysis of muscle fiber power output, with new experimental approaches such as digital particle image velocimetry promises a more integrated understanding of the mechanics of organismal motion through fluids. By combining data on muscle physiology and internal force production with patterns of propulsor movement and measurement of the forces exerted externally on the fluid, we will in future work be well-equipped to address long-standing questions about the mechanics and evolution of locomotion in aquatic animals.
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ACKNOWLEDGMENTS |
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Discussions with Erik Anderson, Jamie Anderson, Ellen Freund, Jon Posner, Eric Tytell and Danny Weihs provided many insights into wake dynamics and the mechanisms of fish locomotion. Collaborative research conducted with Jimmy Liao, Jen Nauen and Cheryl Wilga was instrumental in formulating the ideas presented in this paper. We thank Mark Westneat and an anonymous reviewer for constructive criticisms of the manuscript. The research described herein and the preparation of this manuscript was supported by NSF grants DBI-9750321, IBN-9807012 and IBN-0090896 to E.G.D. and G.V.L.
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1 From the symposium Molecules, Muscles, and Macroevolution: Integrative Functional Morphology presented at the Annual Meeting of the Society for Integrative and Comparative Biology, 3–7 January 2001, at Chicago, Illinois.
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