Fish locomotion: kinematics and hydrodynamics of flexible foil-like fins
- First Online:
- Cite this article as:
- Lauder, G.V. & Madden, P.G.A. Exp Fluids (2007) 43: 641. doi:10.1007/s00348-007-0357-4
- 1.1k Downloads
The fins of fishes are remarkable propulsive devices that appear at the origin of fishes about 500 million years ago and have been a key feature of fish evolutionary diversification. Most fish species possess both median (midline) dorsal, anal, and caudal fins as well as paired pectoral and pelvic fins. Fish fins are supported by jointed skeletal elements, fin rays, that in turn support a thin collagenous membrane. Muscles at the base of the fin attach to and actuate each fin ray, and fish fins thus generate their own hydrodynamic wake during locomotion, in addition to fluid motion induced by undulation of the body. In bony fishes, the jointed fin rays can be actively deformed and the fin surface can thus actively resist hydrodynamic loading. Fish fins are highly flexible, exhibit considerable deformation during locomotion, and can interact hydrodynamically during both propulsion and maneuvering. For example, the dorsal and anal fins shed a vortex wake that greatly modifies the flow environment experienced by the tail fin. New experimental kinematic and hydrodynamic data are presented for pectoral fin function in bluegill sunfish. The highly flexible sunfish pectoral fin moves in a complex manner with two leading edges, a spanwise wave of bending, and substantial changes in area through the fin beat cycle. Data from scanning particle image velocimetry (PIV) and time-resolved stereo PIV show that the pectoral fin generates thrust throughout the fin beat cycle, and that there is no time of net drag. Continuous thrust production is due to fin flexibility which enables some part of the fin to generate thrust at all times and to smooth out oscillations that might arise at the transition from outstroke to instroke during the movement cycle. Computational fluid dynamic analyses of sunfish pectoral fin function corroborate this conclusion. Future research on fish fin function will benefit considerably from close integration with studies of robotic model fins.
Studying fish fin structure and function is critical to understanding how fish maintain stability and generate force during propulsion and maneuvering, especially in locomotor gaits during which fins are the only propulsive surfaces active and the body is not used (Drucker and Lauder 2000). And yet fins have been subject to only relatively limited experimental study until recently. In this paper we first present a brief general overview of recent experimental studies on fish fin kinematics and hydrodynamics, and then provide new experimental data on the hydrodynamic function of fish pectoral fins obtained using both scanning particle image velocimetry (PIV) and stereo PIV in freely swimming fish.
2 Overview of fish fin structure and function
The hallmark of fish fin functional design is the bending of the fin rays which permits considerable flexibility of the propulsive surface. The fin rays of the large fish group termed ray-finned fishes (but not sharks), possess a remarkable bilaminar structure and muscular control that allows fish to actively control fin surface conformation and camber during locomotion. As illustrated in Fig. 2, each bony fin ray is composed of two halves (termed hemitrichs) which are connected along their length by short collagen fibers and may be attached at the end of the ray (Alben et al. 2007; Geerlink and Videler 1987; Lauder 2006). Each fin ray is actuated by four separate muscles, and thus a single fin such as the pectoral fin of a bluegill sunfish (Lepomis macrochirus), which has about 14 fin rays, potentially has over 50 separate actuators that allow the fin to be reoriented in three dimensions with control over the position of each ray. Neural control of fin ray motion has yet to be studied in detail, and the extent to which anatomically homologous muscles on neighboring fin rays can be controlled independently is unknown. Most importantly, displacement of the two ray halves through the contraction of fin ray musculature at the base of the fin causes the fin ray to curve. Fish can thus actively alter the conformation of their propulsive surface by actively bending fin rays, and can resist hydrodynamic loading, a phenomenon that is observed most clearly during maneuvering (Fig. 2d). One result of the complex control and bilaminar fin ray design in fish fins is that, as illustrated in Sect. 5, fins can undergo rather complex three-dimensional changes in shape during locomotion.
3 Methodology for experimental analyses of fish locomotion
Although experimental kinematic and hydrodynamic studies of fishes swimming in large bodies of water and under natural settings would be ideal, recent progress in understanding the functional design of fishes has relied heavily on inducing locomotion in laboratory flow tanks, which permit precise speed control and the induction of replicated maneuvering stimuli. Such studies have allowed both detailed kinematic studies of fin function and experimental hydrodynamic recordings of wake flow patterns resulting from fin and body movement using PIV (e.g., Anderson 1996; Drucker and Lauder 1999, 2002a; Lauder and Drucker 2002, 2004; Liao et al. 2003; Nauen and Lauder 2002a, b; Wilga and Lauder 2002; Wolfgang et al. 1999).
Two critical enabling technologies that have been responsible for considerable progress in understanding fish locomotor function in recent years are (1) the use of high-resolution (at least megapixel) high-speed video cameras acquiring images between 200 and 1000 frames per second or more, and (2) the use of time-resolved PIV (Lauder and Madden 2008). Often these two techniques are used in conjunction with other approaches such as electrical recordings of fin and body muscle activity patterns and measurement of muscle strain (e.g., Lauder et al. 2006), or the use of biorobotic fish-like devices that enable precise control of kinematics and exploration of broad (and even non-biological) parameter spaces (Lauder et al. 2007). The rapid development of high-speed digital video technology over the past decade coupled with the availability of lower cost continuous wave lasers has also permitted their use in PIV studies by biologists. This has allowed time-resolved PIV (typically at 200–1,000 Hz) recordings of fin and body wake flows with a temporal resolution 10–50 times that of the fin beat frequency, giving a detailed picture of vorticity production and the generation of biological flows near the body and fins (Drucker and Lauder 1999, 2002a, 2003; Lauder 2000; Lauder and Drucker 2004). Megapixel high-speed video cameras have made the motion of individual fin rays visible (see Fig. 5, for example) and have permitted the accurate quantification of fin surface conformation (especially the bending of individual fin rays) which is critical to interpreting the kinematic causes of wake flow patterns.
While time-resolved two-dimensional PIV with high-speed cameras and continuous lasers has been used to study fin function in several species of fishes to date (Drucker and Lauder 2000, 2003; Liao and Lauder 2000; Müller et al. 2000; Nauen and Lauder 2002a; Tytell 2004; Tytell and Lauder 2004; Wilga and Lauder 1999, 2000, 2001), three-dimensional information on fish fin flow patterns is highly desirable. Such data can be obtained in part by using stereo PIV (Nauen and Lauder 2002b) or using multiple light sheet orientations (Drucker and Lauder 1999), but even this approach only generates the three vector components of flow confined to one or more narrow (1–2 mm thick) planes. Reconstructions of three-dimensional flow patterns then requires piecing together data from several different fin beat cycles which is difficult as freely swimming fishes often do not move their fins in precisely the same manner from stroke to stroke or maintain strict control of body position. Phase averaging of fin PIV data from freely swimming fishes is possible (e.g., Tytell and Lauder 2004) but often difficult to do without introducing considerable variation into the data.
In Sect. 6 below we describe data obtained on the hydrodynamics of the bluegill sunfish pectoral fin using both scanning PIV, and a transverse-plane PIV approach that samples flow with high temporal resolution downstream of swimming fish with cameras that view the wake from behind (Fig. 3). These approaches, especially when used in conjunction with each other, provide a reasonably complete picture of fin-induced three-dimensional flow patterns.
In scanning PIV, a continuous wave horizontal light sheet is scanned, using a moving mirror, down through the moving pectoral fin and its wake (Fig. 3b). The light sheet scans through 5–10 cm vertical distance in 50–100 ms, and particle flows are imaged with a high-speed camera (1,024 × 1,024 pixel resolution) at 500 Hz from below the light sheet looking up at the fish and the fin wake. A side-view camera provides data on the position of the light sheet relative to the fish fin, and gives basic kinematic data on the motion of the fin. Brucker (1997), Rockwell et al. (1993), and Burgmann et al. (2006) provide further discussion of PIV scanning approaches.
In another set of experiments, we used a continuous laser light sheet oriented transversely to the fish body axis and placed downstream of the fish fin (Fig. 3c). Fin wake flows move toward and then through the laser light sheet as the fish maintains position in the flow tank while swimming at a slow pectoral fin swimming speed. With a temporal sampling rate of 500–1,000 Hz and short shutter speeds (1/2,000 s or less), stereo PIV images can be obtained of wake flow patterns moving toward the camera, and reconstructed into a three-dimensional representation of fin flows. Brücker (2001) discusses PIV using a light sheet orientation orthogonal to free-stream flow and issues involved in imaging such flows from downstream. This approach has the advantage of imaging the full wake from the body surface to a distance of several fin chords away into the free-stream as flow moves into the transverse light sheet. An additional feature of these experiments is the use of another camera to image fish body position in a side view (Fig. 3c), allowing quantification of fish body acceleration during the fin beat synchronously with the stereo PIV images. As shown in Fig. 3c, we used red light to illuminate the swimming fish, and a Photron PCI 1024 high-speed digital video camera with a highpass filter on the lens to allow red light through but block green light from the continuous wave argon–ion laser. This camera (#1 in Fig. 3c) imaged body position and fin movement. Two additional identical synchronized Photron cameras (#2 and #3 in Fig. 3c) were aimed in stereo configuration with Scheimpflug adapters at a mirror in the flow tank downstream from the swimming fish. These two cameras were focused onto the laser light sheet located upstream of the mirror (Fig. 3c) and had lowpass filters on each lens to block red light but allow the green light from the argon–ion laser through to the camera sensors. This experimental arrangement allows simultaneous acquisition of body and fin position through time and fin wake flows in stereo view. Since fin wake flows advect through the laser plane, a three-dimensional view of the fin wake can be formed. However, since the wake is sampled at only one location, any interactions among vortices downstream of the laser plane will not be visualized. All camera views were calibrated and u, v, and w velocity vector components calculated using Davis 7.1.1 software from LaVision Inc., Ypsilanti, MI, USA. Multiple replicate experiments were conducted on individual bluegill sunfish (Lepomis macrochirus) of mean total body length (L) of 18 cm swimming at 0.5 Ls−1. Swimming bluegill naturally positioned themselves at slightly different positions in the flow tank during the replicate trials, and thus data were obtained with the fin at different distances upstream of the transverse light sheet. In most sequences, the posterior region of the body can be seen in the PIV views as the tail extends toward the PIV cameras (Figs. 3c, 7a, 8). PIV sequences of the pectoral fin wake were obtained of steady swimming and also a variety of maneuvers, but in this paper we focus on the steady swimming data. These experimental analyses are conducted in conjunction with computational fluid dynamic analyses of sunfish pectoral fin function (Lauder et al. 2006; Mittal et al. 2006).
4 Overview of dorsal and anal fin function
In this section we present kinematic and hydrodynamic data from fish dorsal and anal fins to illustrate the extent to which flows generated by these fins modify the hydrodynamic environment experienced by the tail, and as an example of the hydrodynamics of median fin function.
Standen and Lauder (2007) studied the function of both dorsal and anal fins in swimming brook trout, and found that both fins generate significant wake vorticity that is directed to the same side of the fish resulting in balanced roll torques (Fig. 4b). Neither the dorsal nor the anal fins generate significant thrust, while both fins produce nearly synchronous side momentum jets even though the dorsal and anal fins are located at different longitudinal positions on the trout. Differences in dorsal and anal fin shape and heave and pitch motions combine to result in temporally coincident jet formation which in turn balances roll torques.
The observation that the caudal fin moves through the dorsal and anal fin wake suggests that, if the motion of the caudal fin is phased appropriately, additional thrust may be obtained resulting from the increase in angle of attack at the tail that results from the change in free-stream flow generated by the dorsal and anal fins (Drucker and Lauder 2001b; Standen and Lauder 2007). Computational fluid dynamic analysis of two foils in series using the pattern of motion from the sunfish dorsal fin and tail (Akhtar et al. 2007), showed that indeed considerable increases in thrust are realized by the sunfish tail as a direct result of the dorsal fin wake initiating the formation of a stronger leading edge vortex on the tail than would otherwise be present. Interestingly, the phase difference between the sunfish dorsal fin and tail (108°) was not the optimal phase possible. Exploration of the phase parameter space showed that a phase of 48° produced optimal thrust enhancement by the tail, although this is a phase relationship never seen in a swimming sunfish due to the coupling between the dorsal fin and tail through the body.
Experimental data on median fin hydrodynamics in fishes (Fig. 4) indicate that the these fins play a substantial role in the maintenance of body stability, in modifying the flow environment encountered by the tail, and, in the case of sunfish, generating thrust during steady rectilinear propulsion. There is a considerable diversity of median fin structure in fishes, and yet the hydrodynamic significance of this variation is as yet unknown, and there are a plethora of questions for future experimental hydrodynamic research on the median fins of fishes.
5 Pectoral fin function: kinematics
Early in the retraction stroke of the pectoral fin, the upper fin wave has progressed nearly two-thirds of the way along the fin span and causes a “dimpling” of the fin surface behind the upper edge (Fig. 5f) which appears to stabilize the vortex formed on the upper fin edge (Lauder et al. 2006). On the return or retraction stroke, fin area increases and the fin moves rapidly back to lie flat along the body. There is often an extended time in between fin beats during which the fin is held along the body wall (Gibb et al. 1994) before the next beat begins.
Pectoral fin kinematics in bluegill sunfish are broadly representative of how many bony fishes use their pectoral fins using a complex and time-varying combination of lift-and-drag forces to generate thrust. But some species exemplify more clearly the ends of the lift-and-drag continuum, and use primarily drag-based propulsion (Walker 2004) or lift-based mechanisms (Walker and Westneat 1997).
Fin kinematics during maneuvering locomotion are substantially different from propulsion, and may involve much more substantial bending of fin rays, greater angular excursions, and dramatic differences between pectoral fin conformation on the left and right sides of the body during a turn (Drucker and Lauder 2001a; Higham et al. 2005; Lauder et al. 2006). This contrasts with patterns of wing motion in birds and insects where left–right differences in wing kinematics during turns are relatively slight (Dickinson 2005; Warrick et al. 1998).
6 Pectoral fin function: hydrodynamics
Given the complex deformation and movement of fish pectoral fins, it is perhaps not surprising that the flows induced by fin motion can also be complex. PIV has been used to understand the hydrodynamic effect and force production of pectoral fin movement during both propulsion and maneuvering in a diversity of fishes (sharks, sturgeon, bluegill sunfish, and trout, Drucker and Lauder 1999, 2000, 2001a, 2002b, 2003; Lauder et al. 2006; Wilga and Lauder 1999, 2000, 2001), but these studies have to date relied on more traditional PIV approaches using two-dimensional laser light sheets, usually oriented horizontally (perpendicular to the body axis) or vertically (parallel to the fish body). Two useful modifications to the traditional PIV approach (Fig. 3) are (1) to scan a laser light sheet through the pectoral fin and its wake, and (2) to use a light sheet in a transverse, orthogonal orientation to free-stream flow and image flow from downstream. Both the modifications of the usual PIV approach provide increased three-dimensional information on the hydrodynamic consequences of fin function.
Transverse plane PIV at the level of the pectoral fin shows that on the fin downstroke (data not shown here), the kinematic cupping of the fin in which both the upper and lower fin rays move away from the body simultaneously (Fig. 5b), produces dual leading edge vortices (Lauder et al. 2006). The simultaneous presence of opposite sign vortices on the pectoral fin may act to minimize vertical body oscillations compared to a heaving and pitching foil in which significant momentum is added to the water orthogonal to the free-stream on each half stroke.
This pattern of pectoral fin thrust production measured experimentally in sunfish is consistent with that calculated using CFD based on sunfish pectoral fin kinematics (Mittal et al. 2006): the pectoral fin generates thrust throughout the fin beat. This result contrasts with data from many previous experiments and computational work on forces generated by heaving and pitching foils, in which there is a period of net drag force produced as foils reverse direction at the extremes of the stroke cycle. For example, data on flapping foils by Read et al. (2003), computations of foil thrust coefficients by Dong et al. (2006) and Guglielmini and Blondeaux (2004), all show a time of net drag at stroke reversal. A computational fluid dynamic analysis of the pectoral fin of a wrasse, a fish with a more flapping foil-like fin stroke (Ramamurti et al. 2002), also shows a significant period of drag at the fin reversal, and experimental estimates of thrust coefficients in fishes using flapping and rowing propulsion (Walker and Westneat 2002; Walker 2004) show long periods of drag. In contrast, the data presented here and our previous experimental and computational analyses of the sunfish pectoral fin which exhibits a more complex movement pattern than simple rowing or flapping, shows that thrust is generated throughout the fin beat and that there is no time in the fin beat cycle when net drag is produced (Lauder and Madden 2006; Lauder et al. 2006; Mittal et al. 2006).
Our observation of continuous thrust by the sunfish pectoral fin is understandable in terms of fin kinematics, which contrast with those of rowing and flapping fishes studied previously. Movement of the sunfish pectoral fin, with the cupping shape on the outstroke, the flexible fin surface, the outer third of which is oriented downstream on the outstroke, the wave of bending that passes along the upper third of the fin, area minimization at the transition between downstroke and upstroke, and area expansion on the return stroke, all combine to generate continuous thrust throughout the beat (Fig. 5). Many features of this kinematic pattern are general components of fish fin function (Fish and Lauder 2006; Lauder 2006), and this result suggests that one important role for flexibility of the propulsive fin surface in fishes is to modulate force production and smooth out oscillations that might arise at transitions during the movement cycle. Bending of the fin surface and of individual fin rays allows continued thrust production by at least some portion of the fin at all times during the fin stroke that is sufficient to overcome drag produced by other fin regions.
7 Conclusions and prospectus
The experimental study of fish locomotion has undergone a renaissance in recent decades as new technologies for visualizing fin and body movement and for quantifying water flow produced by the body and fins have matured and become more widely available to biologists. Studying freely swimming fish moving under controlled conditions in laboratory flow tanks has allowed detailed analyses of fin deformation, the role of flexibility in generating propulsive forces, and the forces produced by flexible fins. Fish fins are remarkable in having active camber control and the consequent ability to resist hydrodynamic loading. Furthermore, fin-fin hydrodynamic interactions are substantial, especially among median fins. There are currently no experimental data that suggest an interaction between paired fins and median fins, although such interactions are certainly possible and remain to be demonstrated.
Experimental analyses of living fishes are, by their very nature, limited to studying what nature provides in the way of fin position, structure, and activation pattern. Although surgical modifications of fish fin shape are possible (e.g., Webb 1977), such modifications provide for only a relatively limited range of shape changes, and do not permit major alterations in fin position or movement pattern, and fish may alter the way fins are moved post-surgically. Another approach, and one that allows for much more control over movement pattern and for greater exploration of the parameter space of fin phase, frequency, and amplitude is to use robotic models of fish fins (Kato 1998, 2000; Lauder et al. 2007; Tangorra et al. in press; Triantafyllou and Triantafyllou 1995; Triantafyllou et al. 2004). Both robotic models of a specific fin type such as the pectoral fin, and the use of more abstract robotic models such as dual-flapping foils to approximate median fin interactions, provide invaluable flexibility for understanding how fish fins function. Analyses of such robotic systems will likely prove to be an important path for future work on fish fin function.
Finally, we anticipate that computational fluid dynamic approaches will increasingly use as input experimentally measured fin kinematics to more accurately estimate locomotor forces, and allow direct comparisons with experimental force measurements. Such studies are, to date, few (but see Akhtar et al. 2007; Mittal 2004; Mittal et al. 2006; Ramamurti et al. 2002). But the promise of a closer integration of computational approaches, the use of robotic models, and increasingly detailed experimental analyses of fish fin function, suggests that the next decade will witness major progress in understanding the function of fish fins, and improved ability to use them to design bio-inspired propulsors for AUVs.
This work was supported by an ONR-MURI Grant N00014-03-1-0897 on fish pectoral fin function, monitored by Dr. Thomas McKenna and initiated by Dr. Promode Bandyopadhyay, and by NSF grant IBN0316675 to G.V.L. We thank Drs. Rajat Mittal and Promode Bandyopadhyay for many helpful discussions on bio-inspired propulsion. Dr. Wolf Hanke designed the laser scanning system and we are very grateful for his assistance with those experiments. Karsten Hartel and Chris Kenaley kindly provided the grouper photograph in Fig. 1a, Em Standen took the image in Fig. 3a, and Eric Tytell provided the bluegill picture used in Fig. 3c. Tony Julius and Julie Idlet provided invaluable assistance in the lab. Thanks also to two anonymous reviewers who provided comments helpful in clarifying the manuscript.