Wake dynamics and fluid forces of turning maneuvers in sunfish

Dynamics of pectoral fin rowing in a fish with an extreme rowing stroke:the threespine stickleback (Gasterosteus aculeatus)

The dynamics of pectoral fin rowing in the threespine stickleback are investigated by measuring the instantaneous force balance on freely swimming fish throughout the stroke cycle and comparing the measured forces with fin motions and an unsteady, blade-element model of pectoral fin propulsion. Both measured and modeled forces suggest that attached vortex and circulatory forces and not inertial (added mass) forces dominate the force balance. Peak forces occur at midstrokes. There is no evidence for large force peaks at the stroke transitions due to either rapid fin rotation (supination) or rapid fin closure against the body. The energetics of pectoral fin rowing are estimated using the unsteady blade-element model and an indirect method based on the center of mass dynamics. The results indicate that the mechanical efficiency of pectoral fin rowing is low (0.1–0.3) relative to a flapping mechanism and possibly relative to axial undulation at comparable speeds.

Response latencies to postural disturbances in three species of teleostean fishes

Flow in aquatic systems is characterized by unsteadiness that creates destabilizing perturbations. Appropriate correction responses depend on response latency. The time between a disturbance induced by either removal of a flow refuge or striking various parts of the body with a narrow water jet was measured for three species, chosen as examples of modes in teleostean body/fin organization that are expected to affect stability. Creek chub Semotilus atromaculatus is representative of fusiform-bodied soft-rayed teleosts, smallmouth bass Micropterus dolomieu of fusiform-bodied spiny-rayed forms and bluegill Lepomis macrochirus of deep-bodied spiny-rayed forms. Observations were made at 23°C. Loss of refuge resulted in a surge that fish corrected by starting to swim within 129±29 ms (mean ± 2 s.e.m.) for chub, which was significantly shorter than minimal times of approximately 200 ms for bluegill and bass. Slips and heaves induced by water jets initially resulted in extension of the median and paired fins that would damp growth of the disturbance, but otherwise these disturbances were ignored. Yaws and pitches were more likely to cause fish to swim away from the stimulus, making corrections as they did so. There were no differences in latencies for slip,heave, yaw and pitch disturbances within each species, but latencies varied among species. For these disturbances, responses averaged 123±19 ms for chub, again significantly smaller than those of 201±24 ms for bass and 208±52 ms for bluegill. Values for the two centrarchids were not significantly different (P>0.08). The response latency for rolling disturbances did not differ among species but was significantly smaller than that for other disturbances, with an overall latency of 70±15 ms. The greater responsiveness to hydrostatic rolling instability is attributed to functions requiring an upright posture and differences among species in habitat preferences.

Function of pectoral fins in rainbow trout: behavioral repertoire and hydrodynamic forces

Salmonid fishes (trout, salmon and relatives) have served as a model system for study of the mechanics of aquatic animal locomotion, yet little is known about the function of non-axial propulsors in this major taxonomic group. In this study we examine the behavioral and hydromechanical repertoire of the paired pectoral fins of rainbow trout Oncorhynchus mykiss, performing both steady rectilinear swimming and unsteady maneuvering locomotion. A combination of kinematic analysis and quantitative flow visualization (using digital particle image velocimetry) enables identification of the propulsive roles played by pectoral fin motions. During constant-speed swimming (0.5 and 1.0 body length s(-1)), the pectoral fins remain adducted against the body. These fins are actively recruited, however, for a variety of maneuvering behaviors, including station holding in still water (hovering), low-speed (i.e. non-fast-start) turning, and rapid deceleration of the body during braking. Despite having a shallow pectoral-fin base orientation (the plesiomorphic teleost condition), trout are capable of rotating the fin base over 30 degrees during maneuvering, which affords the fin an impressive degree of kinematic versatility. When hovering, the pectoral fins are depressed beneath the body and twisted along their long axes to allow anteroposterior sculling. During turning and braking, the fins undergo spanwise rotation in the opposite direction and exhibit mediolateral and dorsoventral excursions. Water velocity fields and calculated momentum flows in the wake of the pectoral fins reveal that positive thrust is not generated during maneuvering, except during the retraction half-stroke of hovering. Relatively large laterally directed fluid force (mean 2.7 mN) is developed during turning, whose reaction powers yawing rotation of the body (4-41 degrees s(-1)). During deceleration, the wake-force line of action falls below the center of mass of the body, and this result supports a long-standing mechanical model of braking by fishes with ventrally positioned paired fins. Despite its traditional categorization as a propulsor of limited functional importance, the salmoniform pectoral fin exhibits a diverse locomotor repertoire comparable to that of higher teleostean fishes.

Hydrodynamic stability of swimming in ostraciid fishes: role of the carapace in the smooth trunkfish Lactophrys triqueter (Teleostei: Ostraciidae)

The hydrodynamic bases for the stability of locomotory motions in fishes are poorly understood, even for those fishes, such as the rigid-bodied smooth trunkfish Lactophrys triqueter, that exhibit unusually small amplitude recoil movements during rectilinear swimming. We have studied the role played by the bony carapace of the smooth trunkfish in generating trimming forces that self-correct for instabilities. The flow patterns, forces and moments on and around anatomically exact, smooth trunkfish models positioned at both pitching and yawing angles of attack were investigated using three methods: digital particle image velocimetry (DPIV), pressure distribution measurements, and force balance measurements. Models positioned at various pitching angles of attack within a flow tunnel produced well-developed counter-rotating vortices along the ventro-lateral keels. The vortices developed first at the anterior edges of the ventro-lateral keels, grew posteriorly along the carapace, and reached maximum circulation at the posterior edge of the carapace. The vortical flow increased in strength as pitching angles of attack deviated from 0 degrees, and was located above the keels at positive angles of attack and below them at negative angles of attack. Variation of yawing angles of attack resulted in prominent dorsal and ventral vortices developing at far-field locations of the carapace; far-field vortices intensified posteriorly and as angles of attack deviated from 0 degrees. Pressure distribution results were consistent with the DPIV findings, with areas of low pressure correlating well with regions of attached, concentrated vorticity. Lift coefficients of boxfish models were similar to lift coefficients of delta wings, devices that also generate lift through vortex generation. Furthermore, nose-down and nose-up pitching moments about the center of mass were detected at positive and negative pitching angles of attack, respectively. The three complementary experimental approaches all indicate that the carapace of the smooth trunkfish effectively generates self-correcting forces for pitching and yawing motions--a characteristic that is advantageous for the highly variable velocity fields experienced by trunkfish in their complex aquatic environment. All important morphological features of the carapace contribute to producing the hydrodynamic stability of swimming trajectories in this species.

Escape manoeuvres in damsel-fly larvae: kinematics and dynamics

The kinematics and hydrodynamics of rapid escape manoeuvres executed by final-stage larvae of Enallagma cyathigerum were investigated using videography combined with a simple wake-visualisation technique. Two kinds of escape manoeuvres were identified: first, a 'rapid flex', comparable with the rapid C-start of fish, and, second, a 'rapid twist' that involves a helical contraction of the body inducing motion in the yaw, pitch and roll planes. In both cases, the initial flexion phase is concerned with re-orientating the body, the extensional phase with acceleration of the body in the new direction. The behaviour of the caudal fin during twist indicates considerable independence of movement and aspect control within the three constituent lobes. Dye deposited beneath the resting larvae showed a thrust jet shed into the wake at the end of the extension phase. The estimated momentum of the ring vortex containing the jet was similar to that imparted to the body at the start of the translational phase. Similarities between the swimming dynamics of damsel-fly larvae and fish are discussed, as well as the wider implications of these findings to other aquatic invertebrates whose normal, steady swimming appears to be based on unsteady manoeuvres.

Maneuvering in juvenile carcharhinid and sphyrnid sharks: the role of the hammerhead shark cephalofoil

The peculiar head morphology of hammerhead sharks has spawned a variety of untested functional hypotheses. One of the most intuitively appealing ideas is that the anterior foil acts, as in canard-winged aircraft, to increase maneuverability. We tested this hypothesis by determining whether juveniles of two hammerhead species (Sphyrna tiburo and S. lewini) turn more sharply, more often, and with greater velocity than a juvenile carcharhinid shark (Carcharhinus plumbeus). Although the hammerheads were more maneuverable, further investigation revealed that they do not roll their body during turns, suggesting that the cephalofoil does not act as a steering wing. We also show that hammerhead sharks demonstrate greater lateral flexure in a turn than carcharhinids, and that this flexibility may be due to cross sectional shape rather than number of vertebrae.

Force transmission via axial tendons in undulating fish: a dynamic analysis

Sonomicrometrics of in vivo axial strain of muscle has shown that the swimming fish body bends like a homogenous, continuous beam in all species except tuna. This simple beam-like behavior is surprising because the underlying tendon structure, muscle structure and behavior are complex. Given this incongruence, our goal was to understand the mechanical role of various myoseptal tendons. We modeled a pumpkinseed sunfish, Lepomis gibbosus, using experimentally-derived physical and mechanical attributes, swimming from rest with steady muscle activity. Axially oriented muscle-tendons, transverse and axial myoseptal tendons, as suggested by current morphological knowledge, interacted to replicate the force and moment distribution. Dynamic stiffness and damping associated with muscle activation, realistic muscle force generation, and force distribution following tendon geometry were incorporated. The vertebral column consisted of 11 rigid vertebrae connected by joints that restricted bending to the lateral plane and endowed the body with its passive viscoelasticity. In reaction to the acceleration of the body in an inviscid fluid and its internal transmission of moment via the vertebral column, the model predicted the kinematic response. Varying only tendon geometry and stiffness, four different simulations were run. Simulations with only intrasegmental tendons produced unstable axial and lateral tail forces and body motions. Only the simulation that included both intra- and intersegmental tendons, muscle-enhanced segment stiffness, and a stiffened caudal joint produced stable and large lateral and axial forces at the tail. Thus this model predicts that axial tendons function within a myomere to (1) convert axial force to moment (moment transduction), (2) transmit axial forces between adjacent myosepta (segment coupling), and, intersegmentally, to (3) distribute axial forces (force entrainment), and (4) stiffen joints in bending (flexural stiffening). The fact that all four functions are needed to produce the most realistic swimming motions suggests that axial tendons are essential to the simple beam-like behavior of fish.

Forces, fishes, and fluids: hydrodynamic mechanisms of aquatic locomotion

Understanding how fishes generate external fluid force to swim steadily and maneuver has proven to be difficult because water does not provide a stable platform for force measurement. But new methods in experimental fluid mechanics provide insights into the physiological mechanisms of aquatic force generation and limits to locomotor performance.

Quantification of the wake of rainbow trout (Oncorhynchus mykiss) using three-dimensional stereoscopic digital particle image velocimetry

Although considerable progress has been made within the last decade in experimental hydrodynamic analyses of aquatic locomotion using two-dimensional digital particle image velocimetry (two-dimensional DPIV), data have been limited to simultaneous calculation of two out of the three flow velocity variables: downstream (U), vertical (V) and lateral(W). Here, we present the first biological application of stereo-DPIV, an engineering technique that allows simultaneous calculation of U, V and W velocity vectors. We quantified the wakes of rainbow trout (Oncorhynchus mykiss, 16.5-21.5 cm total body length, BL), swimming steadily in a recirculating flow tank at a slow cruising speed of 1.2 BL s-1. These data extend the comparative basis of current hydromechanical data on the wakes of free-swimming fishes to the salmoniforms and are used to test current hypotheses of fin function by calculations of mechanical performance and Froude efficiency.

Stereo-DPIV wake images showed three-dimensional views of oscillating jet flows high in velocity relative to free-stream values. These jet flows are consistent with the central momentum jet flows through the cores of shed vortex rings that have been previously viewed for caudal fin swimmers using two-dimensional DPIV. The magnitude and direction of U, V and W flows in these jets were determined over a time series of 6-8 consecutive strokes by each of four fish.

Although the fish swam at the same relative speed, the absolute magnitudes of U, V and W were dependent on individual because of body size variation. Vertical flows were small in magnitude (<1 cm s-1) and variable in direction, indicating limited and variable vertical force production during slow, steady, forward swimming. Thus, in contrast to previous data from sunfish (Lepomis macrochirus) and mackerel (Scomber japonicus), the trout homocercal caudal fin does not appear to generate consistent vertical forces during steady swimming. U flows were of the order of 3-6 cm s-1; lateral flows were typically strongest, with W magnitudes of 4-6 cm s-1. Such strong lateral flows have also been shown for more derived euteleosts with homocercal caudal fins.

The ratios of the magnitudes of wake flow, U/(U+V+W), which is a flow equivalent to mechanical performance, were also dependent on individual and ranged from 0.32 to 0.45, a range similar to the range of mechanical performance values previously determined using standard two-dimensional DPIV methods for caudal fin locomotion by more derived euteleosts. Strong lateral jet flow appears to be a general feature of caudal fin locomotion by teleosts and may reflect the nature of undulatory propulsion as a posteriorly propagated wave of bending. Froude efficiency (ηp) was independent of individual; meanη p was 0.74, which is similar to previous findings for trout.

Hydrodynamics of caudal fin locomotion by chub mackerel,Scomber japonicus(Scombridae)

As members of the derived teleost fish clade Scombridae, mackerel exhibit high-performance aquatic locomotion via oscillation of the homocercal forked caudal fin. We present the first quantitative flow visualization of the wake of a scombrid fish, chub mackerel Scomber japonicus (20-26cm fork length, FL), swimming steadily in a recirculating flow tank at cruising speeds of 1.2 and 2.2FLs-1. Thrust was calculated from wake measurements made separately in the horizontal (frontal) plane and vertical (parasagittal) planes using digital particle image velocimetry (DPIV)and compared with drag measurements obtained by towing the same specimens of S. japonicus post mortem.

Patterns of flow indicated that the wake consisted of a series of linked elliptical vortex rings, each with central jet flow. The length of the minor axis (height) of the vortex rings was approximately equal to caudal fin span;the length of the major ring axis was dependent on swimming speed and was up to twice the magnitude of ring height. Profiles of wake velocity components were similar to theoretical profiles of vortex rings.

Lift, thrust and lateral forces were calculated from DPIV measurements. At 1.2FLs-1, lift forces measured relative to the Xaxis were low in magnitude (-1±1mN, mean ± S.D., N=20)but oriented at a mean angle of 6° to the body axis. Reaction forces tend to rotate the fish about its center of mass, tipping the head down. Thus, the homocercal caudal fin of S. japonicus functions asymmetrically in the vertical plane. Pitching moments may be balanced anteriorly via lift generation by the pectoral fins. Thrust estimates for the two smallest fish based on DPIV analysis were not significantly different from drag measurements made by towing those same animals. At a speed of 1.2FLs-1,thrust magnitude was 11±6mN (mean ± S.D, N=40). Lateral force magnitudes were approximately double thrust magnitudes (22±6mN,mean ± S.D., N=20), resulting in a mean mechanical performance ratio (thrust/total force) of 0.32 at 1.2FLs-1. An increase in speed by a factor of 1.8 resulted in a mean increase in thrust by a factor of 4.4, a mean increase in lateral forces by a factor of 3, no change in the magnitude of lift produced and an increase in mean mechanical performance to 0.42. The relatively high lateral forces generated during swimming may be a necessary consequence of force production viapropagated waves of bending.

Maneuvering in an arboreal habitat: the effects of turning angle on the locomotion of three sympatric ecomorphs ofAnolislizards

Although the maximal speeds of straight-ahead running are well-documented for many species of Anolis and other lizards, no previous study has experimentally determined the effects of turning on the locomotor performance of a lizard. Anolis lizards are a diverse group of arboreal species, and the discrete paths created by networks of perches in arboreal environments often force animals to turn in their natural habitats. For three species of Anolis with similar overall body size but different shape, we quantified the escape locomotor performance for arboreal locomotion on 4.8 cm diameter perches that were straight (0°) or had turning angles of 30° and 90°. The turning angle had widespread significant effects that were often species-dependent. This was shown by measuring the average gross velocity (including the times while the lizards paused) of the three species covering the middle 30 cm of a racetrack with either 30° or 90° turns. The results were expressed as a percentage of the gross velocity over the same distance on a straight racetrack. The values obtained for A. grahami (99 % for 30° turns and 79 % for 90° turns) showed a smaller effect of turning angle than for A. lineatopus (79 % for 30° turns and 50 % for 90° turns) and A. valencienni (74 % for 30° turns and 48 % for 90° turns). Consequently, the rank order of species based on speed depended on the angle of the turn. Some of the magnitudes of decreased locomotor speed associated with turning exceeded those reported previously for the effects of decreasing perch diameter for these species. For all species, more pausing occurred with increased turning angle, with the twig ecomorph (A. valencienni) pausing the most. Approximately half the individuals of each species jumped to traverse the 90° turn, but some of the potential benefits of jumping for increasing speed were offset by pauses associated with preparing to jump or recovering balance immediately after a jump. The tail of Anolis lizards may facilitate the substantial rotation (>60°) of the body that often occurred in the airborne phase of the jumps.

Performance and maneuverability of three species of teleostean fishes

Whole-animal behavior and performance are assembled from functional capabilities that are dependent on morphology, such as body form and fin-distribution patterns. We compared hovering, median and paired fin (MPF), body and caudal fin (BCF), and burst-and-coast gaits and maneuvers permitted within these gaits, turning, backward swimming, and braking for three species: goldfish, Carassius auratus, silver dollar, Metynnis hypsauchen, and angelfish, Pterophyllum scalare. Goldfish have a fusiform body with a relatively small surface area and depth. Silver dollars and angelfish had larger areas and depths. The smaller surface area was expected to be associated with greater use and higher speeds in BCF swimming behaviors for goldfish but little support was found. Larger body depth was expected to be associated with higher turning rates and maneuverability of silver dollars versus goldfish, but data were again equivocal. Body depth may be more important in defense than in locomotion. Goldfish and silver dollars have ventral paired fins. Angelfish have more derived lateral pectoral fins, anterior pelvic fins, and larger median fins. This fin pattern was expected to be associated with greater use of MPF behaviors at higher speeds, and with greater maneuverability. Support for this expectation was found, but there were sufficient exceptions to indicate that other factors were important.

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

A key evolutionary transformation of the locomotor system of ray-finned fishes is the morphological elaboration of the dorsal fin. Within Teleostei, the dorsal fin primitively is a single midline structure supported by soft, flexible fin rays. In its derived condition, the fin is made up of two anatomically distinct portions: an anterior section supported by spines, and a posterior section that is soft-rayed. We have a very limited understanding of the functional significance of this evolutionary variation in dorsal fin design. To initiate empirical hydrodynamic study of dorsal fin function in teleost fishes, we analyzed the wake created by the soft dorsal fin of bluegill sunfish (Lepomis macrochirus) during both steady swimming and unsteady turning maneuvers. Digital particle image velocimetry was used to visualize wake structures and to calculate in vivo locomotor forces. Study of the vortices generated simultaneously by the soft dorsal and caudal fins during locomotion allowed experimental characterization of median-fin wake interactions.

During high-speed swimming (i.e. above the gait transition from pectoral- to median-fin locomotion), the soft dorsal fin undergoes regular oscillatory motion which, in comparison with analogous movement by the tail, is phase-advanced (by 30% of the cycle period) and of lower sweep amplitude (by 1.0cm). Undulations of the soft dorsal fin during steady swimming at 1.1bodylengths−1 generate a reverse von Kármán vortex street wake that contributes 12% of total thrust. During low-speed turns, the soft dorsal fin produces discrete pairs of counterrotating vortices with a central region of high-velocity jet flow. This vortex wake, generated in the latter stage of the turn and posterior to the center of mass of the body, counteracts torque generated earlier in the turn by the anteriorly positioned pectoral fins and thereby corrects the heading of the fish as it begins to translate forward away from the turning stimulus. One-third of the laterally directed fluid force measured during turning is developed by the soft dorsal fin. For steady swimming, we present empirical evidence that vortex structures generated by the soft dorsal fin upstream can constructively interact with those produced by the caudal fin downstream. Reinforcement of circulation around the tail through interception of the dorsal fin’s vortices is proposed as a mechanism for augmenting wake energy and enhancing thrust.

Swimming in fishes involves the partitioning of locomotor force among several independent fin systems. Coordinated use of the pectoral fins, caudal fin and soft dorsal fin to increase wake momentum, as documented for L. macrochirus, highlights the ability of teleost fishes to employ multiple propulsors simultaneously for controlling complex swimming behaviors.