Eric Tytell

The hydrodynamics of eel swimming: I. Wake structure.

SUMMARY Eels undulate a larger portion of their bodies while swimming than many other fishes, but the hydrodynamic consequences of this swimming mode are poorly understood. In this study, we examine in detail the hydrodynamics of American eels (Anguilla rostrata) swimming steadily at 1.4 L s-1 and compare them with previous results from other fishes. We performed high-resolution particle image velocimetry (PIV) to quantify the wake structure, measure the swimming efficiency, and force and power output. The wake consists of jets of fluid that point almost directly laterally, separated by an unstable shear layer that rolls up into two or more vortices over time. Previously, the wake of swimming eels was hypothesized to consist of unlinked vortex rings, resulting from a phase offset between vorticity distributed along the body and vorticity shed at the tail. Our high-resolution flow data suggest that the body anterior to the tail tip produces relatively low vorticity, and instead the wake structure results from the instability of the shear layers separating the lateral jets, reflecting pulses of high vorticity shed at the tail tip. We compare the wake structure to large-amplitude elongated body theory and to a previous computational fluid dynamic model and note several discrepancies between the models and the measured values. The wake of steadily swimming eels differs substantially in structure from the wake of previously studied carangiform fishes in that it lacks any significant downstream flow, previously interpreted as signifying thrust. We infer that the lack of downstream flow results from a spatial and temporal balance of momentum removal (drag) and thrust generated along the body, due to the relatively uniform shape of eels. Carangiform swimmers typically have a narrow caudal peduncle, which probably allows them to separate thrust from drag both spatially and temporally. Eels seem to lack this separation, which may explain why they produce a wake with little downstream momentum while carangiform swimmers produce a wake with a clear thrust signature.

Hydrodynamics of Undulatory Propulsion

Publisher Summary The chapter focuses on recent experimental hydrodynamic data on undulatory locomotion in fishes, and provides a general description of the major theoretical model of undulatory propulsion. The investigations of fish propulsion have had to infer hydrodynamic function from kinematics and theoretical models. Biologists and engineers interested in how fishes interact with their fluid environment have had no quantitative way to visualize this interaction, despite the critical importance of understanding fluid flow patterns produced by swimming fishes for testing theoretical models and for understanding the hydrodynamic effects of different body and fin designs. The combination of high‐resolution high‐speed video systems, high-powered continuous wave lasers, and an image analysis technique called digital particle image velocimetry (DPIV), developed over the past decade, has permitted the direct visualization of water flow over the surface and in the wake of swimming fishes. These data have provided a wealth of new information on the fluid flows generated by the body, tail, and fins of freely swimming fishes, and represent a significant new arena of investigation.

Interactions between internal forces, body stiffness, and fluid environment in a neuromechanical model of lamprey swimming

Animal movements result from a complex balance of many different forces. Muscles produce force to move the body; the body has inertial, elastic, and damping properties that may aid or oppose the muscle force; and the environment produces reaction forces back on the body. The actual motion is an emergent property of these interactions. To examine the roles of body stiffness, muscle activation, and fluid environment for swimming animals, a computational model of a lamprey was developed. The model uses an immersed boundary framework that fully couples the Navier–Stokes equations of fluid dynamics with an actuated, elastic body model. This is the first model at a Reynolds number appropriate for a swimming fish that captures the complete fluid-structure interaction, in which the body deforms according to both internal muscular forces and external fluid forces. Results indicate that identical muscle activation patterns can produce different kinematics depending on body stiffness, and the optimal value of stiffness for maximum acceleration is different from that for maximum steady swimming speed. Additionally, negative muscle work, observed in many fishes, emerges at higher tail beat frequencies without sensory input and may contribute to energy efficiency. Swimming fishes that can tune their body stiffness by appropriately timed muscle contractions may therefore be able to optimize the passive dynamics of their bodies to maximize peak acceleration or swimming speed.

The hydrodynamics of eel swimming II. Effect of swimming speed

SUMMARY Simultaneous swimming kinematics and hydrodynamics are presented for American eels, Anguilla rostrata, swimming at speeds from 0.5 to 2 L s-1. Body outlines and particle image velocimetry (PIV) data were collected using two synchronized high-speed cameras, and an empirical relationship between swimming motions and fluid flow is described. Lateral impulse in the wake is estimated assuming that the flow field represents a slice through small core vortex rings and is shown to be significantly larger than forces estimated from the kinematics via elongated body theory (EBT) and via quasi-steady resistive drag forces. These simple kinematic models predict only 50% of the measured wake impulse, indicating that unsteady effects are important in undulatory force production. EBT does, however, correctly predict both the magnitude and time course of the power shed into the wake. Other wake flow structures are also examined relative to the swimming motions. At all speeds, the wake contains almost entirely lateral jets of fluid, separated by an unstable shear layer that rapidly breaks down into two vortices. The jets mean velocity grows with swimming speed, but jet diameter varies only weakly with swimming speed. Instead, it follows the body wavelength, which changes more among individuals than at different speeds. Circulation of the stop-start vortex, shed each time the tail changes direction, can also be predicted at low speeds by the integral of squared tail velocity over half of a tail beat. At high speeds, these kinematics predict more circulation than is actually present in the stop-start vortex. Finally, the cost of producing the wake, one component of the total cost of transport, increases with swimming speed to the 1.48 power, lower than would be expected if the power coefficient remained constant over the speed range examined.

Hydrodynamics of the escape response in bluegill sunfish, Lepomis macrochirus.

SUMMARY Escape responses of fishes are one of the best characterized vertebrate behaviors, with extensive previous research on both the neural control and biomechanics of startle response performance. However, very little is known about the hydrodynamics of escape responses, despite the fact that understanding fluid flow patterns during the escape is critical for evaluating how body movement transfers power to the fluid, for defining the time course of power generation, and for characterizing the wake signature left by escaping fishes, which may provide information to predators. In this paper, we present an experimental hydrodynamic analysis of the C-start escape response in bluegill sunfish (Lepomis macrochirus). We used time-resolved digital particle image velocimetry at 1000 frames s–1 (fps) to image flow patterns during the escape response. We analyzed flow patterns generated by the body separately from those generated by the dorsal and anal fins to assess the contribution of these median fins to escape momentum. Each escape response produced three distinct jets of fluid. Summing the components of fluid momentum in the jets provided an estimate of fish momentum that did not differ significantly from momentum measured from the escaping fish body. In contrast to conclusions drawn from previous kinematic analyses and theoretical models, the caudal fin generated momentum that opposes the escape during stage one, whereas the body bending during stage one contributed substantial propulsive momentum. Additionally, the dorsal and anal fins each contributed substantial momentum. The results underscore the importance of the dorsal and anal fins as propulsors and suggest that the size and placement of these fins may be a key determinant of fast start performance.

Median fin function in bluegill sunfish Lepomis macrochirus:streamwise vortex structure during steady swimming

SUMMARY Fishes have an enormous diversity of body shapes and fin morphologies. From a hydrodynamic standpoint, the functional significance of this diversity is poorly understood, largely because the three-dimensional flow around swimming fish is almost completely unknown. Fully three-dimensional volumetric flow measurements are not currently feasible, but measurements in multiple transverse planes along the body can illuminate many of the important flow features. In this study, I analyze flow in the transverse plane at a range of positions around bluegill sunfish Lepomis macrochirus, from the trailing edges of the dorsal and anal fins to the near wake. Simultaneous particle image velocimetry and kinematic measurements were performed during swimming at 1.2 body lengths s–1 to describe the streamwise vortex structure, to quantify the contributions of each fin to the vortex wake, and to assess the importance of three-dimensional flow effects in swimming. Sunfish produce streamwise vortices from at least eight distinct places, including both the dorsal and ventral margins of the soft dorsal and anal fins, and the tips and central notched region of the caudal fin. I propose a three-dimensional structure of the vortex wake in which these vortices from the caudal notch are elongated by the dorso-ventral cupping motion of the tail, producing a structure like a hairpin vortex in the caudal fin vortex ring. Vortices from the dorsal and anal fin persist into the wake, probably linking up with the caudal fin vortices. These dorsal and anal fin vortices do not differ significantly in circulation from the two caudal fin tip vortices. Because the circulations are equal and the length of the trailing edge of the caudal fin is approximately equal to the combined trailing edge length of the dorsal and anal fins, I argue that the two anterior median fins produce a total force that is comparable to that of the caudal fin. To provide additional detail on how different positions contribute to total force along the posterior body, the change in vortex circulation as flow passes down the body is also analyzed. The posterior half of the caudal fin and the dorsal and anal fins add vortex circulation to the flow, but circulation appears to decrease around the peduncle and anterior caudal fin. Kinematic measurements indicate that the tail is angled correctly to enhance thrust through this interaction. Finally, the degree to which the caudal fin acts like a idealized two-dimensional plate is examined: approximately 25% of the flow near the tail is accelerated up and down, rather than laterally, producing wasted momentum, a loss not present in ideal two-dimensional theories.

Disentangling the Functional Roles of Morphology and Motion in the Swimming of Fish

In fishes the shape of the body and the swimming mode generally are correlated. Slender-bodied fishes such as eels, lampreys, and many sharks tend to swim in the anguilliform mode, in which much of the body undulates at high amplitude. Fishes with broad tails and a narrow caudal peduncle, in contrast, tend to swim in the carangiform mode, in which the tail undulates at high amplitude. Such fishes also tend to have different wake structures. Carangiform swimmers generally produce two staggered vortices per tail beat and a strong downstream jet, while anguilliform swimmers produce a more complex wake, containing at least two pairs of vortices per tail beat and relatively little downstream flow. Are these differences a result of the different swimming modes or of the different body shapes, or both? Disentangling the functional roles requires a multipronged approach, using experiments on live fishes as well as computational simulations and physical models. We present experimental results from swimming eels (anguilliform), bluegill sunfish (carangiform), and rainbow trout (subcarangiform) that demonstrate differences in the wakes and in swimming performance. The swimming of mackerel and lamprey was also simulated computationally with realistic body shapes and both swimming modes: the normal carangiform mackerel and anguilliform lamprey, then an anguilliform mackerel and carangiform lamprey. The gross structure of simulated wakes (single versus double vortex row) depended strongly on Strouhal number, while body shape influenced the complexity of the vortex row, and the swimming mode had the weakest effect. Performance was affected even by small differences in the wakes: both experimental and computational results indicate that anguilliform swimmers are more efficient at lower swimming speeds, while carangiform swimmers are more efficient at high speed. At high Reynolds number, the lamprey-shaped swimmer produced a more complex wake than the mackerel-shaped swimmer, similar to the experimental results. Finally, we show results from a simple physical model of a flapping fin, using fins of different flexural stiffness. When actuated in the same way, fins of different stiffnesses propel themselves at different speeds with different kinematics. Future experimental and computational work will need to consider the mechanisms underlying production of the anguilliform and carangiform swimming modes, because anguilliform swimmers tend to be less stiff, in general, than are carangiform swimmers.

Escaping Flatland: three-dimensional kinematics and hydrodynamics of median fins in fishes

SUMMARY Fish swimming has often been simplified into the motions of a two-dimensional slice through the horizontal midline, as though fishes live in a flat world devoid of a third dimension. While fish bodies do undulate primarily horizontally, this motion has important three-dimensional components, and fish fins can move in a complex three-dimensional manner. Recent results suggest that an understanding of the three-dimensional body shape and fin motions is vital for explaining the mechanics of swimming, and that two-dimensional representations of fish locomotion are misleading. In this study, we first examine axial swimming from the two-dimensional viewpoint, detailing the limitations of this view. Then we present data on the kinematics and hydrodynamics of the dorsal fin, the anal fin and the caudal fin during steady swimming and maneuvering in brook trout, Salvelinus fontinalis, bluegill sunfish, Lepomis macrochirus, and yellow perch, Perca flavescens. These fishes actively move the dorsal and anal fins during swimming, resulting in curvature along both anterio-posterior and dorso-ventral axes. The momentum imparted to the fluid by these fins comprises a substantial portion of total swimming force, adding to thrust and contributing to roll stability. While swimming, the caudal fin also actively curves dorso-ventrally, producing vortices separately from both its upper and lower lobes. This functional separation of the lobes may allow additional control of three-dimensional orientation, but probably reduces swimming efficiency. In contrast, fish may boost the caudal fins efficiency by taking advantage of the flow from the dorsal and anal fins as it interacts with the flow around the caudal fin itself. During maneuvering, fish readily use their fins outside of the normal planes of motion. For example, the dorsal fin can flick laterally, orienting its surface perpendicular to the body, to help in turning and braking. These data demonstrate that, while fish do move primarily in the horizontal plane, neither their bodies nor their motions can accurately be simplified in a two-dimensional representation. To begin to appreciate the functional consequences of the diversity of fish body shapes and locomotor strategies, one must escape Flatland to examine all three dimensions.

Hydrodynamics of the bluegill sunfish C-start escape response: three-dimensional simulations and comparison with experimental data.

SUMMARY In this work we study the hydrodynamics of a bluegill sunfish performing a C-start maneuver in unprecedented detail using 3-D numerical simulations guided by previous laboratory experiments with live fish. The 3-D fish body geometry and kinematics are reconstructed from the experiments using high-speed video and prescribed as input to the numerical simulation. The calculated instantaneous flow fields at various stages of the C-start maneuver are compared with the two-dimensional particle image velocimetry measurements, and are shown to capture essentially all flow features observed in the measurements with good quantitative accuracy; the simulations reveal the experimentally observed three primary jet flow patterns whose momentum time series are in very good agreement with the measured flow field. The simulations elucidate for the first time the complex 3-D structure of the wake during C-starts, revealing an intricate vortical structure consisting of multiple connected vortex loops at the end of the C-start. We also find that the force calculated based on the 3-D flow field has higher magnitudes than that implied by the jet momentum on the midplane, and it exhibits large and rapid fluctuations during the two stages of the C-start. These fluctuations are physical and are related to the change in the direction of the acceleration of the fish body, which changes the location of the high and low pressure pockets around the fish.

Spikes alone do not behavior make: why neuroscience needs biomechanics.

Neural circuits do not function in isolation; they interact with the physical world, accepting sensory inputs and producing outputs via muscles. Since both these pathways are constrained by physics, the activity of neural circuits can only be understood by considering biomechanics of muscles, bodies, and the exterior world. We discuss how animal bodies have natural stable motions that require relatively little activation or control from the nervous system. The nervous system can substantially alter these motions, by subtly changing mechanical properties such as body or leg stiffness. Mechanics can also provide robustness to perturbations without sensory reflexes. By considering a complete neuromechanical system, neuroscientists and biomechanicians together can provide a more integrated view of neural circuitry and behavior.