A pressure-based force and torque prediction technique for the study of fish-like swimming

In-line swimming dynamics revealed by fish interacting with a robotic mechanism

Schooling in fish is linked to a number of factors such as increased foraging success, predator avoidance, and social interactions. In addition, a prevailing hypothesis is that swimming in groups provides energetic benefits through hydrodynamic interactions. Thrust wakes are frequently occurring flow structures in fish schools as they are shed behind swimming fish. Despite increased flow speeds in these wakes, recent modeling work has suggested that swimming directly in-line behind an individual may lead to increased efficiency. However, only limited data are available on live fish interacting with thrust wakes. Here we designed a controlled experiment in which brook trout, Salvelinus fontinalis, interact with thrust wakes generated by a robotic mechanism that produces a fish-like wake. We show that trout swim in thrust wakes, reduce their tail-beat frequencies, and synchronize with the robotic flapping mechanism. Our flow and pressure field analysis revealed that the trout are interacting with oncoming vortices and that they exhibit reduced pressure drag at the head compared to swimming in isolation. Together, these experiments suggest that trout swim energetically more efficiently in thrust wakes and support the hypothesis that swimming in the wake of one another is an advantageous strategy to save energy in a school.

A tale of two fish tails: does a forked tail really perform better than a truncate tail when cruising?

Many fishes use their tail as the main thrust producer during swimming. This fin's diversity in shape and size influences its physical interactions with water as well as its ecological functions. Two distinct tail morphologies are common in bony fishes: flat, truncate tails which are best suited for fast accelerations via drag forces, and forked tails that promote economical, fast cruising by generating lift-based thrust. This assumption is based primarily on studies of the lunate caudal fin of Scombrids (i.e. tuna, mackerel), which is comparatively stiff and exhibits an airfoil-type cross-section. However, this is not representative of the more commonly observed and taxonomically widespread flexible forked tail, yet similar assumptions about economical cruising are widely accepted. Here, we present the first comparative experimental study of forked versus truncate tail shape and compare the fluid mechanical properties and energetics of two common nearshore fish species. We examined the hypothesis that forked tails provide a hydrodynamic advantage over truncate tails at typical cruising speeds. Using experimentally derived pressure fields, we show that the forked tail produces thrust via acceleration reaction forces like the truncate tail during cruising but at increased energetic costs. This reduced efficiency corresponds to differences in the performance of the two tail geometries and body kinematics to maintain similar overall thrust outputs. Our results offer insights into the benefits and tradeoffs of two common fish tail morphologies and shed light on the functional morphology of fish swimming to guide the development of bio-inspired underwater technologies.

Hydrodynamic stress and phenotypic plasticity of the zebrafish regenerating fin

Understanding how extrinsic factors modulate genetically encoded information to produce a specific phenotype is of prime scientific interest. In particular, the feedback mechanism between abiotic forces and locomotory organs during morphogenesis to achieve efficient movement is a highly relevant example of such modulation. The study of this developmental process can provide unique insights on the transduction of cues at the interface between physics and biology. Here, we take advantage of the natural ability of adult zebrafish to regenerate their amputated fins to assess its morphogenic plasticity upon external modulations. Using a variety of surgical and chemical treatments, we could induce phenotypic responses to the structure of the fin. Through the ablation of specific rays in regenerating caudal fins, we generated artificially narrowed appendages in which the fin cleft depth and the positioning of rays bifurcations were perturbed compared with normal regenerates. To dissect the role of mechanotransduction in this process, we investigated the patterns of hydrodynamic forces acting on the surface of a zebrafish fin during regeneration by using particle tracking velocimetry on a range of biomimetic hydrofoils. This experimental approach enabled us to quantitatively compare hydrodynamic stress distributions over flapping fins of varying sizes and shapes. As a result, viscous shear stress acting on the distal margin of regenerating fins and the resulting internal tension are proposed as suitable signals for guiding the regulation of ray growth dynamics and branching pattern. Our findings suggest that mechanical forces are involved in the fine-tuning of the locomotory organ during fin morphogenesis.

Metachronal motion across scales: current challenges and future directions

Metachronal motion is used across a wide range of organisms for a diverse set of functions. However, despite its ubiquity, analysis of this behavior has been difficult to generalize across systems. Here we provide an overview of known commonalities and differences between systems that use metachrony to generate fluid flow. We also discuss strategies for standardizing terminology and defining future investigative directions that are analogous to other established subfields of biomechanics. Lastly, we outline key challenges that are common to many metachronal systems, opportunities that have arisen due to the advent of new technology (both experimental and computational), and next steps for community development and collaboration across the nascent network of metachronal researchers.

Hydrodynamic stress maps on the surface of a flexible fin-like foil

We determine the time dependence of pressure and shear stress distributions on the surface of a pitching and deforming hydrofoil from measurements of the three dimensional flow field. Period-averaged stress maps are obtained both in the presence and absence of steady flow around the foil. The velocity vector field is determined via volumetric three-component particle tracking velocimetry and subsequently inserted into the Navier-Stokes equation to calculate the total hydrodynamic stress tensor. In addition, we also present a careful error analysis of such measurements, showing that local evaluations of stress distributions are possible. The consistency of the force time-dependence is verified using a control volume analysis. The flapping foil used in the experiments is designed to allow comparison with a small trapezoidal fish fin, in terms of the scaling laws that govern the oscillatory flow regime. As a complementary approach, unsteady Euler-Bernoulli beam theory is employed to derive instantaneous transversal force distributions on the flexible hydrofoil from its deflection and the results are compared to the spatial distributions of hydrodynamic stresses obtained from the fluid velocity field.

The Hydrodynamics of Jellyfish Swimming

Jellyfish have provided insight into important components of animal propulsion, such as suction thrust, passive energy recapture, vortex wall effects, and the rotational mechanics of turning. These traits are critically important to jellyfish because they must propel themselves despite severe limitations on force production imposed by rudimentary cnidarian muscular structures. Consequently, jellyfish swimming can occur only by careful orchestration of fluid interactions. Yet these mechanics may be more broadly instructive because they also characterize processes shared with other animal swimmers, whose structural and neurological complexity can obscure these interactions. In comparison with other animal models, the structural simplicity, comparative energetic efficiency, and ease of use in laboratory experimentation allow jellyfish to serve as favorable test subjects for exploration of the hydrodynamic bases of animal propulsion. These same attributes also make jellyfish valuable models for insight into biomimetic or bioinspired engineeringof swimming vehicles. Here, we review advances in understanding of propulsive mechanics derived from jellyfish models as a pathway toward the application of animal mechanics to vehicle designs.

The role of suction thrust in the metachronal paddles of swimming invertebrates

An abundance of swimming animals have converged upon a common swimming strategy using multiple propulsors coordinated as metachronal waves. The shared kinematics suggest that even morphologically and systematically diverse animals use similar fluid dynamic relationships to generate swimming thrust. We quantified the kinematics and hydrodynamics of a diverse group of small swimming animals who use multiple propulsors, e.g. limbs or ctenes, which move with antiplectic metachronal waves to generate thrust. Here we show that even at these relatively small scales the bending movements of limbs and ctenes conform to the patterns observed for much larger swimming animals. We show that, like other swimming animals, the propulsors of these metachronal swimmers rely on generating negative pressure along their surfaces to generate forward thrust (i.e., suction thrust). Relying on negative pressure, as opposed to high pushing pressure, facilitates metachronal waves and enables these swimmers to exploit readily produced hydrodynamic structures. Understanding the role of negative pressure fields in metachronal swimmers may provide clues about the hydrodynamic traits shared by swimming and flying animals.

How zebrafish turn: analysis of pressure force dynamics and mechanical work

Whereas many fishes swim steadily, zebrafish regularly exhibit unsteady burst-and-coast swimming, which is characterized by repeated sequences of turns followed by gliding periods. Such a behavior offers the opportunity to investigate the hypothesis that negative mechanical work occurs in posterior regions of the body during early phases of the turn near the time of maximal body curvature. Here, we used a modified particle image velocimetry (PIV) technique to obtain high-resolution flow fields around the zebrafish body during turns. Using detailed swimming kinematics coupled with body surface pressure computations, we estimated fluid-structure interaction forces and the pattern of forces and torques along the body during turning. We then calculated the mechanical work done by each body segment. We used estimated patterns of positive and negative work along the body to evaluate the hypothesis (based on fish midline kinematics) that the posterior body region would experience predominantly negative work. Between 10% and 20% of the total mechanical work was done by the fluid on the body (negative work), and negative work was concentrated in the anterior and middle areas of the body, not along the caudal region. Energetic costs of turning were calculated by considering the sum of positive and negative work and were compared with previous metabolic estimates of turning energetics in fishes. The analytical workflow presented here provides a rigorous way to quantify hydrodynamic mechanisms of fish locomotion and facilitates the understanding of how body kinematics generate locomotor forces in freely swimming fishes.

Jellyfish and Fish Solve the Challenges of Turning Dynamics Similarly to Achieve High Maneuverability

Turning maneuvers by aquatic animals are essential for fundamental life functions such as finding food or mates while avoiding predation. However, turning requires resolution of a fundamental dilemma based in rotational mechanics: the force powering a turn (torque) is favored by an expanded body configuration that maximizes lever arm length, yet minimizing the resistance to a turn (the moment of inertia) is favored by a contracted body configuration. How do animals balance these opposing demands? Here, we directly measure instantaneous forces along the bodies of two animal models—the radially symmetric Aurelia aurita jellyfish, and the bilaterally symmetric Danio rerio zebrafish—to evaluate their turning dynamics. Both began turns with a small, rapid shift in body kinematics that preceded major axial rotation. Although small in absolute magnitude, the high fluid accelerations achieved by these initial motions generated powerful pressure gradients that maximized torque at the start of a turn. This pattern allows these animals to initially maximize torque production before major body curvature changes. Both animals then subsequently minimized the moment of inertia, and hence resistance to axial rotation, by body bending. This sequential solution provides insight into the advantages of re-arranging mass by bending during routine swimming turns.

Airfoil-like mechanics generate thrust on the anterior body of swimming fishes

The anterior body of many fishes is shaped like an airfoil turned on its side. With an oscillating angle to the swimming direction, such an airfoil experiences negative pressure due to both its shape and pitching movements. This negative pressure acts as thrust forces on the anterior body. Here, we apply a high-resolution, pressure-based approach to describe how two fishes, bluegill sunfish (Lepomis macrochirus Rafinesque) and brook trout (Salvelinus fontinalis Mitchill), swimming in the carangiform mode, the most common fish swimming mode, generate thrust on their anterior bodies using leading-edge suction mechanics, much like an airfoil. These mechanics contrast with those previously reported in lampreys-anguilliform swimmers-which produce thrust with negative pressure but do so through undulatory mechanics. The thrust produced on the anterior bodies of these carangiform swimmers through negative pressure comprises 28% of the total thrust produced over the body and caudal fin, substantially decreasing the net drag on the anterior body. On the posterior region, subtle differences in body shape and kinematics allow trout to produce more thrust than bluegill, suggesting that they may swim more effectively. Despite the large phylogenetic distance between these species, and differences near the tail, the pressure profiles around the anterior body are similar. We suggest that such airfoil-like mechanics are highly efficient, because they require very little movement and therefore relatively little active muscular energy, and may be used by a wide range of fishes since many species have appropriately shaped bodies.

Thrust generation during steady swimming and acceleration from rest in anguilliform swimmers

Escape swimming is a crucial behavior by which undulatory swimmers evade potential threats. The hydrodynamics of escape swimming have not been well studied, particularly for anguilliform swimmers, such as the sea lamprey Petromyzon marinus. For this study, we compared the kinematics and hydrodynamics of larval sea lampreys with those of lampreys accelerating from rest during escape swimming. We used experimentally derived velocity fields to calculate pressure fields and distributions of thrust and drag along the body. Lampreys initiated acceleration from rest with the formation of a high-amplitude body bend at approximately one-quarter body length posterior to the head. This deep body bend produced two high-pressure regions from which the majority of thrust for acceleration was derived. In contrast, steady swimming was characterized by shallower body bends and negative-pressure-derived thrust, which was strongest near the tail. The distinct mechanisms used for steady swimming and acceleration from rest may reflect the differing demands of the two behaviors. High-pressure-based mechanisms, such as the one used for acceleration from rest, could also be important for low-speed maneuvering during which drag-based turning mechanisms are less effective. The design of swimming robots may benefit from the incorporation of such insights from unsteady swimming.

Reorientation and propulsion in fast-starting zebrafish larvae: an inverse dynamics analysis

Most fish species use fast starts to escape from predators. Zebrafish larvae perform effective fast starts immediately after hatching. They use a C-start, where the body curls into a C-shape, and then unfolds to accelerate. These escape responses need to fulfil a number of functional demands, under the constraints of the fluid environment and the larva's body shape. Primarily, the larvae need to generate sufficient escape speed in a wide range of possible directions, in a short-enough time. In this study, we examined how the larvae meet these demands. We filmed fast starts of zebrafish larvae with a unique five-camera setup with high spatiotemporal resolution. From these videos, we reconstructed the 3D swimming motion with an automated method and from these data calculated resultant hydrodynamic forces and, for the first time, 3D torques. We show that zebrafish larvae reorient mostly in the first stage of the start by producing a strong yaw torque, often without using the pectoral fins. This reorientation is expressed as the body angle, a measure that represents the rotation of the complete body, rather than the commonly used head angle. The fish accelerates its centre of mass mostly in stage 2 by generating a considerable force peak while the fish 'unfolds'. The escape direction of the fish correlates strongly with the amount of body curvature in stage 1, while the escape speed correlates strongly with the duration of the start. This may allow the fish to independently control the direction and speed of the escape.

Multichannel stroboscopic videography (MSV): a technique for visualizing multiple channels for behavioral measurements

Biologists commonly visualize different features of an organism using distinct sources of illumination. Such multichannel imaging has largely not been applied to behavioral studies because of the challenges posed by a moving subject. We address this challenge with the technique of multichannel stroboscopic videography (MSV), which synchronizes multiple strobe lights with video exposures of a single camera. We illustrate the utility of this approach with kinematic measurements of a walking cockroach (Gromphadorhina portentosa) and calculations of the pressure field around a swimming fish (Danio rerio). In both, transmitted illumination generated high-contrast images of the animal's body in one channel. Other sources of illumination were used to visualize the points of contact for the feet of the cockroach and the water flow around the fish in separate channels. MSV provides an enhanced potential for high-throughput experimentation and the capacity to integrate changes in physiological or environmental conditions in freely-behaving animals.

Propulsive design principles in a multi-jet siphonophore

Coordination of multiple propulsors can provide performance benefits in swimming organisms. Siphonophores are marine colonial organisms that orchestrate the motion of multiple swimming zooids for effective swimming. However, the kinematics at the level of individual swimming zooids (nectophores) have not been examined in detail. We used high speed, high resolution microvideography and particle image velocimetry (PIV) of the physonect siphonophore, Nanomia bijuga, to study the motion of the nectophores and the associated fluid motion during jetting and refilling. The integration of nectophore and velum kinematics allow for a high-speed (maximum ∼1 m s−1), narrow (1-2 mm) jet and rapid refill as well as a 1:1 ratio of jetting to refill time. Scaled to the 3 mm nectophore length, jet speeds reach >300 lengths s−1. Overall swimming performance is enhanced by velocity gradients produced in the nectophore during refill, which lead to a high pressure region that produces forward thrust. Generating thrust during both the jet and refill phases augments the distance travelled by 17% over theoretical animals, which generate thrust only during the jet phase. The details of velum kinematics and associated fluid mechanics elucidate how siphonophores effectively navigate three-dimensional space and could be applied to exit flow parameters in multijet underwater vehicles.

Passive bristling of mako shark scales in reversing flows

Shark skin has been shown to reduce drag in turbulent boundary layer flows, but the flow control mechanisms by which it does so are not well understood. Drag reduction has generally been attributed to static effects of scale surface morphology, but possible drag reduction effects of passive or active scale actuation, or 'bristling', have been recognized more recently. Here, we provide the first direct documentation of passive scale bristling due to reversing, turbulent boundary layer flows. We recorded and analysed high-speed videos of flow over the skin of a shortfin mako shark, Isurus oxyrinchus These videos revealed rapid scale bristling events with mean durations of approximately 2 ms. Passive bristling occurred under flow conditions representative of cruise swimming speeds and was associated with two flow features. The first was a downward backflow that pushed a scale-up from below. The second was a vortex just upstream of the scale that created a negative pressure region, which pulled up a scale without requiring backflow. Both flow conditions initiated bristling at lower velocities than those required for a straight backflow. These results provide further support for the role of shark scale bristling in drag reduction.