Form and function of anguilliform swimming

Anguilliform swimmers are long and narrow animals that propel themselves by undulating their bodies. Observations in nature and recent investigations suggest that anguilliform swimming is highly efficient. However, understanding the underlying reasons for the efficiency of this type of locomotion requires interdisciplinary studies spanning from biology to hydrodynamics. Regrettably, these different fields are rarely discussed together, which hinders our ability to understand the repeated evolution of this swimming mode in vertebrates. This review compiles the current knowledge of the anatomical features that drive anguilliform swimming, compares the resulting kinematics across a wide range of anguilliform swimmers, and describes the resulting hydrodynamic interactions using data from both in vivo experiments and computational studies.

The hydrodynamics of jet propulsion swimming in hatchling and juvenile European common cuttlefish, Sepia officinalis

Cuttlefish swim using jet propulsion, taking a small volume of fluid into the mantle cavity before it is expelled through the siphon to generate thrust. Jet propulsion swimming has been shown to be more metabolically expensive than undulatory swimming, which has been suggested to be due to the lower efficiency of jet propulsion. The whole-cycle propulsive efficiency of cephalopod molluscs ranges from 38 to 76%, indicating that in some instances jet propulsion can be relatively efficient. Here, we determined the hydrodynamics of hatchling and juvenile cuttlefish during jet propulsion swimming to understand the characteristics of their jets, and whether their whole-cycle propulsive efficiency changes during development. Cuttlefish were found to utilise two jet types: isolated jet vortices (termed jet mode I) and elongated jets (leading edge vortex ring followed by a trailing jet; termed jet mode II). The use of these jet modes differed between the age classes, with newly hatched animals nearly exclusively utilising mode I jets, while juveniles showed no strong preferences. Whole-cycle propulsive efficiency was found to be high, ranging from 72 to 80%, and did not differ between age classes. During development, Strouhal number decreased as Reynolds number increased, which is consistent with animals adjusting their jetting behaviour in order to maximise whole-cycle propulsive efficiency and locomotor performance. Although jet propulsion swimming can have a relatively high energetic cost, in cuttlefish and nautilus, both neutrally buoyant species, the whole-cycle propulsive efficiency is actually relatively high.

Measuring the 3D wake of swimming snakes (Natrix tessellata) using volumetric particle image velocimetry

We describe a method for measuring the 3D vortical structures produced by an anguilliform swimmer using volumetric velocimetry. The wake of freely swimming dice snakes (Natrix tessellata) was quantified, revealing the creation of multiple vortices along the body of the snake due to its undulation. The 3D structure of the vortices generally consisted of paired vortex tubes, some of which were linked together to form a hairpin structure. The observations match predictions from computational fluid dynamic studies of other anguilliform swimmers. Quantitative measurements allowed us to study vortex circulation and size, and global kinetic energy of the flow, which varied with swimming speed, vortex topology and individual characteristics. Our findings provide a baseline for comparing wake structures of snakes with different morphologies and ecologies and investigating the energetic efficiency of anguilliform swimming.

The limits of convergence in the collective behavior of competing marine taxa

Collective behaviors in biological systems such as coordinated movements have important ecological and evolutionary consequences. While many studies examine within-species variation in collective behavior, explicit comparisons between functionally similar species from different taxonomic groups are rare. Therefore, a fundamental question remains: how do collective behaviors compare between taxa with morphological and physiological convergence, and how might this relate to functional ecology and niche partitioning? We examined the collective motion of two ecologically similar species from unrelated clades that have competed for pelagic predatory niches for over 500 million years-California market squid, Doryteuthis opalescens (Mollusca) and Pacific sardine, Sardinops sagax (Chordata). We (1) found similarities in how groups of individuals from each species collectively aligned, measured by angular deviation, the difference between individual orientation and average group heading. We also (2) show that conspecific attraction, which we approximated using nearest neighbor distance, was greater in sardine than squid. Finally, we (3) found that individuals of each species explicitly matched the orientation of groupmates, but that these matching responses were less rapid in squid than sardine. Based on these results, we hypothesize that information sharing is a comparably important function of social grouping for both taxa. On the other hand, some capabilities, including hydrodynamically conferred energy savings and defense against predators, could stem from taxon-specific biology.

Free swimming of a squid-inspired axisymmetric system through jet propulsion

An axisymmetric fluid-structure interaction model based on the immersed-boundary approach is developed to study the self-propelled locomotion of a squid-inspired swimmer in relatively low Reynolds numbers (O(102)). Through cyclic deformation, the swimmer generates intermittent jet flow, which, together with the added-mass effect associated with the body deformation, provides thrust. Through a control volume analysis we are able to determine the jet-related thrust. By adding it to the added-mass-related thrust we separate the net thrust on the body from the drag effect due to forward motion, so that the propulsion efficiency in free swimming is found. This numerical algorithm and thrust-drag decomposition method are used to study the dynamics of the bio-inspired locomotion system in different conditions, whereby the performance is characterized by the aforementioned propulsion efficiency as well as the conventionally defined cost of transport.

Cool your jets: biological jet propulsion in marine invertebrates

Pulsatile jet propulsion is a common swimming mode used by a diverse array of aquatic taxa from chordates to cnidarians. This mode of locomotion has interested both biologists and engineers for over a century. A central issue to understanding the important features of jet-propelling animals is to determine how the animal interacts with the surrounding fluid. Much of our knowledge of aquatic jet propulsion has come from simple theoretical approximations of both propulsive and resistive forces. Although these models and basic kinematic measurements have contributed greatly, they alone cannot provide the detailed information needed for a comprehensive, mechanistic overview of how jet propulsion functions across multiple taxa, size scales and through development. However, more recently, novel experimental tools such as high-speed 2D and 3D particle image velocimetry have permitted detailed quantification of the fluid dynamics of aquatic jet propulsion. Here, we provide a comparative analysis of a variety of parameters such as efficiency, kinematics and jet parameters, and review how they can aid our understanding of the principles of aquatic jet propulsion. Research on disparate taxa allows comparison of the similarities and differences between them and contributes to a more robust understanding of aquatic jet propulsion.

Squids use multiple escape jet patterns throughout ontogeny

Throughout their lives, squids are both predators and prey for a multitude of animals, many of which are at the top of ocean food webs, making them an integral component of the trophic structure of marine ecosystems. The escape jet, which is produced by the rapid expulsion of water from the mantle cavity through a funnel, is central to a cephalopod's ability to avoid predation throughout its life. Although squid undergo morphological and behavioral changes and experience remarkably different Reynolds number regimes throughout their development, little is known about the dynamics and propulsive efficiency of escape jets throughout ontogeny. We examine the hydrodynamics and kinematics of escape jets in squid throughout ontogeny using 2D/3D velocimetry and high-speed videography. All life stages of squid produced two escape jet patterns: (1) 'escape jet I' characterized by short rapid pulses resulting in vortex ring formation and (2) 'escape jet II' characterized by long high-volume jets, often with a leading-edge vortex ring. Paralarvae exhibited higher propulsive efficiency than adult squid during escape jet ejection, and propulsive efficiency was higher for escape jet I than escape jet II in juveniles and adults. These results indicate that although squid undergo major ecological transitions and morphology changes from paralarvae to adults, all life stages demonstrate flexibility in escape jet responses and produce escape jets of surprisingly high propulsive efficiency.This article has an associated First Person interview with the first author of the paper.

Locomotor transition: how squid jet from water to air

The amazing multi-modal locomotion of flying squid helps to achieve fast-speed migration and predator-escape behavior. Observation of flying squid has been rarely reported in recent years, since it is challenging to clearly record the flying squid's aquatic-aerial locomotion in a marine environment. The existing reports of squid-flying events are rare and merely record the in-air motion. Therefore, the water-air locomotor transition of flying squid is still unknown. This paper proposes the idea of using CFD to simulate the process of the flying squid (Sthenoteuthis oualaniensis (S. oualaniensis)) launching from water into air. The results for the first time reveal the flow field information of squid in launching phase and show the kinematic parameters of flying squid in quantification. Both a trailing jet and pinch-off vortex rings are formed to generate launching thrust, and the formation number L _ω /D _ω is 5.22, demonstrating that the jet strategy is to produce greater time-averaged thrust rather than higher propulsion efficiency. The results also indicate that the maximum flying speed negatively correlates with the launch angle, indicating that a lower launch angle could result in a larger flying speed for the flying squid to escape. These findings explore the multi-modal locomotion of flying squid from a new perspective, helping to explain the trade-off strategy of water-to-air transition, and further enhance the performance of aquatic-aerial vehicles.

Dynamics of a squid-inspired swimmer in free swimming

The untethered swimming performance of a two-dimensional squid-inspired swimmer is studied. Our model includes fully-coupled fluid-structure interaction and an idealized activation algorithm that drives periodic shape change of the body. We present results of both escape jetting via a single deflation-coasting motion and long-distance swimming via repeated inflation-deflation cycles. In both cases added-mass-related force is found to contribute significantly to thrust generation. Moreover, we find that the increase of the jet speed and oscillation frequency leads to higher swimming velocity. This, however, is achieved at the cost of reduced propulsion efficiency (i.e. higher cost of transport). During long-distance swimming, the system experiences three successive stages, acceleration, steady-state swimming, and off-track swimming caused by symmetry-breaking instability in the wake. Associated with these stages, three wake patterns are observed, nozzle-vortex-dominated wake, transit wake, and asymmetrical wake.

Quantitative classification of vortical flows based on topological features using graph matching

Vortical flow patterns generated by swimming animals or flow separation (e.g. behind bluff objects such as cylinders) provide important insight to global flow behaviour such as fluid dynamic drag or propulsive performance. The present work introduces a new method for quantitatively comparing and classifying flow fields using a novel graph-theoretic concept, called a weighted Gabriel graph, that employs critical points of the velocity vector field, which identify key flow features such as vortices, as graph vertices. The edges (connections between vertices) and edge weights of the weighted Gabriel graph encode local geometric structure. The resulting graph exhibits robustness to minor changes in the flow fields. Dissimilarity between flow fields is quantified by finding the best match (minimum difference) in weights of matched graph edges under relevant constraints on the properties of the edge vertices, and flows are classified using hierarchical clustering based on computed dissimilarity. Application of this approach to a set of artificially generated, periodic vortical flows demonstrates high classification accuracy, even for large perturbations, and insensitivity to scale variations and number of periods in the periodic flow pattern. The generality of the approach allows for comparison of flows generated by very different means (e.g. different animal species).

Maneuvering Performance in the Colonial Siphonophore, Nanomia bijuga

The colonial cnidarian, Nanomia bijuga, is highly proficient at moving in three-dimensional space through forward swimming, reverse swimming and turning. We used high speed videography, particle tracking, and particle image velocimetry (PIV) with frame rates up to 6400 s^-1 to study the kinematics and fluid mechanics of N. bijuga during turning and reversing. N. bijuga achieved turns with high maneuverability (mean length-specific turning radius, R/L = 0.15 ± 0.10) and agility (mean angular velocity, ω = 104 ± 41 deg. s^-1). The maximum angular velocity of N. bijuga, 215 deg. s^-1, exceeded that of many vertebrates with more complex body forms and neurocircuitry. Through the combination of rapid nectophore contraction and velum modulation, N. bijuga generated high speed, narrow jets (maximum = 1063 ± 176 mm s^-1; 295 nectophore lengths s^-1) and thrust vectoring, which enabled high speed reverse swimming (maximum = 134 ± 28 mm s^-1; 37 nectophore lengths s^-1) that matched previously reported forward swimming speeds. A 1:1 ratio of forward to reverse swimming speed has not been recorded in other swimming organisms. Taken together, the colonial architecture, simple neurocircuitry, and tightly controlled pulsed jets by N. bijuga allow for a diverse repertoire of movements. Considering the further advantages of scalability and redundancy in colonies, N. bijuga is a model system for informing underwater propulsion and navigation of complex environments.

Quantifying the swimming gaits of veined squid (Loligo forbesi) using bio-logging tags

Squid are mobile, diverse, ecologically important marine organisms whose behavior and habitat use can have substantial impacts on ecosystems and fisheries. However, due in part to the inherent challenges of monitoring squid in their natural marine environment, fine-scale behavioral observations of these free-swimming, soft-bodied animals are rare. Bio-logging tags provide an emerging way to remotely study squid behavior in their natural environments. Here we apply a novel, high-resolution bio-logging tag (ITAG) to seven veined squid Loligo forbesi in a controlled experimental environment to quantify their short-term (24-hr) behavioral patterns. Tag accelerometer, magnetometer and pressure data were used to develop automated gait classification algorithms based on overall dynamic body acceleration, and a subset of the events were assessed and confirmed using concurrently collected video data. Finning, flapping, and jetting gaits were observed, with the low-acceleration finning gaits detected most often. The animals routinely used a finning gait to ascend (climb) and then glide during descent with fins extended in the tank's water column, a possible strategy to improve swimming efficiency for these negatively buoyant animals. Arms and mantle-first directional swimming were observed in approximately equal proportions, and the squid were slightly but significantly more active at night. These tag-based observations are novel for squid and suggest a more efficient mode of movement then suggested by some previous observations. The combination of sensing, classification, and estimation developed and applied here will enable the quantification of squid activity patterns in the wild to provide new biological information, such as in situ identification of behavioral states, temporal patterns, habitat requirements, energy expenditure, and interactions of squid through space-time in the wild.

Development of Swimming Abilities in Squid Paralarvae: Behavioral and Ecological Implications for Dispersal

This study investigates the development of swimming abilities and its relationship with morphology, growth, and nourishment of reared Doryteuthis opalescens paralarvae from hatching to 60 days of age. Paralarvae (2.5-11 mm mantle length - ML) were videotaped, and their behavior quantified throughout development using computerized motion analysis. Hatchlings swim dispersed maintaining large nearest neighbor distances (NND, 8.7 ML), with swimming speeds (SS) of 3-8 mm s-1 and paths with long horizontal displacements, resulting in high net to gross displacement ratios (NGDR). For 15-day-old paralarvae, swimming paths are more consistent between jets, growth of fins, length, and mass increases. The swimming pattern of 18-day-old paralarvae starved for 72 h exhibited a significant reduction in mean SS and inability to perform escape jets. A key morphological, behavioral, and ecological transition occurs at about 6 mm ML (>35-day old), when there is a clear change in body shape, swimming performance, and behavior, paths are more regularly repeated and directional swimming is evident, suggesting that morphological changes incur in swimming performance. These squid are able to perform sustained swimming and hover against a current at significantly closer NND (2.0 ML), as path displacement is reduced and maneuverability increases. As paralarvae reach 6-7 mm ML, they are able to attain speeds up to 562 mm s-1 and to form schools. Social feeding interactions (kleptoparasitism) are often observed prior to the formation of schools. Schools are always formed within areas of high flow gradient in the tanks and are dependent on squid size and current speed. Fin development is a requisite for synchronized and maneuverable swimming of schooling early juveniles. Although average speeds of paralarvae are within intermediate Reynolds numbers (Re < 100), they make the transition to the inertia-dominated realm during escape jets of high propulsion (Re > 3200), transitioning from plankton to nekton after their first month of life. The progressive development of swimming capabilities and social interactions enable juvenile squid to school, while also accelerates learning, orientation and cognition. These observations indicate that modeling of the lifecycle should include competency to exert influence over small currents and dispersal patterns after the first month of life.

New approaches for assessing squid fin motions: coupling proper orthogonal decomposition with volumetric particle tracking velocimetry

Squid, which swim using a coupled fin/jet system powered by muscular hydrostats, pose unique challenges for the study of locomotion. The high flexibility of the fins and complex flow fields generated by distinct propulsion systems require innovative techniques for locomotive assessment. For this study, we used proper orthogonal decomposition (POD) to decouple components of the fin motions and defocusing digital particle tracking velocimetry (DDPTV) to quantify the resultant 3D flow fields. Kinematic footage and DDPTV data were collected from brief squid, Lolliguncula brevis [3.1-6.5 cm dorsal mantle length (DML)], swimming freely in a water tunnel at speeds of 0.39-7.20 DML s^-1 Both flap and wave components were present in all fin motions, but the relative importance of the wave components was higher for arms-first swimming than for tail-first swimming and for slower versus higher speed swimming. When prominent wave components were present, more complex interconnected vortex ring wakes were observed, while fin movements dominated by flapping resulted in more spatially separated vortex ring patterns. Although the jet often produced the majority of the thrust for steady rectilinear swimming, our results demonstrated that the fins can contribute more thrust than the jet at times, consistently produce comparable levels of lift to the jet during arms-first swimming, and can boost overall propulsive efficiency. By producing significant drag signatures, the fins can also aid in stabilization and maneuvering. Clearly, fins play multiple roles in squid locomotion, and when coupled with the jet, allow squid to perform a range of swimming behaviors integral to their ecological success.

Swimming mechanics and propulsive efficiency in the chambered nautilus

The chambered nautilus (Nautilus pompilius) encounters severe environmental hypoxia during diurnal vertical movements in the ocean. The metabolic cost of locomotion (Cmet) and swimming performance depend on how efficiently momentum is imparted to the water and how long on-board oxygen stores last. While propulsive efficiency is generally thought to be relatively low in jet propelled animals, the low Cmet in Nautilus indicates that this is not the case. We measured the wake structure in Nautilus during jet propulsion swimming, to determine their propulsive efficiency. Animals swam with either an anterior-first or posterior-first orientation. With increasing swimming speed, whole cycle propulsive efficiency increased during posterior-first swimming but decreased during anterior-first swimming, reaching a maximum of 0.76. The highest propulsive efficiencies were achieved by using an asymmetrical contractile cycle in which the fluid ejection phase was relatively longer than the refilling phase, reducing the volume flow rate of the ejected fluid. Our results demonstrate that a relatively high whole cycle propulsive efficiency underlies the low Cmet in Nautilus, representing a strategy to reduce the metabolic demands in an animal that spends a significant part of its daily life in a hypoxic environment.

Flowtrace: simple visualization of coherent structures in biological fluid flows

We present a simple, intuitive algorithm for visualizing time-varying flow fields that can reveal complex flow structures with minimal user intervention. We apply this technique to a variety of biological systems, including the swimming currents of invertebrates and the collective motion of swarms of insects. We compare our results with more experimentally difficult and mathematically sophisticated techniques for identifying patterns in fluid flows, and suggest that our tool represents an essential 'middle ground' allowing experimentalists to easily determine whether a system exhibits interesting flow patterns and coherent structures without resorting to more intensive techniques. In addition to being informative, the visualizations generated by our tool are often striking and elegant, illustrating coherent structures directly from videos without the need for computational overlays. Our tool is available as fully documented open-source code for MATLAB, Python or ImageJ at www.flowtrace.org.

Archer fish jumping prey capture: kinematics and hydrodynamics

Smallscale archer fish, Toxotes microlepis, are best known for spitting jets of water to capture prey, but also hunt by jumping out of the water to heights of up to 2.5 body lengths. In this study, high-speed imaging and particle image velocimetry were used to characterize the kinematics and hydrodynamics of this jumping behavior. Jumping used a set of kinematics distinct from those of in-water feeding strikes and was segmented into three phases: (1) hovering to sight prey at the surface, (2) rapid upward thrust production and (3) gliding to the prey once out of the water. The number of propulsive tail strokes positively correlated with the height of the bait, as did the peak body velocity observed during a jump. During the gliding stage, the fish traveled ballistically; the kinetic energy when the fish left the water balanced with the change in potential energy from water exit to the maximum jump height. The ballistic estimate of the mechanical energy required to jump was comparable with the estimated mechanical energy requirements of spitting a jet with sufficient momentum to down prey and subsequently pursuing the prey in water. Particle image velocimetry showed that, in addition to the caudal fin, the wakes of the anal, pectoral and dorsal fins were of nontrivial strength, especially at the onset of thrust production. During jump initiation, these fins were used to produce as much vertical acceleration as possible given the spatial constraint of starting directly at the water's surface to aim.

Turning performance of brief squid Lolliguncula brevis during attacks on shrimp and fish

Although squid are generally considered to be effective predators, little is currently known quantitatively about how squid maneuver and position themselves during prey strikes. In this study, high-speed video and kinematic analyses were used to study attacks by brief squid Lolliguncula brevis on both shrimp and fish. Squid attack success was high (&gt;80%) and three behavioral phases were identified: (1) approach, (2) strike and (3) recoil. Lolliguncula brevis demonstrated greater maneuverability (i.e., a smaller length-specific turning radius) and employed more body adjustments (i.e., mantle angle posturing) during approaches toward shrimp versus fish. Squid exhibited higher linear approach/strike velocities and accelerations with faster swimming fish prey compared to slower shrimp prey. Agility (i.e., turning rate) during prey encounters was comparable to performance extremes observed during non-predatory turns, and did not differ according to prey type or distance. Despite having the ability to modulate tentacle extension velocity, squid instead increased their own swimming velocity rather than increasing tentacle velocity when targeting faster fish prey during the strike phase, but this was not the case for shrimp prey. Irrespective of prey type, L. brevis consistently positioned themselves above the prey target prior to the tentacle strike, possibly to facilitate a more advantageous downward projection of the tentacles. During the recoil, L. brevis demonstrated length-specific turning radii similar to those recorded during the approach despite vigorous escape attempts by some prey. Clearly, turning performance is integral to prey attacks in squid, with differences in attack strategy varying depending on the prey target.

Turning performance in squid and cuttlefish: unique dual mode, muscular hydrostatic systems

Although steady swimming has received considerable attention in prior studies, unsteady swimming movements represent a larger portion of many aquatic animals' locomotive repertoire and have not been examined extensively. Squids and cuttlefishes are cephalopods with unique muscular hydrostat-driven, dual mode propulsive systems involving paired fins and a pulsed jet. These animals exhibit a wide range of swimming behavior, but turning performance has not been examined quantitatively. Brief squid Lolliguncula brevis and dwarf cuttlefish Sepia bandensis were filmed during turns using high-speed cameras. Kinematic features were tracked, including the length specific radius of the turn (R/L), a measure of maneuverability, and angular velocity (ω), a measure of agility. Both L. brevis and S. bandensis demonstrated high maneuverability, with (R/L)min values=3.4x10−3±5.9x10−4 and 1.2x10−3±4.7x10−4 (mean±s.e.m.), respectively, which are the lowest measures of (R/L) reported for any aquatic taxa. Lolliguncula brevis exhibited higher agility than S. bandensis (ωamax=725.8° s−1 vs. ωamax=485.0° s−1), and both cephalopods have intermediate agility when compared with flexible-bodied and rigid-bodied nekton of similar size, reflecting their hybrid body architecture. In L. brevis, jet flows were the principal driver of angular velocity. Asymmetric fin motions played a reduced role, and arm wrapping increased turning performance to varying degrees depending on the species. This study indicates that coordination between the jet and fins is important for turning performance, with L. brevis achieving faster turns than S. bandensis and S. bandensis achieving tighter, more controlled turns than L. brevis.