Control of vortex rings for manoeuvrability

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.

Turning kinematics of the scyphomedusaAurelia aurita

Scyphomedusae are widespread in the oceans and their swimming has provided valuable insights into the hydrodynamics of animal propulsion. Most of this research has focused on symmetrical, linear swimming. However, in nature, medusae typically swim circuitous, nonlinear paths involving frequent turns. Here we describe swimming turns by the scyphomedusaAurelia auritaduring which asymmetric bell margin motions produce rotation around a linearly translating body center. These jellyfish 'skid' through turns and the degree of asynchrony between opposite bell margins is an approximate predictor of turn magnitude during a pulsation cycle. The underlying neuromechanical organization of bell contraction contributes substantially to asynchronous bell motions and inserts a stochastic rotational component into the directionality of scyphomedusan swimming. These mechanics are important for natural populations because asynchronous bell contraction patterns are commonin situand result in frequent turns by naturally swimming medusae.

A physics-based model of swarming jellyfish

We propose a model for the structure formation of jellyfish swimming based on active Brownian particles. We address the phenomena of counter-current swimming, avoidance of turbulent flow regions and foraging. We motivate corresponding mechanisms from observations of jellyfish swarming reported in the literature and incorporate them into the generic modelling framework. The model characteristics is tested in three paradigmatic flow environments.

The Large and Strong Vortex Around the Trunk and Behind the Swimmer is Associated with Great Performance in Underwater Undulatory Swimming

Swimmers can produce horizontal body velocity by generating and shedding vortices around their body during underwater undulatory swimming (UUS). It has been hypothesized that the horizontal shedding velocity, area and circulation of the vortex around the swimmer’s body are associated with UUS performance. The purpose of this study was to investigate whether the shedding velocity, area and circulation of vortices around swimmers’ bodies are correlated with the horizontal body velocity during UUS. Computational fluid dynamics (CFD) was conducted to obtain the vortex structure during UUS in nine male swimmers. Morphological and kinematic data of each subject were obtained and used to reconstruct the UUS movement on CFD. The horizontal velocity of the center of vorticity, the area and circulation of vortices around the ventral side of the trunk, dorsal side of shoulder and waist, and behind the swimmer were determined from the simulation results. Positive correlations were found between the vortex area and circulation around the ventral side of the trunk (area r = 0.938, p < 0.05; circulation r = 0.915, p < 0.05) and behind the swimmer (area r = 0.738, p < 0.05; circulation r = -0.680, p < 0.05), and the horizontal body velocity. The horizontal shedding velocity of the center of vorticity of the vortices around the swimmer’s body was not significantly correlated with the horizontal body velocity. These results suggest that the generation of a large and strong vortex around the trunk and behind the swimmer is associated with great UUS performance.

Vectored jets power arms-first and tail-first turns differently in brief squid with assistance from fins and keeled arms

Squids maneuver to capture prey, elude predators, navigate complex habitats, and deny rivals access to mates. Despite the ecological importance of this essential locomotive function, limited quantitative data on turning performance and wake dynamics of squids are available. To better understand the contribution of the jet, fins, and arms to turns, the role of orientation (i.e., arms-first vs tail-first) in maneuvering, and relationship between jet flow and turning performance, kinematic and 3D velocimetry data were collected in tandem from brief squid Lolliguncula brevis. The pulsed jet, which can be vectored to direct flows, was the primary driver of most turning behaviors, producing flows with the highest impulse magnitude and angular impulse about the main axis of the turn (yaw) and secondary axes (roll and pitch). The fins and keeled arms played subordinate but important roles in turning performance, contributing to angular impulse, stabilizing the maneuver along multiple axes, and/or reducing rotational resistance. Orientation affected turning performance and dynamics, with tail-first turns being associated with greater impulse and angular impulse, longer jet structures, higher jet velocities, and greater angular turning velocities than arms-first turns. Conversely, arms-first turns involved shorter, slower jets with less impulse, but these directed short pulses resulted in lower minimum length-specific turning radii. Although the length-to-diameter ratio (L/D) of ejected jet flow was a useful metric for characterizing vortical flow features, it, by itself, was not a reliable predictor of angular velocity or turning radii, which reflects the complexity of the squid multi-propulsor system.

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.

Developing Biohybrid Robotic Jellyfish (Aurelia aurita) for Free-swimming Tests in the Laboratory and in the Field

Biohybrid robotics is a growing field that incorporates both live tissues and engineered materials to build robots that address current limitations in robots, including high power consumption and low damage tolerance. One approach is to use microelectronics to enhance whole organisms, which has previously been achieved to control the locomotion of insects. However, the robotic control of jellyfish swimming offers additional advantages, with the potential to become a new ocean monitoring tool in conjunction with existing technologies. Here, we delineate protocols to build a self-contained swim controller using commercially available microelectronics, embed the device into live jellyfish, and calculate vertical swimming speeds in both laboratory conditions and coastal waters. Using these methods, we previously demonstrated enhanced swimming speeds up to threefold, compared to natural jellyfish swimming, in laboratory and in situ experiments. These results offered insights into both designing low-power robots and probing the structure-function of basal organisms. Future iterations of these biohybrid robotic jellyfish could be used for practical applications in ocean monitoring.

Neuromechanical wave resonance in jellyfish swimming

For organisms to have robust locomotion, their neuromuscular organization must adapt to constantly changing environments. In jellyfish, swimming robustness emerges when marginal pacemakers fire action potentials throughout the bell's motor nerve net, which signals the musculature to contract. The speed of the muscle activation wave is dictated by the passage times of the action potentials. However, passive elastic material properties also influence the emergent kinematics, with time scales independent of neuromuscular organization. In this multimodal study, we examine the interplay between these two time scales during turning. A three-dimensional computational fluid-structure interaction model of a jellyfish was developed to determine the resulting emergent kinematics, using bidirectional muscular activation waves to actuate the bell rim. Activation wave speeds near the material wave speed yielded successful turns, with a 76-fold difference in turning rate between the best and worst performers. Hyperextension of the margin occurred only at activation wave speeds near the material wave speed, suggesting resonance. This hyperextension resulted in a 34-fold asymmetry in the circulation of the vortex ring between the inside and outside of the turn. Experimental recording of the activation speed confirmed that jellyfish actuate within this range, and flow visualization using particle image velocimetry validated the corresponding fluid dynamics of the numerical model. This suggests that neuromechanical wave resonance plays an important role in the robustness of an organism's locomotory system and presents an undiscovered constraint on the evolution of flexible organisms. Understanding these dynamics is essential for developing actuators in soft body robotics and bioengineered pumps.

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.

Fluid and Predator-Prey Interactions of Scyphomedusae Fed Calanoid Copepods

The feeding current of scyphomedusae entrains and transports surrounding fluids and prey through trailing tentacles to initiate encounters with prey. After contact, most prey are retained for ingestion. However, the probability that a contact will occur depends on several factors including capture surface morphology, prey size and behavior. We examined how hydrodynamics, capture surface morphology and prey behavior affect the capture probability of copepods. To do this, we documented medusa-copepod interactions of four species of scyphomedusae (two semeostomes and two rhizostomes) possessing different capture surface morphologies. We tracked the movement and behavior of entrained copepods throughout the feeding process to quantify prey behavior effects upon capture efficiency (# captures/# encounters). The feeding currents generated by all the medusan species generated fluid shear deformation rates well above the detection limits of copepods. Despite strong hydrodynamic signals, copepod behavior was highly variable and only 58% of the copepods reacted to entrainment within feeding currents. Furthermore, copepod behavior (categorized as no reaction, escape jump or adjustment jump) did not significantly affect the capture efficiency. The scale and complexity of the feeding current generated by scyphomedusae may help explain the poor ability of copepods to avoid capture.

From single neurons to behavior in the jellyfish Aurelia aurita

Jellyfish nerve nets provide insight into the origins of nervous systems, as both their taxonomic position and their evolutionary age imply that jellyfish resemble some of the earliest neuron-bearing, actively-swimming animals. Here, we develop the first neuronal network model for the nerve nets of jellyfish. Specifically, we focus on the moon jelly Aurelia aurita and the control of its energy-efficient swimming motion. The proposed single neuron model disentangles the contributions of different currents to a spike. The network model identifies factors ensuring non-pathological activity and suggests an optimization for the transmission of signals. After modeling the jellyfish's muscle system and its bell in a hydrodynamic environment, we explore the swimming elicited by neural activity. We find that different delays between nerve net activations lead to well-controlled, differently directed movements. Our model bridges the scales from single neurons to behavior, allowing for a comprehensive understanding of jellyfish neural control of locomotion.

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.

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.

Jet-paddling jellies: swimming performance in the Rhizostomeae jellyfish Catostylus mosaicus

Jellyfish are a successful and diverse class of animals that swim via jet propulsion, with swimming performance and propulsive efficiency being related to the animal's feeding ecology and body morphology. The Rhizostomeae jellyfish lack tentacles but possess four oral lobes and eight trailing arms at the centre of their bell, giving them a body morphology quite unlike that of other free-swimming medusae. The implications of this body morphology on the mechanisms by which thrust is produced are unknown. Here, we determined the wake structure and propulsive efficiency in the blue-blubber jellyfish Catostylus mosaicus (order: Rhizostomeae). The animal is propelled during both bell contraction and bell relaxation by different thrust-generating mechanisms. During bell contraction, a jet of fluid is expelled from the subumbrellar cavity, which results from the interaction between the counter-rotating stopping (from the preceding contraction cycle) and starting vortices, creating a vortex superstructure and propulsion. This species is also able to utilise passive energy recapture, which increases the animal's swimming velocity towards the end of the bell expansion phase when the bell diameter is constant. The thrust produced during this phase is the result of the flexible bell margin manoeuvring the stopping vortex into the subumbrellar cavity during bell relaxation, enhancing its circulation, and creating a region of high pressure on the inner surface of the bell and, consequently, thrust. These mechanisms of thrust generation result in C. mosaicus having a relatively high propulsive efficiency compared with other swimmers, indicating that economical locomotion could be a contributing factor in the ecological success of these medusan swimmers.

Thrust force characterization of free-swimming soft robotic jellyfish

Five unique soft robotic jellyfish were manufactured with eight pneumatic network tentacle actuators extending radially from their centers. These jellyfish robots were able to freely swim untethered in the ocean, to steer from side to side, and to swim through orifices more narrow than the nominal diameter of the jellyfish. Each of the five jellyfish robots were manufactured with a different composition of body and tentacle actuator Shore hardness. A three-factor study was performed with these five jellyfish robots to determine the impact that actuator material Shore hardness, actuation frequency, and tentacle stroke actuation amplitude had upon the measured thrust force. It was found that all three of these factors significantly impacted mean thrust force generation, which peaked with a half-stroke actuation amplitude at a frequency of 0.8 Hz.

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.

Widespread utilization of passive energy recapture in swimming medusae

Recently, it has been shown that some medusae are capable of swimming very efficiently, i.e.; with a low cost of transport, and that this is in part due to passive energy recapture (PER) which occurs during bell relaxation. We compared the swimming kinematics among a diverse array of medusae, varying in taxonomy, morphology and propulsive and foraging modes, in order to evaluate the prevalence of PER in medusae. We found that while PER is commonly observed among taxa, the magnitude of the contribution to overall swimming varied greatly. The ability of medusae to utilize PER was not related to morphology and swimming performance but was controlled by their swimming kinematics. Utilizing PER required the medusae to pause after bell expansion and individuals could modulate their PER by changing their pause duration. Passive energy recapture can greatly enhance swimming efficiency but there appear to be trade-offs associated with utilizing PER.

Can gelatinous zooplankton influence the fate of crude oil in marine environments?

Gelatinous zooplankton are known for their capacity to excrete copious amounts of mucus that can be utilized by other organisms. The release of mucus is exacerbated by stressful conditions. Despite the recognized importance of cnidarian mucus to production and material flux in marine ecosystems, the role of gelatinous zooplankton in influencing the fate of oil spills is unknown. In this study we used laboratory experiments to observe the influence of mucus from the moon jellyfish (Aurelia aurita) on the aggregation and degradation of crude oil. The results show that jellyfish swimming in a dispersed solution of oil droplets produced copious amounts of mucus and the mucus aggregates that were shed by the animals contained 26 times more oil than the surrounding water. Incubation experiments showed that hydrocarbon degrading bacteria cell densities more than doubled in the presence of mucus and after 14days, resulted in a significant increase in oil degradation. These results suggest that jellyfish can aggregate dispersed oil droplets and embed them within a matrix that favors hydrocarbon degrading bacteria. While this study lends support to the hypothesis that the presence of gelatinous zooplankton can impact oil spills large scale mesocosm studies will be needed to fully quantify the influence on a natural system.

Instabilities of interacting vortex rings generated by an oscillating disk

We propose a natural model to probe in a controlled fashion the instability of interacting vortex rings shed from the edge of an oblate spheroid disk of major diameter c, undergoing oscillations of frequency f_{0} and amplitude A. We perform a Floquet stability analysis to determine the characteristics of the instability modes, which depend strongly on the azimuthal (integer) wave number m. We vary two key control parameters, the Keulegan-Carpenter number K_{C}=2πA/c and the Stokes number β=f_{0}c^{2}/ν, where ν is the kinematic viscosity of the fluid. We observe two distinct flow regimes. First, for sufficiently small β, and hence low frequency of oscillation corresponding to relatively weak interaction between sequentially shedding vortex rings, symmetry breaking occurs directly to a single unstable mode with m=1. Second, for sufficiently large yet fixed values of β, corresponding to a higher oscillation frequency and hence stronger ring-ring interaction, the onset of asymmetry is predicted to occur due to two branches of high m instabilities as the amplitude is increased, with m=1 structures being dominant only for sufficiently large values of K_{C}. These two branches can be distinguished by the phase properties of the vortical structures above and below the disk. The region in (K_{C},β) parameter space where these two high m instability branches arise can be described accurately in terms of naturally defined Reynolds numbers, using appropriately chosen characteristic length scales. We subsequently carry out direct numerical simulations of the fully three-dimensional flow to verify the principal characteristics of the Floquet analysis, in particular demonstrating that high wave-number symmetry-breaking generically occurs when vortex rings sequentially interact sufficiently strongly.

Vortex ring behavior provides the epigenetic blueprint for the human heart

The laws of fluid dynamics govern vortex ring formation and precede cardiac development by billions of years, suggesting that diastolic vortex ring formation is instrumental in defining the shape of the heart. Using novel and validated magnetic resonance imaging measurements, we show that the healthy left ventricle moves in tandem with the expanding vortex ring, indicating that cardiac form and function is epigenetically optimized to accommodate vortex ring formation for volume pumping. Healthy hearts demonstrate a strong coupling between vortex and cardiac volumes (R² = 0.83), but this optimized phenotype is lost in heart failure, suggesting restoration of normal vortex ring dynamics as a new, and possibly important consideration for individualized heart failure treatment. Vortex ring volume was unrelated to early rapid filling (E-wave) velocity in patients and controls. Characteristics of vortex-wall interaction provide unique physiologic and mechanistic information about cardiac diastolic function that may be applied to guide the design and implantation of prosthetic valves, and have potential clinical utility as therapeutic targets for tailored medicine or measures of cardiac health.

Simultaneous measurement of 3D zooplankton trajectories and surrounding fluid velocity field in complex flows

We describe an automated, volumetric particle image velocimetry (PIV) and tracking method that measures time-resolved, 3D zooplankton trajectories and surrounding volumetric fluid velocity fields simultaneously and non-intrusively. The method is demonstrated for groups of copepods flowing past a wall-mounted cylinder. We show that copepods execute escape responses when subjected to a strain rate threshold upstream of a cylinder, but the same threshold range elicits no escape responses in the turbulent wake downstream. The method was also used to document the instantaneous slip velocity of zooplankton and the resulting differences in trajectory between zooplankton and non-inertial fluid particles in the unsteady wake flow, showing the method's capability to quantify drift for both passive and motile organisms in turbulent environments. Applications of the method extend to any group of organisms interacting with the surrounding fluid environment, where organism location, larger-scale eddies and smaller-scale fluid deformation rates can all be tracked and analyzed.