Spatiotemporal Asymmetry in Metachronal Rowing at Intermediate Reynolds Numbers.

In drag-based swimming, individual propulsors operating at low Reynolds numbers (where viscous forces dominate over inertial forces) must execute a spatially asymmetric stroke to produce net fluid displacement. Temporal asymmetry (that is, differing duration between the power vs. recovery stroke) does not affect the overall generated thrust in this time-reversible regime. Metachronal rowing, in which multiple appendages beat sequentially, is used by a wide variety of organisms from low to intermediate Reynolds numbers. At the upper end of this range, inertia becomes important, and increasing temporal asymmetry can be an effective way to increase thrust. However, the combined effects of spatial and temporal asymmetry are not fully understood in the context of metachronal rowing. To explore the role of spatiotemporal asymmetry in metachronal rowing, we combine laboratory experiments and reduced-order analytical modeling. We measure beat kinematics and generated flows in two species of lobate ctenophores across a range of body sizes, from 7 to 40 mm in length. We observe characteristically different flows in ctenophores of differing body size and Reynolds number, and a general decrease in spatial asymmetry and increase in temporal asymmetry with increasing Reynolds number. We also construct a one-dimensional mathematical model consisting of a row of oscillating flat plates whose flow-normal areas change with time, and use it to explore the propulsive forces generated across a range of Reynolds numbers and kinematic parameters. The model results show that while both types of asymmetry increase force production, they have different effects in different regions of the parameter space. These results may have strong biological implications, as temporal asymmetry can be actively controlled while spatial asymmetry is likely to be partially or entirely driven by passive fluid-structure interaction.

Metachronal Swimming of Mantis Shrimp: Kinematics and Interpleopod Vortex Interactions.

Mantis shrimp swim via metachronal rowing, a pattern in which the pleopods (swimming limbs) stroke sequentially, starting with the last pair and followed by anterior neighbors. A similar swimming pattern is used at various sizes, Reynolds numbers, and advance ratios by diverse organisms including ciliates, ctenophores, copepods, krill, and lobsters. Understanding this type of locomotion is important because it is widespread and may inspire the design of underwater vehicles where efficiency, robustness, and maneuverability are desired. However, detailed measurements of the flow around free-swimming, metachronally rowing organisms are scarce, especially for organisms swimming in a high Reynolds number regime (Re ≥ 104). In this study, we present time-resolved, planar PIV measurements of a swimming peacock mantis shrimp (Odontodactylus scyllarus). Simultaneous kinematics measurements of the animal, which had body and pleopod lengths of 114 and 20 mm, respectively, reveal mean swimming speeds of 0.2-1.9 m s-1 and pleopod beat frequencies of 3.6-13 Hz, corresponding to advance ratios of 0.75-1.84 and body-based Reynolds numbers of 23,000-217,000. Further, the animal's stroke is not purely metachronal, with a long phase lag between initiation of the first and fifth pleopod power strokes. Flow measurements in the sagittal plane show that each stroking pleopod pair creates a posteriorly moving tip vortex which evades destruction by the recovery strokes of other pleopod pairs. The vortex created by the anteriormost pleopod pair is the strongest and, owing to the animal's high advance ratio, is intercepted by the power stroke of the posteriormost pleopod pair. The vortex strength increases as a result of this interaction, which may increase swimming speed or efficiency. A relationship for vortex interception by the posterior pleopod is proposed that relates the phase lag between the interacting pleopods to the beat frequency, distance between those pleopods, and speed of the vortex relative to the animal. We describe this interaction with a novel parameter called the interpleopod vortex phase matching Strouhal number StIVPM which is equal to the phase lag between interacting pleopods. This new nondimensional parameter may be useful in predicting the conditions where a constructive interaction may occur in other species or in physical models. Finally, we relate the advance ratio to the Reynolds number ratio, the ratio between the body-based Reynolds number and the pleopod-based Reynolds number. The importance of these parameters in promoting the interpleopod vortex interactions identified here, in dynamically scaled experiments, and in wake signatures behind schooling metachronal swimmers is discussed.

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. Finally, 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.

Allan Deviation of Atomic Clock Frequency Corrections: A New Diagnostic Tool for Characterizing Clock Disturbances.

As atomic clocks and frequency standards are increasingly operated in situations where they are exposed to environmental disturbances, it becomes more necessary to understand how variations of each clock component impact the clock output, in particular the local oscillator (LO). Most microwave atomic clocks in operation today use quartz crystal LOs with excellent short-term noise variation but large unwanted long-term drift. Fortunately, this slow drift is mitigated by repeatedly comparing the atomic reference frequency to the LO and applying corrections each iteration through a control algorithm. This article focuses on the shot-to-shot corrections themselves. To optimize clock performance, it is important to determine whether disturbances on the output are due to variations of the LO that the control loop failed to remove or variations of the reference frequency itself. Some of this can be diagnosed using the output frequency's Allan deviation (ADEV), the traditional measure of clock performance. However, the ADEV of the corrections reveals somewhat different information, specifically more direct information about all disturbances that the measurement system detects and compensates for, from the LO or elsewhere. In this article: we 1) derive the baseline shot-noise-limited noise floor for this ADEV, 2) validate and adjust for the complexities of our control loop with a computer model, and 3) examine model results and laboratory data that lie on or diverge from the noise floor to understand what divergences reveal about LO and/or clock behavior. Ultimately, we show how to use this corrections-ADEV as a diagnostic to help identify the source of disturbances and drift observed on the clock output.

Effects of crude oil vapors on the cardiovascular flow of embryonic Gulf killifish.

Direct contact with toxicants in crude oil during embryogenesis causes cardiovascular defects, but the effects of exposure to airborne volatile organic compounds released from spilled oil are not well understood. The effects of crude oil-derived airborne toxicants on peripheral blood flow were examined in Gulf killifish (Fundulus grandis) since this model completes embryogenesis in the air. Particle image velocimetry was used to measure in vivo blood flow in intersegmental arteries of control and oil-exposed embryos. Significant effects in oil-exposed embryos included increased pulse rate, reduced mean blood flow speed and volumetric flow rate, and decreased pulsatility, demonstrating that normal-appearing oil-exposed embryos retain underlying cardiovascular defects. Further, hematocrit moderately increased in oil-exposed embryos. This study highlights the potential for fine-scale physiological measurement techniques to better understand the sub-lethal effects of oil exposure and demonstrates the efficacy of Gulf killifish as a unique teleost model for aerial toxicant exposure studies.

A novel cylindrical overlap-and-fling mechanism used by sea butterflies.

The clap-and-fling mechanism is a well-studied, unsteady lift generation mechanism widely used by flying insects and is considered obligatory for tiny insects flying at low to intermediate Reynolds numbers, Re However, some aquatic zooplankters including some pteropod (i.e. sea butterfly) and heteropod species swimming at low to intermediate Re also use the clap-and-fling mechanism. These marine snails have extremely flexible, actively deformed, muscular wings which they flap reciprocally to create propulsive force, and these wings may enable novel lift generation mechanisms not available to insects, which have less flexible, passively deformed wings. Using high-speed stereophotogrammetry and micro-particle image velocimetry, we describe a novel cylindrical overlap-and-fling mechanism used by the pteropod species Cuvierina atlantica In this maneuver, the pteropod's wingtips overlap at the end of each half-stroke to sequentially form a downward-opening cone, a cylinder and an upward-opening cone. The transition from downward-opening cone to cylinder produces a downward-directed jet at the trailing edges. Similarly, the transition from cylinder to upward-opening cone produces downward flow into the gap between the wings, a leading edge vortex ring and a corresponding sharp increase in swimming speed. The ability of this pteropod species to perform the cylindrical overlap-and-fling maneuver twice during each stroke is enabled by its slender body and highly flexible wings. The cylindrical overlap-and-fling mechanism observed here may inspire the design of new soft robotic aquatic vehicles incorporating highly flexible propulsors to take advantage of this novel lift generation technique.

Random sequential addition simulations of animal aggregations provide null models of group structure.

Apparent structure in animal aggregations such as fish and Antarctic krill schools may result from the tight packing of these elongated animals. This geometrical structure may be difficult to differentiate from behavior-induced structure resulting from individuals preferentially taking up certain positions relative to conspecifics to gain an adaptive advantage such as reduced locomotive cost. Here we use random sequential addition (RSA) simulations to quantify the effect of animal shape, aggregation organization, and aggregation density on 2D school structure. This technique allows for the generation of a null model for nearest neighbor distance and nearest neighbor position angle for a specific body shape and aggregation density, thus isolating the effect of geometry from that of behavior. We further identify a shape-specific aggregation density threshold above which the animal shape affects the spatial distribution of nearest neighbors. Nearest neighbor distance data of fish schools with densities above and below the threshold are found to agree well with nearest neighbor statistics found from RSA-generated schools.

The Three Dimensional Spatial Structure of Antarctic Krill Schools in the Laboratory.

Animal positions within moving groups may reflect multiple motivations including saving energy and sensing neighbors. These motivations have been proposed for schools of Antarctic krill, but little is known about their three-dimensional structure. Stereophotogrammetric images of Antarctic krill schooling in the laboratory are used to determine statistical distributions of swimming speed, nearest neighbor distance, and three-dimensional nearest neighbor positions. The krill schools swim at speeds of two body lengths per second at nearest neighbor distances of one body length and reach similarly high levels of organization as fish schools. The nearest neighbor position distribution is highly anisotropic and shows that Antarctic krill prefer to swim in the propulsion jet of their anterior neighbor. This position promotes communication and coordination among schoolmates via hydrodynamic signals within the pulsed jet created by the metachronal stroking of the neighboring krill's pleopods. The hydrodynamic communication channel therefore plays a large role in structuring the school. Further, Antarctic krill avoid having a nearest neighbor directly overhead, possibly to avoid blockage of overhead light needed for orientation. Other factors, including the elongated body shape of Antarctic krill and potential energy savings, also may help determine the three dimensional spatial structure of tightly packed krill schools.

Using a shell as a wing: pairing of dissimilar appendages in atlantiid heteropod swimming.

Atlantiid heteropods are zooplanktonic marine snails which have a calcium carbonate shell and single swimming fin. They actively swim to hunt prey and vertically migrate. Previous accounts of atlantiid heteropod swimming described these animals sculling with the swimming fin while the shell passively hung beneath the body. Here, we show, via high-speed stereophotogrammetric measurements of body, fin and shell kinematics, that the atlantiid heteropod Atlanta selvagensis actively flaps both the swimming fin and shell in a highly coordinated wing-like manner in order to swim in the intermediate Reynolds number regime (Re=10-100). The fin and shell kinematics indicate that atlantiid heteropods use unsteady hydrodynamic mechanisms such as clap-and-fling and delayed stall. Unique features of atlantiid heteropod swimming include the coordinated pairing of dissimilar appendages, use of the clap and fling mechanism twice during each stroke cycle, and the fin's extremely large stroke amplitude, which exceeds 180 deg.

Drifts and Environmental Disturbances in Atomic Clock Subsystems: Quantifying Local Oscillator, Control Loop, and Ion Resonance Interactions.

Linear ion trap frequency standards are among the most stable continuously operating frequency references and clocks. Depending on the application, they have been operated with a variety of local oscillators (LOs), including quartz ultrastable oscillators, hydrogen-masers, and cryogenic sapphire oscillators. The short-, intermediate-, and long-term stability of the frequency output is a complicated function of the fundamental performances, the time dependence of environmental disturbances, the atomic interrogation algorithm, the implemented control loop, and the environmental sensitivity of the LO and the atomic system components. For applications that require moving these references out of controlled lab spaces and into less stable environments, such as fieldwork or spaceflight, a deeper understanding is needed of how disturbances at different timescales impact the various subsystems of the clock and ultimately the output stability. In this paper, we analyze which perturbations have an impact and to what degree. We also report on a computational model of a control loop, which keeps the microwave source locked to the ion resonance. This model is shown to agree with laboratory measurements of how well the feedback removes various disturbances and also with a useful analytic approach we developed for predicting these impacts.

Underwater flight by the planktonic sea butterfly.

In a remarkable example of convergent evolution, we show that the zooplanktonic sea butterfly Limacina helicina 'flies' underwater in the same way that very small insects fly in the air. Both sea butterflies and flying insects stroke their wings in a characteristic figure-of-eight pattern to produce lift, and both generate extra lift by peeling their wings apart at the beginning of the power stroke (the well-known Weis-Fogh 'clap-and-fling' mechanism). It is highly surprising to find a zooplankter 'mimicking' insect flight as almost all zooplankton swim in this intermediate Reynolds number range (Re=10-100) by using their appendages as paddles rather than wings. The sea butterfly is also unique in that it accomplishes its insect-like figure-of-eight wing stroke by extreme rotation of its body (what we call 'hyper-pitching'), a paradigm that has implications for micro aerial vehicle (MAV) design. No other animal, to our knowledge, pitches to this extent under normal locomotion.

Sensory-Motor Systems of Copepods involved in their Escape from Suction Feeding.

Copepods escape well by detecting minute gradients in the flow field; they react quickly, and swim away strongly. As a key link in the aquatic food web, these small planktonic organisms often encounter suction-feeding fish. Studies have identified certain hydrodynamic features that are created by the approach of this visual predator and the generation of its suction flow for capturing food. Similarly, studies have identified certain hydrodynamic features that evoke the evasive response of copepods. This is a review of the copepod sensory motor system as pertains to understanding their response to suction-feeding fish. Analyses of the reaction time, threshold sensitivity, structure of sensors, and evasive behavior by this key prey of fish can be useful for evaluating the effectiveness of feeding tactics in response to suction flow. To illustrate, we present results comparing a copepod from a fishless lake (Hesperodiaptomus shoshone) to a copepod from a rich fishing ground (Calanus finmarchicus). We designed a flow mimic that produces a realistic mushroom-cap-shaped flow field and realistic accelerations of flow; the copepods treated the mimic as a threat and performed jumps directed up and away from the siphon. Calanus finmarchicus responded at an average threshold strain rate of 18.7/s, escaped at 0.46 m/s, and traveled 5.99 mm, most frequently as a single jump. Hesperodiaptomus shoshone responded at a strain rate of 15.1/s that is not significantly different, escaped more slowly at 0.22 m/s and traveled a shorter distance of 3.01 mm using a series of hops. The high variability noted in the initial angle of the body and the maximum change in body angle suggests that unpredictability in the escape maneuver is another aspect of the tactic of copepods. The speed of the escape by small copepods 2-3 mm long is overwhelmed by the speed of the attack by the much larger, faster fish; if the copepod reacts when it is within the fish's arena of capture (<1.5 mm from mouth), it will be eaten. The copepod, however, has an acutely sensitive array of mechanosensors that perceive the flow field of the fish at distances of 3-6 mm, or outside the fish's range of capture. The copepod also has a rapid and strong locomotory response, thereby increasing the odds that the copepod will survive-but speed is unlikely to be the best tactic for staying alive. Instead, the copepod accelerates from 61.3 to 96.5 m/s(2) or more than 20 times stronger than the lunge of a fish. This collection of capabilities of copepods enables them to remain one of the most abundant multicellular organisms on our planet.

Reduction of procoagulant potential of b-datum leakage jet flow in bileaflet mechanical heart valves via application of vortex generator arrays.

Current designs of bileaflet mechanical heart valves put patients at an increased risk of thromboembolism. In particular, regurgitant flow through the b-datum line is associated with nonphysiologic flow characteristics such as elevated shear stresses, regions of recirculation, and increased mixing, all of which may promote thrombus formation. We have previously shown that passive flow control in the form of vortex generators mounted on the downstream leaflet surfaces can effectively diminish turbulent stresses. The objective of the current work is thus to determine the effect of vortex generators on the thromboembolic potential of the b-datum line leakage jet and to correlate that effect with the vortex generator-induced changes to the flow structure. Flow experiments were performed using a steady model of the transient b-datum line jet. These experiments encompassed flow visualization to gain an overall picture of the flow system, particle image velocimetry to quantify the flow field in detail, and in vitro experiments with human blood to quantify thrombus formation in response to the applied passive flow control. Thrombus formation was quantified over time by an assay for thrombin-antithrombin III (TAT III). In comparing results with and without vortex generators, significantly lower mean TAT III levels were observed at one time point for the case with vortex generators. Also, the TAT III growth rate of the case with vortex generators was significantly lower. While no differences in jet spreading were found with and without vortex generators, lower peak turbulent stresses were observed for the case with vortex generators. The results thus demonstrate the potential of applying passive flow control to cardiovascular hardware in order to mitigate the hemodynamic factors leading to thrombus formation.

Passive flow control of bileaflet mechanical heart valve leakage flow.

Blood damage and platelet activation are inherent problems with present day mechanical heart valve designs. We investigate the approach of passive flow control applied to bileaflet mechanical heart valve (BMHV) flows as a means of optimizing leakage flow hemodynamics at length scales relevant to blood damage and platelet activation. Rectangular and hemispherical vortex generator (VG) arrays were mounted on the downstream surfaces of a 25 mm St. Jude Medical valve adjacent to the b-datum leaflet edge (central line where the two leaflets touch in closed position). The effect of VGs on the flow structure emanating from the b-datum line under both pulsatile and steady flow conditions was measured using high resolution particle image velocimetry technique. The VGs were seen to spatially disperse and dissipate the coherent leakage jet structure emanating from the b-datum line. This resulted in a significant diminution of turbulence stresses, particularly with the rectangular VG configuration. This study shows that passive flow control techniques deployed on BHMVs is potentially beneficial as significant control of flow at small length scales may be achieved without altering large scale designs of the valve.