Aquatic wing flapping at low Reynolds numbers: swimming kinematics of the Antarctic pteropod, Clione antarctica

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.

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.

Active downward propulsion by oyster larvae in turbulence

Oyster larvae (Crassostrea virginica) could enhance their settlement success by moving toward the seafloor in the strong turbulence associated with coastal habitats. We characterized the behavior of individual oyster larvae in grid-generated turbulence by measuring larval velocities and flow velocities simultaneously using infrared particle image velocimetry. We estimated larval behavioral velocities and propulsive forces as functions of the kinetic energy dissipation rate ε, strain rate γ, vorticity ξ and acceleration α. In calm water most larvae had near-zero vertical velocities despite propelling themselves upward (swimming). In stronger turbulence all larvae used more propulsive force, but relative to the larval axis, larvae propelled themselves downward (diving) instead of upward more frequently and more forcefully. Vertical velocity magnitudes of both swimmers and divers increased with turbulence, but the swimming velocity leveled off as larvae were rotated away from their stable, velum-up orientation in strong turbulence. Diving speeds rose steadily with turbulence intensity to several times the terminal fall velocity in still water. Rapid dives may require a switch from ciliary swimming to another propulsive mode such as flapping the velum, which would become energetically efficient at the intermediate Reynolds numbers attained by larvae in strong turbulence. We expected larvae to respond to spatial or temporal velocity gradients, but although the diving frequency changed abruptly at a threshold acceleration, the variation in propulsive force and behavioral velocity was best explained by the dissipation rate. Downward propulsion could enhance oyster larval settlement by raising the probability of larval contact with oyster reef patches.

Temperature compensation of aerobic capacity and performance in the Antarctic pteropod, Clione antarctica, compared to its northern congener, C. limacina

In ectotherms living in cold waters, locomotory performance is constrained by a slower generation of the ATP that is needed to fuel muscle contraction. Both polar and temperate pteropods of the genus Clione, however, are able to swim continuously by flapping their parapodia (wings) at comparable frequencies, despite the latitudinal temperature gradient. Therefore, we expected polar species to have increased aerobic capacities in their wing muscles. We investigated muscle and mitochondrial ultrastructure of Clione antarctica from the Southern Ocean (-1.8ºC) and populations of a sister species, Clione limacina, from the Arctic (-0.5-3ºC) and from the N. Atlantic (10ºC). We also measured oxygen consumption and the activity of the mitochondrial enzyme citrate synthase (CS), in isolated wings of the two species. The Antarctic species showed a substantial up-regulation of the density of oxidative muscle fibers, but at the expense of fast-twitch muscle fibers. Mitochondrial capacity was also substantially increased in the Antarctic species, with the cristae surface density (58.2±1.3 µm2/µm3) more than twice that found in temperate species (34.3±0.8 µm2/µm3). Arctic C. limacina was intermediate between these two populations (43.7±0.5 µm2/µm3). The values for cold adapted populations are on par with those found in high-performance vertebrates. As a result of oxidative muscle proliferation, CS activity was 4-fold greater in C. antarctica wings than in temperate C. limacina when measured at a common temperature (20°C). Oxygen consumption of isolated wing preparations was comparable in the two species when measured at their respective habitat temperatures. These findings indicate complete compensation of ATP generation in wing muscles across a 10°C temperature range, which supports similar wing-beat frequencies during locomotion at each species' respective temperature. The elevated capacity in the wing muscles is reflected in whole-animal oxygen consumption and feeding rates.

Changes in wingstroke kinematics associated with a change in swimming speed in a pteropod mollusk, Clione limacina

In pteropod mollusks, the gastropod foot has evolved into two broad, wing-like structures that are rhythmically waved through the water for propulsion. The flexibility of the wings lends a tremendous range of motion, an advantage that could be exploited when changing locomotory speed. Here, we investigated the kinematic changes that take place during an increase in swimming speed in the pteropod mollusk Clione limacina. Clione demonstrates two distinct swim speeds: a nearly constant slow swimming behavior and a fast swimming behavior used for escape and hunting. The neural control of Clione's swimming is well documented, as are the neuromuscular changes that bring about Clione's fast swimming. This study examined the kinematics of this swimming behavior at the two speeds. High speed filming was used to obtain 3D data from individuals during both slow and fast swimming. Clione's swimming operates at a low Reynolds number, typically under 200. Within a given swimming speed, we found that wing kinematics are highly consistent from wingbeat to wingbeat, but differ between speeds. The transition to fast swimming sees a significant increase in wing velocity and angle of attack, and range of motion increases as the wings bend more during fast swimming. Clione likely uses a combination of drag-based and unsteady mechanisms for force production at both speeds. The neuromuscular control of Clione's speed change points to a two-gaited swimming behavior, and we consider the kinematic evidence for Clione's swim speeds being discrete gaits.

Mechanisms of temperature-dependent swimming: the importance of physics, physiology and body size in determining protist swimming speed

Body temperatures and thus physiological rates of poikilothermic organisms are determined by environmental temperature. The power an organism has available for swimming is largely dependent on physiological rates and thus body temperature. However, retarding forces such as drag are contingent on the temperature-dependent physical properties of water and on an organism's size. Consequently, the swimming ability of poikilotherms is highly temperature dependent. The importance of the temperature-dependent physical properties of water (e.g. viscosity) in determining swimming speed is poorly understood. Here we propose a semi-mechanistic model to describe how biological rates, size and the physics of the environment contribute to the temperature dependency of microbial swimming speed. Data on the swimming speed and size of a predatory protist and its protist prey were collected and used to test our model. Data were collected by manipulating both the temperature and the viscosity (independently of temperature) of the organism's environment. Protists were either cultured in their test environment (for several generations) or rapidly exposed to their test environment to assess their ability to adapt or acclimate to treatments. Both biological rates and the physics of the environment were predicted to and observed to contribute to the swimming speed of protists. Body size was not temperature dependent, and protists expressed some ability to acclimate to changes in either temperature or viscosity. Overall, using our parameter estimates and novel model, we are able to suggest that 30 to 40% (depending on species) of the response in swimming speed associated with a reduction in temperature from 20 to 5°C is due to viscosity. Because encounter rates between protist predators and their prey are determined by swimming speed, temperature- and viscosity-dependent swimming speeds are likely to result in temperature- and viscosity-dependent trophic interactions.

Hydrodynamic pumping by serial gill arrays in the mayfly nymph Centroptilum triangulifer

Aquatic nymphs of the mayfly Centroptilum triangulifer produce ventilatory flow using a serial array of seven abdominal gill pairs that operates across a Reynolds numbers (Re) range from 2 to 22 during ontogeny. Net flow in small animals is directed ventrally and essentially parallel to the stroke plane (i.e. rowing), but net flow in large animals is directed dorsally and essentially transverse to the stroke plane (i.e. flapping). Detailed flow measurements based on Particle Image Velocimetry (PIV) ensemble-correlation analysis revealed that the phasing of the gills produces a time-dependent array of vortices associated with a net ventilatory current, a fluid kinematic pattern, here termed a ‘phased vortex pump’. Absolute size of vortices does not change with increasing animal size or Re, and thus the vortex radius (Rv) decreases relative to inter-gill distance (Lis) during mayfly growth. Given that effective flapping in appendage-array animals requires organized flow between adjacent appendages, we hypothesize that rowing should be favored when Lis/Rv<1 and flapping should be favored when Lis/Rv>1. Significantly, the rowing-to-flapping transition in Centroptilum occurs at Re∼5, when the mean dynamic inter-gill distance equals the vortex radius. This result suggests that the Re-based rowing–flapping demarcation observed in appendage-array aquatic organisms may be determined by the relative size of the propulsive mechanism and its self-generated vortices.

In-line motion causes high thrust and efficiency in flapping foils that use power downstroke

We show experimentally that flapping foil kinematics consisting of a power downstroke and a feathering upstroke together with a properly timed in-line motion, similar to those employed in forelimb propulsion of sea turtles, can produce high thrust and be hydrodynamically as efficient as symmetrically flapping foils. The crucial parameter for such asymmetrically flapping foils is a properly sized and timed in-line motion, whose effect is quantified by a new parameter, the advance angle, defined as the angle of the foil trajectory with respect to the horizontal, evaluated at the middle of the power downstroke. We show, in particular, that optimal efficiency in high aspect ratio rigid foils, accompanied by significant thrust production, is obtained for Strouhal numbers in the range 0.2–0.6 for Reynolds number equal to 13,000, and for values of the advance angle around 0.55π (100 deg.). The optimized kinematics consist of the foil moving back axially during the downstroke, in the direction of the oncoming flow, and rotating with a large pitch angle. This causes the force vector to rotate and become nearly parallel to the steady flow, thus providing a large thrust and a smaller transverse force. During the upstroke, the foil is feathering while it moves axially forward, i.e. away from the vorticity shed during the power stroke; as a result, the transverse force remains relatively small and no large drag force is produced. Observations from turtles confirm qualitatively the findings from the foil experiments.

Aerodynamic effects of flexibility in flapping wings

Recent work on the aerodynamics of flapping flight reveals fundamental differences in the mechanisms of aerodynamic force generation between fixed and flapping wings. When fixed wings translate at high angles of attack, they periodically generate and shed leading and trailing edge vortices as reflected in their fluctuating aerodynamic force traces and associated flow visualization. In contrast, wings flapping at high angles of attack generate stable leading edge vorticity, which persists throughout the duration of the stroke and enhances mean aerodynamic forces. Here, we show that aerodynamic forces can be controlled by altering the trailing edge flexibility of a flapping wing. We used a dynamically scaled mechanical model of flapping flight (Re approximately 2000) to measure the aerodynamic forces on flapping wings of variable flexural stiffness (EI). For low to medium angles of attack, as flexibility of the wing increases, its ability to generate aerodynamic forces decreases monotonically but its lift-to-drag ratios remain approximately constant. The instantaneous force traces reveal no major differences in the underlying modes of force generation for flexible and rigid wings, but the magnitude of force, the angle of net force vector and centre of pressure all vary systematically with wing flexibility. Even a rudimentary framework of wing veins is sufficient to restore the ability of flexible wings to generate forces at near-rigid values. Thus, the magnitude of force generation can be controlled by modulating the trailing edge flexibility and thereby controlling the magnitude of the leading edge vorticity. To characterize this, we have generated a detailed database of aerodynamic forces as a function of several variables including material properties, kinematics, aerodynamic forces and centre of pressure, which can also be used to help validate computational models of aeroelastic flapping wings. These experiments will also be useful for wing design for small robotic insects and, to a limited extent, in understanding the aerodynamics of flapping insect wings.

Pulsed jet dynamics of squid hatchlings at intermediate Reynolds numbers

Squid paralarvae (hatchlings) rely predominantly on a pulsed jet for locomotion, distinguishing them from the majority of aquatic locomotors at low/intermediate Reynolds numbers (Re), which employ oscillatory/undulatory modes of propulsion. Although squid paralarvae may delineate the lower size limit of biological jet propulsion, surprisingly little is known about the hydrodynamics and propulsive efficiency of paralarval jetting within the intermediate Re realm. To better understand paralarval jet dynamics, we used digital particle image velocimetry(DPIV) and high-speed video to measure bulk vortex properties (e.g. circulation, impulse, kinetic energy) and other jet features [e.g. average and peak jet velocity along the jet centerline (Uj and Ujmax, respectively), jet angle, jet length based on the vorticity and velocity extents (Lω and LV, respectively), jet diameter based on the distance between vorticity peaks (Dω), maximum funnel diameter (DF), average and maximum swimming speed(U and Umax, respectively)] in free-swimming Doryteuthis pealeii paralarvae (1.8 mm dorsal mantle length)(Resquid=25–90). Squid paralarvae spent the majority of their time station holding in the water column, relying predominantly on a frequent, high-volume, vertically directed jet. During station holding,paralarvae produced a range of jet structures from spherical vortex rings(Lω/Dω=2.1, LV/DF=13.6) to more elongated vortex ring structures with no distinguishable pinch-off(Lω/Dω=4.6, LV/DF=36.0). To swim faster,paralarvae increased pulse duration and Lω/Dω, leading to higher impulse but kept jet velocity relatively constant. Paralarvae produced jets with low slip, i.e. ratio of jet velocity to swimming velocity(Uj/U or Ujmax/Umax), and exhibited propulsive efficiency [ηpd=74.9±8.83% (±s.d.) for deconvolved data] comparable with oscillatory/undulatory swimmers. As slip decreased with speed, propulsive efficiency increased. The detection of high propulsive efficiency in paralarvae is significant because it contradicts many studies that predict low propulsive efficiency at intermediate Re for inertial forms of locomotion.

Trade-off between aerobic capacity and locomotor capability in an Antarctic pteropod

At -1.8 degrees C, the waters of Antarctica pose a formidable physiological barrier for most ectotherms. The few taxa that inhabit this zone have presumably made specific adjustments to their neuromuscular function and have enhanced their metabolic capacity. However, support for this assertion is equivocal and the details of specific compensations are largely unknown. This can generally be attributed to the fact that most Antarctic organisms are either too distantly related to their temperate relatives to permit direct comparisons (e.g., notothenioid fishes) or because they are not amenable to neuromuscular recording. Here, as a comparative model, we take advantage of 2 pelagic molluscs in the genus Clione to conduct a broadly integrative investigation on neuromuscular adaptation to the extreme cold. We find that for the Antarctic congener aerobic capacity is enhanced, but at a cost. To support a striking proliferation of mitochondria, the Antarctic species has shed a 2-gear swim system and the associated specialized neuromuscular components, resulting in greatly reduced scope for locomotor activity. These results suggest that polar animals have undergone substantial tissue-level reorganizations to accommodate their environment, which may reduce their capacity to acclimate to a changing climate.