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

The aerodynamics of flapping flight by insects, birds and other organisms is highly complex, and many unsteady lift-enhancing flow phenomena have been discovered (Weis-Fogh, 1973; Dickinson et al., 1999; Bomphrey et al., 2017). The best known of these is the clap-and-fling mechanism, originally described by Weis-Fogh (1973). The clap-and-fling mechanism is widely used by insects and seems to be obligatory in the smallest insects (Kolomenskiy et al., 2011; Sane, 2016; Cheng and Sun, 2018). In the clap-and-fling mechanism, the wings closely approach each other at the end of the recovery stroke (the clap phase) and force the flow in the gap between them downwards in a jet-like flow to enhance lift generation. The wings then rotate apart from each other about their trailing edges (the fling phase), creating a V-shaped gap into which air flows. In this way, insects overcome the starting Wagner effect, create a low-pressure region between the wings and create enhanced leading edge vortices.

The clap-and-fling mechanism has been widely studied since its discovery. Lighthill (1973) performed theoretical analysis with simplifying assumptions, showing how the clap-and-fling mechanism increases lift generation. Using a dynamically scaled laboratory model, Maxworthy (1979) visualized the leading edge vortices formed in the fling phase and found they comprise a large part of the force generated. Ellington (1984) reported variations of the clap-and-fling maneuver, including the near-clap-and-fling and the clap-and-peel, in various insect species. Lehmann et al. (2005) used dynamically scaled fruit fly wing models to find that the clap-and-fling mechanism enhanced the resultant force by 17%. Kolomenskiy et al. (2011) concluded from their theoretical and computational 2D model that viscosity enhances lift generation in the ‘fling’ as compared with the inviscid case. Computational fluid dynamics studies of the clap-and-fling mechanism have recently highlighted the importance of wing flexibility and porosity in overcoming the large forces needed for tiny insects to clap their wings together and fling them apart (Miller and Peskin, 2005, 2009; Santhanakrishnan et al., 2014) and have shown that flexible wings can reduce the drag force generated during the fling by about 50% (Miller and Peskin, 2009).

Research by Satterlie et al. (1985) and Borrell et al. (2005) on the swimming of the shell-less marine snail Clione limacina and its congener Clione antarctica suggested that the clap-and-fling maneuver is not limited to aerial flight. Based on high-speed filming of tethered organisms, Chang and Yen (2012) showed that the tiny (∼2 mm) shelled pteropod Limacina helicina similarly uses a version of the clap-and-fling maneuver with its pair of highly flexible, wing-like appendages (called parapodia) formed from a modified foot structure. Murphy et al. (2016) used volumetric particle image velocimetry (PIV) to measure the kinematics and flows generated by L. helicina performing its clap-and-fling mechanism, findings which were verified by Adhikari et al. (2016) in Limacina helicina antarctica. Similarly, Karakas et al. (2018) found that the heteropod Atlanta selvagensis performs a clap-and-fling maneuver using its one flexible appendage and its rigid, coiled shell. Here, we report a novel variation of the clap-and-fling mechanism used by another sea butterfly species, Cuvierina atlantica Bé, MacClintock and Currie 1972, which we call a cylindrical overlap-and-fling.

A variety of shelled pteropod species including C. atlantica, Hyalocylis striata, Heliconoides inflatus and Limacina bulimoides were collected offshore of Bermuda using a Reeve net with 150 µm mesh size and a specialized 20 l cod end. Specimens were collected during a night-time cruise, kept in collected seawater, and brought back to a temperature-controlled chamber at the Bermuda Institute of Ocean Sciences (BIOS) in May 2017. The zooplankton were sorted and visually identified under a stereomicroscope and were then stored in filtered seawater at an in situ temperature of 21°C. To ensure that specimens were healthy, experiments were conducted immediately upon return from the cruise and, as the pteropods did not live long after capture, experiments were completed within 36 h of collection. This mixed assemblage of pteropod species was placed together in the experimental systems described below. This study focuses on recordings of swimming C. atlantica. At least two C. atlantica individuals were included in this assemblage, and these could be differentiated in the recordings based on shell length.

A photogrammetry system comprising two synchronized high-speed monochrome Edgertronic cameras (Sanstreak Corp., San Jose, CA, USA) was used to measure the 3D swimming kinematics of the pteropods at high magnification. The cameras, lights and aquarium were mounted on optical rails and a breadboard to rigidly support the system. The two cameras were arranged perpendicular to each other and were equipped with 200 mm Nikon macro lenses with apertures set to f/32 to maximize the depth of the field (∼12 mm). Both cameras filmed at 600 Hz with a resolution of 1024×912 pixels and viewed a glass aquarium with 30×30×30 mm³ (width×depth×height) inner dimensions and 2.5 mm wall thickness, which was filled with 0.2 µm filtered seawater collected with the pteropods to a depth of 28 mm. The field of view of each camera was at least 10 mm above the tank bottom such that only actively swimming pteropods were recorded. The focal planes of the cameras were set to the middle of the aquarium so that only freely swimming pteropods not interacting with the walls would be recorded. The spatial resolution of the cameras was 14.3 µm pixel⁻¹. Collimated backlighting for each camera was provided by an LED fiber optic illuminator with a dual arm gooseneck (Dolan-Jenner Industries, Lawrence, MA, USA). The camera system was spatially calibrated prior to the experiments using the direct linear transform technique (Abdel-Aziz and Karara, 1971; Hedrick, 2008). Briefly, a scaled microscope slide held vertically and oriented 45 deg to both cameras was positioned at 25 predefined locations within the common field of view within the filled aquarium using a microtranslator (PT3/M, Thorlabs, Newton, NJ, USA). Three points on the slide imaged at these 25 locations provided 75 calibration points covering the measurement volume. These points provided the calibration coefficients mapping the 2D camera coordinates into the 3D world coordinates using DLTdv5 (Hedrick, 2008). Up to approximately 10 pteropods of diverse sizes and species were selected for the experiments and were carefully transferred to the test aquarium. Little interference was observed between swimming animals as swimming bouts were intermittent and alternated with periods of lying on the tank bottom. The camera system was manually triggered when a pteropod swam into the field of view common to both cameras. Four videos of C. atlantica representing two different individuals were collected. However, because of the high magnification, parts of the pteropod were often outside the field of view of one camera for part of these videos. Thus, a 0.43 s segment from one recording event in which the animal swam upwards through the field of view and in which both wings were fully visible for almost two complete wing strokes was chosen for further analysis. As shown in Fig. 1, 10 different points on the pteropod were manually tracked in each frame using DLTdv5 in order to quantify the pteropod wing and body kinematics (Hedrick, 2008). Kinematics data from one video in which the pteropod swam upwards through the field of view are presented in the Results.

Brightfield back-illuminated 2D micro-particle image velocimetry (µPIV) was applied to quantify the flow structures and velocity fields around the freely swimming pteropods (Gemmell et al., 2014). In this system, a 2× extra-long working distance (ELWD) microscopic objective (no. 46-142, Mitutoyo) with an image-generating tube lens (no. 58-520, Edmund Optics) provided a depth of field of 91 µm, resulting in a measurement plane width (MPW) of approximately 250 µm (Koutsiaris, 2012). The advantage of this approach is its ability to provide a narrow MPW without the use of a laser. A high-speed camera (Phantom VEO 640S) recorded at 1400 Hz with a spatial resolution of 2560×1600 pixels. The field of view was 12.43×7.77 mm² (vertical×horizontal) and was vertically and horizontally centered within the tank in order to minimize wall and free surface effects. The test tank was seeded with 2–3 µm mean diameter algae (Nannochloropsis oculata), which work well as tracking particles because they are natural food items for pteropods (Thabet et al., 2015) and because no light scattering by the particles is required. The test section was illuminated with a telecentric backlight illuminator (no. 62-760, Edmund Optics). Similar to the kinematics experiments, multiple pteropods were placed in the aquarium simultaneously. Recordings were manually triggered when an animal swam through the focal plane. Six videos of C. atlantica were recorded, but only in one video did this species perform a complete stroke cycle while well positioned in the focal plane. This video, which recorded the same individual for which kinematics data were analyzed, was chosen for further flow analysis. Image processing was applied to the raw µPIV images to invert the images, apply Gaussian filtering to remove out-of-focus particles, and algorithmically mask animals using local intensity values. Velocity fields were calculated by applying multi-pass cross-correlation using a 50% overlap, beginning with a 64×64 window size in the first pass and decreasing to 32×32 window sizes in subsequent passes. Erroneous vectors were removed by the universal outlier detection method. Particle seeding density was high, with about 20 particles distributed in each 64×64 interrogation window. The resulting vector fields comprised 160×100 vectors with a vector grid spacing of 0.0766 mm.

Fig. 1 shows a 3D model of the shelled pteropod C. atlantica with the tracked points labeled, including three points on the body (c–e), the wingtips (a and b), the leading edges (f and h) and trailing edges (g and i) of the right and left wing chords, and a point on the top edge of the shell (j, coinciding with the origin of the body-centered coordinate system). A global (XYZ) coordinate system and a body-centered (X′Y′Z′) coordinate system, which translates and rotates with the animal, also are defined in Fig. 1. As measured from the 3D coordinates taken from the processed kinematics videos, the adult pteropod has a body length of l_b=9±0.03 mm (a mean±s.d. value measured from point c to d over 116.7 ms), a wingspan of l_s=9.4±0.1 mm (a mean±s.d. value measured between points a and b at the three time points in the recording when the wings are fully outstretched, as in Fig. 1A), and a chord length of c=3.0±0.27 mm (a mean±s.d. value measured between points f and g over 408.3 ms). It is important to note that these mean and standard deviation values represent multiple measurements of the same animal taken at different time points within the same recording. The animal beats its wings at a mean frequency of f=5 Hz and has a mean swimming speed of 35 mm s⁻¹. These animals thus swim in an intermediate Reynolds number (Re) regime in which both inertial and viscous forces are important. A body-based Reynolds number Re_b=l_b/ν and chordwise Reynolds number Re_c=2φfl_fc/ν are defined here, where l_f is the length of one wing, φ is wing stroke amplitude and ν is the kinematic viscosity of the seawater at 21°C. Given that C. atlantica has a wing stroke amplitude of φ=160 deg, this pteropod species thus has a Re_b=300 and  Re_c=420, placing its Re_c at the same order of magnitude as that of fruit flies (Vogel, 1966). As shown in Fig. 1B, the animal's pitching angle θ is defined as the angle between the Z and Z′ axes. The wing bending angle β is defined for each wing using points on the wingtip, mid-wing chord and body, as shown in Fig. 1C for the left wing.

Fig. 2 shows a model of C. atlantica which illustrates the motion of its wings as the animal performs an idealized cylindrical overlap-and-fling maneuver as well as simplified schematic diagrams comparing the cylindrical overlap-and-fling maneuver with the classic clap-and-fling maneuver used by insects. High-speed visualization, wingtip and body kinematics, and the resulting flow fields throughout one wing stroke are also presented in order to illustrate the principle of the cylindrical overlap-and-fling mechanism and how it is used by C. atlantica. Fig. 3 shows the C. atlantica wing stroke cycle from two synchronized orthogonal high-speed cameras (Movie 1). Because of the highly flexible nature of the wings, the outer edge of the right wing in both perspectives is highlighted in red for clarity. Fig. 4 shows the time history of the right and left wingtip positions (in the body-centered coordinate system), body angle θ, instantaneous swimming speed U, and the mean wing bending angle averaged between the right and left wings. Fig. 5 shows flow fields recorded in a plane slightly offset from the pteropod's sagittal plane (Movie 2). The approximate location of this plane relative to the pteropod is shown in Fig. 2.

As shown in Figs 2A and 3, at the beginning of the wingbeat cycle (t′=0, where t′ is time normalized by the stroke period of 200 ms), the right and left wings are highly bent along their respective spans, with up to 160 deg (Fig. 4B), and overlap each other to form a circular cylinder on the posterior side of the animal. This wingtip overlap is reflected in the positive Y′ position of the right wingtip and the negative Y′ position of the left wingtip in Fig. 4B. As the power stroke commences (t′=0.1), the wings separate from each other as the right and left wingtip Y′ positions cross (Fig. 4B). As they expand from their cylindrical configuration, decreases (Fig. 4B), the X′ wingtip positions slightly decrease (Fig. 4A), and the Z′ positions increase (Fig. 4C) as the wings elevate and open away from the body simultaneously. As shown in Figs 2B and 3, the leading edges of the wings open from their cylindrical shape more quickly than the trailing edges, thus transforming the cylinder into a conical shape with a larger opening on the top than on the bottom. The result of this fling part of the cylindrical overlap-and-fling maneuver is that a vortex ring seems to form on the wings’ leading edges which feeds flow into the gap opening between the wings, a concept illustrated in Fig. 2A–C. For example, Fig. 5 shows a clockwise vortex developing on the right wing's leading edge at t′=0.12 and strengthening as the wings further separate at t′=0.15–0.19. This fling results in a strong downward flow adjacent to the animal's shell, with flow speeds reaching a maximum of 121 mm s⁻¹ at t′=0.19. This maneuver coincides with a sharp increase in swimming speed from 10 mm s⁻¹ to 30 mm s⁻¹ as shown in Fig. 4D.

Subsequently, the X′ wingtip positions continue to increase as the wing stroke continues toward the anterior side of the animal (Fig. 4A). By t′=0.25 in Fig. 3, the wings are fully extended as the Y′ wingtip coordinates reach their maximum negative and positive values for the right and left wings, respectively (Fig. 4B). The mean wing bending angle approaches zero and subsequently becomes negative as the fully extended wings cross to the anterior side of the animal (Fig. 4B). As shown in Fig. 5, at t′=0.23, a strong clockwise vortex remains on the animal's posterior side and is transported downwards; no significant flow around the wing is seen at this time because the view is obstructed by the other wing and because the focal plane is near the root of the wing (Fig. 2C). As shown in Fig. 4D, this anterior wing flapping coincides with an increase in θ as the top of the shell pitches posteriorly and with the local maximum swimming speed of 50 mm s⁻¹ at approximately t′=0.26. The flow field at t′=0.33 in Fig. 5 shows a tip vortex on the right wing; it is likely that this vortex wraps around the animal to connect with the previously shed vortex on the animal's posterior side.

At t′=0.4 in Fig. 3, the wings have almost finished their respective power strokes and have traveled to the anterior side of the animal, as shown by the Y′ wingtip coordinates converging in Fig. 4B. Here, the wingtips overlap, as shown by the crossing traces of the wingtip Y′ positions, and form a cone. This cone initially has a wider diameter on the bottom than on the top but becomes cylindrical as the wings are pulled back towards the shell, as illustrated in Fig. 2D–F. The local minima in the X′ wingtip positions at approximately t′=0.5 in Fig. 4A also illustrate how the wings must bend to close into a cylinder. The resulting flow, a downward jet of fluid squeezed out from the cone between the wings, is shown at t′=0.40 in Fig. 5. This jet has flow speeds of 78.5 mm s⁻¹, feeds into the existing tip vortex, and rolls up to form what is likely a small vortex ring which travels downwards anterior to the animal. This concept is illustrated in Fig. 2D–F. The weaker flow speeds generated by this cylindrical overlap do not result in an increase in swimming speed as instead the animal continues to decelerate during this time period (Fig. 4D). The downward jet thus may serve to clear the previously generated vortex structures in preparation for the next half-stroke (Dickinson, 1996).

At t′=0.53 in Fig. 3 and t′=0.51 in Fig. 5, the pteropod has finished its power stroke and, with its mean wing bending angle (Fig. 4B) and swimming speed at a minimum, begins its recovery stroke. The pteropod thus performs a second fling maneuver similar to that performed during the power stroke. Specifically, the wings begin to unfold from their cylindrical configuration in which the wingtips overlap with each other, evidenced by increasing (Fig. 4B). This unfolding also is shown by the increase in the X′ wingtip positions and crossing of the Y′ wingtip traces in Fig. 4A,B. As the wings unfold, the leading edges open before the trailing edges, again transforming the cylinder into a cone, as shown in Fig. 2B and at t′=0.66 in Fig. 3. This second fling maneuver again causes a vortex to form around the wing's leading edges and fluid to flow into the opening conical gap between the wings, resulting in a sharp increase in the pteropod's swimming speed (Fig. 4D). This downward flow between the wings is shown at t′=0.64 in Fig. 5 and has a maximum speed of 94 mm s⁻¹, slightly less than the maximum speed measured during the power stroke's fling. This vortex and downward flow continue to develop at t′=0.70 in Fig. 5 as the pteropod continues with its recovery stroke (t′=0.75 in Fig. 3). The body angle reaches its minimum (θ=−7.4 deg) near the end of the recovery stroke and subsequently begins to increase, as shown in Fig. 4D. At the end of the recovery stroke (t′=0.92 in Fig. 3), the swimming speed decreases to 15 mm s⁻¹ and the wings perform a second overlap maneuver as they fold together to form a cone, which transforms into a cylinder. The wings are thus in position to perform the fling associated with the next power stroke.

The lift-enhancing clap-and-fling maneuver used by most insects and some marine snails consists of the close apposition of largely flat wings (Ellington, 1984; Murphy et al., 2016; Karakas et al., 2018). Apposing and separating these flat wings in close proximity to each other during the clap and fling phases, respectively, requires a large amount of power, especially at Re<10, though this drag-induced energetic expense is reduced somewhat by increased wing flexibility and porosity (Miller and Peskin, 2005, 2009; Santhanakrishnan et al., 2014). In contrast, the pteropod species studied here uses its highly flexible wings to sequentially form a downward-opening cone, a cylinder, and an upward-opening cone at the end of each half stroke. We call this novel lift-enhancing technique the cylindrical overlap-and-fling. Though serving the same function as in insects, the geometrical configuration of the wings is dramatically different. This novel geometry allows this pteropod species to take advantage of the lift enhancement offered by the clap-and-fling maneuver without the necessity of wing apposition. The cylindrical overlap-and-fling maneuver may thus offer the possibility of avoiding the large drag associated with the classic ‘planar’ clap-and-fling maneuver. However, the Reynolds number at which C. atlantica uses the overlap-and-fling (Re_b=300 and Re_c=420) is somewhat larger than the Reynolds number at which most insects use the clap-and-fling. Indeed, the clap-and-fling maneuver is thought to be obligatory for tiny insects flying at Re of 100 or less. However, large insects also perform the clap-and-fling maneuver in high Re flight, especially to generate extra lift [e.g. Locusta migratoria in climbing and turning flight (Cooter and Baker, 1977), the butterfly Vanessa atalanta (Srygley and Thomas, 2002), and some other large insects carrying loads (Marden, 1987)]. Indeed, Marden (1987) showed that the use of clap-and-fling by various insects, small birds and bats increases the lift per unit flight muscle mass by about 25% as compared with flight in the absence of the clap-and-fling maneuver, and Lehmann et al. (2005) measured a 17% increase in lift generation in a dynamically scaled Drosophila wing model (Re≈100–200) which performs a near-clap-and-fling maneuver. It is likely that pteropods employing a version of the clap-and-fling at Re_c=5–35 (e.g. L. helicina; Murphy et al., 2016) and the overlap-and-fling at higher Re (e.g. C. atlantica) enjoy similar lift augmentation. However, it is unknown whether the cylindrical overlap-and-fling maneuver is employed by smaller pteropod species or juvenile C. atlantica individuals swimming at Re characteristic of tiny insect flight. The need for such extreme and complex wing deformation may possibly limit use of the overlap-and-fling maneuver to somewhat larger wing sizes and larger Re.

A second significant difference in the ways that pteropods and insects use this type of clap-and-fling maneuver is that C. atlantica performs two complete overlap-and-fling maneuvers in each wing stroke while all insects studied to date and some other pteropod species (e.g. L. helicina) are only able to perform one. This ability in C. atlantica is enabled by its highly flexible wings, which may bend 160 deg in both anterior and posterior directions, and by the fact that its body and elongated shell, a more recent evolutionary shift in pteropod morphology as compared with spiral-shelled pteropods (Peijnenburg et al., in review; Janssen and Peijnenburg, 2017), do not interfere with its wing motion. Insects, in contrast, have relatively less flexible wings, and clapping at the end of the power stroke has not been reported, likely because the presence of their bodies prevents the wings from doing so (Lighthill, 1973; Wootton, 1981; Cheng and Sun, 2017). Similarly, some other pteropod species, though they do have highly flexible wings, are prevented from clapping twice during each stroke because of the presence of their spiral-shaped shell (Chang and Yen, 2012; Adhikari et al., 2016; Murphy et al., 2016). In contrast, enabled by its slender body and extremely large stroke angle, the atlantiid heteropod A. selvagensis performs a double clap-and-fling on each stroke without significant bending of its appendages (Karakas et al., 2018). The ability to use the clap-and-fling maneuver twice during each stroke was theoretically considered by Lighthill (1973), who hypothesized that this double use would create a circular vortex ring on each half-stroke in the animal's wake, thereby maximizing downward momentum per unit kinetic energy. Though volumetric velocity measurements are needed for confirmation, it seems likely that its large wing stroke amplitude and low wingbeat frequency enable C. atlantica to indeed create two independent vortex rings throughout each stroke cycle. The wake in this scenario would represent a real-life case of Dickinson's (1996) idealized fish propelling itself via large amplitude pectoral fin strokes and thus creating a series of disconnected vortex loops in its wake. Indeed, the separation between the vortices created by the power and recovery strokes seen in Fig. 5 shows that this is likely the case. Regardless of the wake structure, the additional lift provided by using the overlap-and-fling mechanism twice during each stroke is beneficial in supporting the heavy shell of C. atlantica as it daily migrates at least 100 m upwards to the ocean surface to feed (Wormuth, 1981).

Another significant difference between pteropods' overlap-and-fling and insects' clap-and-fling is that C. atlantica actively bends its wings whereas the wings of insects are passively deformed depending on the aerodynamic load (Wootton, 1981, 1990; Combes and Daniel, 2003a,b). Indeed, this pteropod is able to bend its wings along the spanwise direction to such an extent that its wingtips overlap at the end of each half-stroke. The active flexibility of pteropod appendages is due to their unique morphology and wing structure. Pteropod wings are modified from the molluscan foot without any rigid support (Borrell et al., 2005), and these organisms have hydrostatic skeletons which are supported by fluid pressure (Szymik and Satterlie, 2017). Further, the wings of pteropods have layers of parallel muscles oriented at different angles across the wing (Satterlie et al., 1985). This unique wing structure enables active spanwise wing bending and high flexibility, with wing bending angle amplitudes up to 160 deg in C. atlantica (Fig. 4B). In contrast, insects have exoskeletons and their wings, which are actuated at their roots, have a complex network of veins with connecting membranes to support the forces on the wings (Wootton, 1981). Active spanwise wing deformation is thus absent, and passive wing deformation in insects is mostly limited to an amplitude of less than 40 deg (Lucas et al., 2014). Wing flexibility in insects has been shown to be beneficial with higher energetic efficiency and aerodynamic performance (Vanella et al., 2009; Colin et al., 2012; Kodali et al., 2017; Wong and Rival, 2017). Wong and Rival (2017) showed that passive spanwise bending of 30–40 deg stabilizes the leading edge vortex (LEV), thus providing augmented lift for an extended period of time. In contrast, these researchers found that active spanwise bending of the same magnitude generates a much stronger yet less stable LEV than that generated either with passive bending or in the absence of bending, thus generating higher levels of instantaneous lift. Cuvierina atlantica utilizes passive spanwise bending as the wings separate after each overlap-and-fling. The mid-span of each convex-shaped wing thus leads during the first part of each half-stroke. Midway through each stroke (i.e. leading into the overlap phase), the convexity of the wing reverses as the tip begins to lead, thus changing into an active spanwise bending configuration. This mechanism may provide an effective way to actively control the strength and stability of the LEV over the wing stroke and thus to manipulate the lift generation.

In addition to controlling spanwise bending, pteropods are also able to actively control chordwise bending owing to their fluid-filled wings, which have infinite degrees of freedom in motion. This chordwise deformation is actively controlled by the fluid pressure and by muscle fibers in the wing, with the control system based on complex feedback from the surrounding flow conditions (Szymik and Satterlie, 2017). Active control over chordwise flexibility likely enables C. atlantica to perform the overlap-and-fling maneuver as it moves its overlapping wings from a cylindrical configuration to a conical configuration. Chordwise wing flexibility similarly enables insects and micro-aerial vehicles to generate greater lift-to-drag ratios when performing the clap-and-fling or clap-and-peel maneuver. For example, Miller and Peskin (2009) numerically showed a 50% decrease in peak drag in the fling due to wing flexibility and an increase in lift force in some cases. Similarly, flow and force measurements on a pair of flexible model wings performing clap-and-peel showed relatively higher force generation as compared with rigid wings (Percin et al., 2017).

Though all pteropod species swim by flapping a pair of structurally similar highly flexible parapodia, swimming kinematics may vary substantially among different species based on size and shell morphology. The species studied here, C. atlantica, uses a unique overlap-and-fling maneuver at the end of each half-stroke and pitches its large, elongated shell by approximately 20 deg while swimming. In contrast, the much smaller, coiled shell thecosomes L. helicina (Chang and Yen, 2012; Murphy et al., 2016) and L. helicina antarctica (Adhikari et al., 2016) use a modified version of the clap-and-fling maneuver only at the end of the power stroke and flap their wings against the shell at the end of the recovery stroke. In addition, these thecosomes pitch their shells to a much greater degree, by up to 60 deg in L. helicina and up to 110 deg in L. helicina antarctica. These coiled shells possess much less rotational drag and moment of inertia in comparison to the elongated shell of C. atlantica, which retards such a large degree of pitching. In addition, the different Reynolds number regimes in which the tiny coiled shell species and C. atlantica operate could contribute to their different swimming kinematics. The coiled shell species generally operate in a highly viscous regime at Re less than 100 whereas C. atlantica, with its elongated shell, operates at a Re an order of magnitude higher (Re=100–600). The relative importance of inertial and viscous forces may have thus led this species to adopt a more streamlined shell in order to reduce the pressure drag, which would be important at this larger Re. Finally, though it would be expected that the larger species would have a lower wingbeat frequency, comparing the wingbeat frequency of C. atlantica with that of the tiny coiled shell species is difficult because of ambient water temperature (and thus viscosity) differences. Cuvierina atlantica lives at a water temperature of ∼21°C (which has a viscosity of 1.05×10⁻⁶ m² s⁻¹) and beats its wings at ∼5 Hz. In contrast, L. helicina lives at ∼12–16°C and has a wingbeat frequency of 5–10 Hz, and L. helicina antarctica lives at ∼0°C (which has a higher viscosity of 1.83×10⁻⁶ m² s⁻¹) and has a lower wingbeat frequency of 2–3 Hz (Chang and Yen, 2012; Adhikari et al., 2016; Murphy et al., 2016). The higher seawater viscosity at colder temperatures thus corresponds to lower wingbeat frequencies, though temperature-induced differences in metabolism may also play a role here (Pétavy et al., 1997).

The swimming of the thecosome species studied here also bears some similarity to that of the shell-less gymnosomes C. limacina (Satterlie et al., 1985; Szymik and Satterlie, 2011) and C. antarctica (Borrell et al., 2005). Cuvierina atlantica and these gymnosomes have a similar elongated shape, have approximately the same body length, and flap their wings in similar, nearly horizontal stroke planes. However, compared with C. atlantica, gymnosomes have relatively short, low aspect ratio wings, and this difference in wing morphology affects their ability to perform a version of the overlap-and-fling maneuver. During slow swimming, the wingtips of C. limacina approach but do not touch each other. However, during fast swimming, it appears that C. limacina may perform a version of the overlap-and-fling maneuver at the end of the downstroke as the wings fold over each other close to the body (Szymik and Satterlie, 2011). Because the wings are shorter, the void between them is compressed in comparison to the cylindrical void formed by the wings of C. atlantica. However, similar to C. atlantica, gymnosome wings unfold in an upward-opening cone, presumably in order to gain lift from a LEV. Another difference between C. atlantica and gymnosomes is the wingbeat frequency. Gymnosomes living at an ambient seawater temperature of 0°C flap their wings at ∼1–3 Hz. This lower beat frequency may be due to the higher viscosity of colder seawater, metabolic and physiologic constraints, and the lack of a heavy calcareous shell. The lack of a shell in gymnosomes would result in a smaller wing loading and thus allow a smaller wingbeat frequency for propulsion (Pétavy et al., 1997). Further, the low aspect ratio wings of gymnosomes are not efficient for long periods of swimming but are well suited for generating high forces necessary for maneuvering. Correspondingly, gymnosomes swim slowly most of the time (at Re<100) but swim very fast (Re>1000) for short periods of time when escaping or hunting. In contrast, C. atlantica has a larger wing aspect ratio and is thus well suited to swim the long distances necessary for diel vertical migration while benefiting from the double overlap-and-fling which aids in generating the forces needed to carry the heavy shell.

It is also worth noting that the cylindrical overlap-and-fling mechanism observed here employs both suction- and jet-based propulsion mechanisms. Specifically, C. atlantica manipulates its wing positions to generate a low-pressure suction region on the upper wing surface in the fling phase and to generate thrust by pushing the flow downward during the overlap phase. It is likely that suction dominates in thrust generation because, as shown in Fig. 4D, the animal accelerates during the fling phase and decelerates during the overlap phase. Many other efficient aquatic swimmers such as jellyfish and lampreys similarly rely on suction for thrust generation (Gemmell et al., 2015). Indeed, the kinematics of the overlap-and-fling mechanism bear some similarity to the bell kinematics of jellyfish medusae (Dabiri et al., 2005; Gemmell et al., 2018) and jellyfish-inspired robots (Nawroth et al., 2012; Ristroph and Childress, 2014; Ren et al., 2019). Finally, the swimming mechanisms of marine mollusks in general (Borrell et al., 2005; Szymik and Satterlie, 2011; Chang and Yen, 2012; Adhikari et al., 2016; Murphy et al., 2016; Zhou and Mittal, 2017, 2018) and the cylindrical overlap-and-fling mechanism observed here in particular may serve as bioinspiration for new soft robotic aquatic vehicles propelled by highly flexible propulsors capable of taking advantage of this and other novel lift generation techniques.

The authors gratefully acknowledge Leocadio Blanco-Bercial for assistance in collecting the pteropods, Joseph Bello for assistance in conducting experiments, and Paola Rossi Bruttini for assistance with digitization.