Introduction

Free swimming errant polychaete worms are ubiquitous members of most aquatic environments. They use unique kinematics for swimming which combine both undulatory body waves (known as S waves) and metachronal paddling of their setae or parapodia. The body wave of polychaetes differs from other swimming animals that use undulatory body waves in that the body waves of polychaete worms travel in the same direction as their swimming direction, moving from tail to head1. As such, the body wave motion has been shown not to generate forward thrust2. Instead, thrust forces have been described to be generated by the “roughness” along the body caused by the protruding setae which are said to produce drag forces parallel to the body3. However, the drag forces do not account for the swimming velocities observed and therefore it was shown that swimming thrust primarily results from paddling by the parapodia2,4,5,6 and later shown that the paddling is due to active, rather than passive, movements by the parapodia7.

The parapodia along the bodies of free swimming polychaetes paddle with antiplectic metachronal waves7,8 with the powerstroke of the parapodia moving in the opposite direction of the wave itself. While the parapodia paddling alone can generate thrust, the coordination of the body wave with the paddling is thought to increase the swimming speed7. The body waves are coordinated with the parapodia paddling so that the power stroke occurs at the crest and the recovery in the trough of the body wave. This would serve to enhance forward forces while reducing resistive drag forces.

Hydrodynamic analysis of the power stroke of individual parapodia of the pelagic polychaete Tomopteris sp. revealed that the thrust generated by the power stroke primarily arises from a negative pressure field that aligns along the leeward side of the moving parapodia6. Furthermore, little is known about how the body wave influences the metachronal kinematics of the parapodia. Thus, in order to understand the combined effects of parapodia paddling and body wave kinematics, a larger scale hydrodynamic analysis of the flow along the body throughout the wave cycle is required.

The goal of this study is to quantify the body wave and parapodia stroke kinematics in conjunction with the hydrodynamics of the fluid around the body in order to determine how the body waves and parapodia interact to enhance thrust and reduce drag throughout the swim cycle. We examined three species of free swimming errant polychaete worms spanning two orders of magnitude in size to better understand the flow between the parapodia and around the body, and how this may differ with animal size.

Methods

Collection and maintenance

Three polychaete species (Pelagobia longicirrata, Platynereis bicanaliculata and Nereis vexillosa) were hand collected from the waters surrounding the Friday Harbor Laboratories, WA, USA and immediately transported to the laboratory. The three species collected ranged in size from 4 to 110 mm. Individuals were maintained in flow-through seawater tables at ambient environmental temperatures (10–12 °C). Prior to filming, individuals were gently transferred to glass vessels and observations were made within 24 h of collection. Details on animal maintenance, use and care of lamprey used in this study can be found in Gemmell, et al.9

Kinematic and hydrodynamic analyses

To quantify the kinematics and hydrodynamics of the free-swimming polychaetes, individuals were placed into glass filming vessels large enough to keep the animals > 5 body lengths from the sides of the vessels. Kinematics were quantified using ImageJ software and bending angle was quantified in the same manner as Colin, et al.6. The hydrodynamics were quantified around the smallest individual using µPIV10. This technique uses brightfield imaging to obtain shadowgraph micro particle image velocimetry on free swimming animals. The brightfield PIV set up used collimated light directed into the camera through a 10 × long-working-distance objective. Images were collected with high speed monochrome video cameras at 500–6400 frames per second at a resolution of 2048 × 2048 pixels. Image stacks were imported into Fiji ImageJ software to quantify the swimming and limb/ctene kinematics. The water was seeded with Isochrysis galbana cells (approx. diameter = 5 µm). Image sequences during swimming were selected where the parapodia were in the focal plane throughout the swimming cycle. The focal depth for the 10 × objective is very narrow (approx. 8 µm) and few sequences satisfied this criteria, which greatly limited the number of replicate sequences of free swimming animals. Image pairs were subsequently analyzed in DaVis 8.3.1 (LaVision GmbH, Goettingen, GER) using a cross-correlation PIV algorithm with a decreasing interrogation window size of 64 × 64 pixels to 32 × 32 pixels or 32 × 32 pixels to 16 × 16 pixels with 50% overlap to produce velocity vectors and vorticity contours. Lamprey kinematics and fluid data was collected in the same manner as Gemmell, et al.11.

The hydrodynamics around the larger individuals (> 1 cm) was quantified using conventional PIV where hollow glass PIV beads (10 µm) were added to the seawater and the vessel was illuminated using a red laser sheet (1 mm thick). The glass beads did not have a visible effect on the swimming and feeding behavior. The swimming sequences were video recorded and analyze using the same camera and methods described above for the µPIV.

Pressure measurement

Velocity fields collected via PIV were input to a custom program in MATLAB that computed the corresponding pressure fields12. The algorithm integrates the Navier–Stokes equations along eight paths emanating from each point in the field of view and terminating at the boundaries of the field of view. As the full 2D Navier–Stokes equations are used, the pressure calculations include the full viscous effects present in the Reynolds number range of the parapodia. The pressure at each point is determined by computing the median pressure from the eight integration results. Parapodia were masked prior to computation to prevent surface artefacts in the pressure and torque results. Masks were generated using a custom MATLAB (MathWorks, Inc.) program that automatically identified the boundary of the animal body based on image contrast at the interface between the animal body and the surrounding fluid, and body outlines were smoothed prior to later analyses. These methods have been previously validated against experimental and computational data, including numerical simulations of anguilliform swimming12 and direct force and torque measurements of a flapping foil13. The MATLAB code is available for free download at https://dabirilab.com/software.

Statistical analysis

Kinematic and fluids data were log-transformed and checked for normality using a Shapiro–Wilks test. Data were subsequently tested using one-way ANOVA or T-test to determine if a significant difference existed between means.

Results

Kinematic properties

All three species of polychaete differed significantly in length from one another (P =  < 0.001, ANOVA, n = 3) and represented three orders of magnitude in scale (millimeter, centimeter, decimeter) (Table 1). Mean swimming speeds also differed significantly between each species (P =  < 0.001, ANOVA, n = 3) with absolute speeds (mm s-1) corresponding to body length and relative speeds (BL s-1) corresponding to the inverse of body length (Table 1). Reynolds number (Re) at the whole-animal scale varied considerably for each species, as expected, given the wide range in body length between species. For the smallest species, P. longicirrata, Re was close to 100, for P. bicanaliculata Re was approximately 3,000 and for N. vexillosa Re was approximately 15,000. Strouhal number was not calculated due to the fact that the polychaetes do not shed discrete vortices despite exhibited body wave undulations. Re at the scale of the propulsor was estimated from the angular speed and length of the parapodia. The smallest species, P. longicirrata, exhibited an appendage Re of approximately 70, close to that of the entire body. Despite N. vexillosa being almost 30 times longer and having a whole-body Re 150 times that of P. longicirrata, the Reynolds number at the scale of the of the propulsors was much less dramatic. P. longicirrata exhibited a propulsor Re of 70 while N. vexillosa had a propulsor Re of 300, only a fourfold difference. Proposulor bending was maximized during the recovery stroke for all three species tested. Maximum bending was measured to be 48 degrees (s.d. 8) and occurred consistently at an inflexion point approximately 1/3 of the propulsor length from the tip.

Table 1 Physical and kinematic parameters of three free-swimming polychaete species (± s.d.).
Full size table

Body waves travelled in the direction of locomotion (tail to head) and in all three species peak body wave speeds were always less than the mean swimming speed (Table 1). For P. longicirrata, mean peak body wave speeds were 60% of the mean swimming speed. The medium size P. bicanaliculata, exhibited body wave speeds that were 90% of mean swimming speed, while the larger N. vexillosa had peak body wave speeds that were 47% of the mean swimming speed. Both body wave speed and body wave amplitude peaked in magnitude along the middle section of the body and decreased both near the tail and the head. The smaller P. longicirrata, exhibited body waves that travelled the entire length of the body, starting at the tail and ending at the head which resulted in noticeable side to side head oscillations. In the two larger species, body waves also began at the tip of the tail however waves ended before reaching the head. For P. bicanaliculata, there was no wave motion observed in the anterior 22% (s.d. 6%) of the body. This was nearly identical for the large N. vexillosa where no body waves occurred in the anterior 21% (s.d. 1%) of the body. During swimming the front 1/5th of the body remained straight and no parapodia movement was observed, despite the fact that there are parapodia present in much of this region. Absolute body wave amplitude in P. longicirrata was significantly smaller than either P. bicanaliculata or N. vexillosa (P =  < 0.001, ANOVA, n = 3) (Table 1). However, there was no difference in the absolute body wave amplitude between P. bicanaliculata or N. vexillosa (P = 0.533, ANOVA, n = 3). The smallest species, P. longicirrata exhibits only 1 full wave along its body length during swimming. The two larger species disaplyed multiple simultaneous waves over the length of the body during free-swimming with P. bicanaliculata having 2–3 and N. vexillosa having 5–7 complete waves.

Fluid properties

A traditional undulatory swimmer (e.g. lamprey) that uses only body bending, creates flow patterns where fluid moves in, towards the body at the wave trough and outwards, away from the body at the wave peak (Fig. 1). No sustained jets or reversing flow regions are observed at any point along the body and fluid exits behind the swimmer as distinct vortices with alternating sign with each tail beat.

Fig. 1
Fig. 1
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Representative flow fields during routine, steady-state swimming for a larval lamprey (Petromyzon marinus) at the create and trough of a body bend. Diagram shows the approximate location of each body bend. Scale bar shows fluid vector magnitude in mm s-1.

In the polychaete swimmers, parapodia perform the power stroke at the top of the body wave crest (Figs. 2, 3). The outward bending extends parapodia away from the body and aids in creating space between neighboring parapodia. This extension of parapodia away from the rest of the body combined with power strokes from neighboring parapodia as the body wave propagates, creates a jet that moves horizontally, parallel to the body, towards the tail (Figs. 2, 3). In P. longicirrata this results in peak jet speeds of approximately 60 mm s−1 while the larger P. bicanaliculata peak jet speeds reached 140 mm s−1 and were significantly higher (T-test, P > 0.001) than the jets of P. longicirrata. During the recovery stroke, parapodia move anteriorly in the body wave troughs and are closely clustered together (See Supplement Videos 1 and 2). The backward movement of the swimming appendages creates a reverse flow region within the body wave trough (Figs. 2, 3). This reverse flow region can exhibit flow magnitudes that match or even exceed that of the power stoke jet.

Fig. 2
Fig. 2
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Representative flow fields during the power stroke (left) and recovery stroke (right) for Pelagobia longicirrata. Diagram shows the approximate location of each stroke relative to the body bends. Scale bar shows fluid vector magnitude in mm s-1.

Fig. 3
Fig. 3
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Representative flow fields during the power stroke (left) and recovery stroke (right) for Platynereis bicanaliculata. Diagram shows the approximate location of each stroke relative to the body bends. Scale bar shows fluid vector magnitude in mm s-1.

As the body wave trough propagates anteriorly, the parapodia in the trough begin to transition to the wave crest. This is the initiation of the power stroke and it occurs while the parapodia are still located within the reverse flow region. Parapodia position relative to body bending is shown in Fig. 4. As the parapodia begin the power stroke, the movement of the appendage is opposite that of the fluid flow direction that surrounds it. This creates a strong negative pressure region on the upstream side of the parapodia with peak negative pressures of − 4 Pa (1.1 s.d.) (Fig. 5) which persists for the majority of the power stroke. Pressures were significantly lower in magnitude (absolute value) on downstream side compared to the upstream side with peaks of 0.4 Pa (s.d. 0.3) (T-test, P > 0.001). We can estimate the total force acting on a single propulsor (parapodia with attached setae) using the equation F = PA where, F is force in Newtons, P is the pressure and A is the propulsor area. Given that the propulsors had a mean length of 1.1 mm (s.d 0.2) and a width, 0.73 mm (s.d. 0.2) and using the pressure on both sides of the propulsor (with the assumption that pressure does not vary over the depth of the propulsor), we estimate that each propulsor can generate a peak force of 3.4 × 10–6 N.

Fig. 4
Fig. 4
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Relationship between propulsor position and body bending during a full stroke cycle for Pelagobia longicirrata. Red lines track a single parapodia as it progresses through a stroke cycle. Top row shows the power stroke and the bottom row shows the recovery stroke. Scale bar = 1 mm.

Fig. 5
Fig. 5
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Pressure field around a Pelagobia longicirrata parapodium at the onset of the power stroke. Scale bar shows pressure in Pa. White arrow indicates direction of swimming. Black arrow indicates direction of propulsor power stroke.

Discussion

Metachronal swimming is widespread in aquatic ecosystems and is employed by a diverse array of taxonomic groups. Likewise, undulating body waves are a common mode of locomotion for many aquatic taxa. However, to our knowledge the combined use of metachronal paddling with active body bending during swimming appears to be unique to polychaetes. To better understand this mechanism used by polychaetes for free-swimming, it is important to consider some of the characteristics of the swimming appendages themselves and how they compare to some of the other metachronal paddling taxa. Other metachronal swimmers, such as ctenophores, have highly flexible propulsors (fused cilia plates known as ctenes) which are capable of both long extension during the power stroke and a recovery stroke in which the propulsor slides closely along the body surface by propagating a sharp bend from base to tip14. This recovery stroke mechanism functions effectively to reduce drag and thus improve propulsive performance15. Crustaceans that swim via metachronal paddling use jointed appendages to create differential bending during power and recovery strokes to maximize thrust and minimize drag16. Polychaetes on the other hand, use the parapodia on each body segment for metachronal paddling2,7.

One of the main differences between polychaete appendages and those of other metachronal swimmers is that the parapodia appear much less flexible, particularly near the base of the appendages, where high amounts of bending are required for an active recovery stroke. Our measurements found maximum bending of 48 degrees (s.d. 8) during recovery strokes and the location of the bend remains fixed at 1/3 of the propulsor length from the tip. This is in sharp contrast to ctenophores where maximum bending of the propulsor reaches 110–140 degrees (extracted from Heimbichner Goebel, et al.17) and the location of bend the travels from base to tip. Crustaceans use their jointed appendages to achieve bending angles up to 90 degrees during fast swimming (from Fig. 4 in Murphy, et al.16). A low degree of bending articulation in an appendage, particularly near the base and mid-point, presents challenges for effective locomotion during metachronal paddling in polychaetes. This is where body bending can play an important role. Instead of folding the propulsive appendages with high bending angles to reduce drag, the limited bending in polychaete parapodia benefits from timing the recovery stroke to coincide with the trough of the body wave. This acts to dip the anteriorly moving parapodia during recovery strokes below the height of the posteriorly moving parapodia during power strokes (Figs. 2, 3). The result is minimal inference with the flows created during power strokes (Figs. 2, 3) which would aid in reducing drag. This also provides a mechanistic explanation for the need of the body wave to travel in the opposite direction (anteriorly) of other body wave generating swimmers. Since the metachronal wave is antiplectic, the body wave must also move in this same direction to ensure that parapodia performing a recovery stroke are always in the trough of the body wave.

It is also relevant to consider how the body waves and parapodia are controlled. Parapodial movements and body waves (i.e. S waves) occur simultaneously during free swimming, but body waves and parapodial motion can be separated by severing certain segmental nerves. For instance, severing segmental nerve IV which supplies the longitudinal muscles will cease body wave motion18. Conversely, experiments that severed the parapodial nerve, segmental nerve II, while leaving IV intact, resulted in the cessation of parapodial movements while body waves were not affected. There is also control across the body as the phase of parapodial movement is phase locked with one side of a segment 180° out of phase with that on the opposite side18. Previous work has shown that it takes between 14 and 20 body segments to comprise a full body wave and that is consistent with the results from this study.

While body bending permits the flow created by the recovery stroke to minimally interact with flows generated during the power stroke, this results in a persistent flow of considerable magnitude that moves anteriorly (Figs. 2, 3). These flows have similar magnitudes to that of the power stroke flows but the size of the reversing (anteriorly moving) flow region is small in comparison to power stroke flows. While pockets of flow reversal near the body are known to generate substantial drag in other swimmers19,20, it is feasible that partitioning the reversing flow from the freestream using body bending could reduce the impact on drag. There is some evidence to support this notion from experimental studies on dimples and depressions on surfaces in water channel experiments. For instance, it was found that depressions on a surface can promote anterior flows and streamwise vorticity in the depression while simultaneously stabilizing the flow above and reducing skin friction drag21. Thus, by generating the recovery stroke in the trough of the body wave, the impact on flow past the body may be minimized and skin friction drag would be reduced. However, Tay, et al.21 also found that pressure drag increases with increased depression size, which suggests a tradeoff in which depressions, or body bending amplitude, can only be so large before the increase in pressure drag overwhelms the benefit from the reduction in skin friction drag.

This study identified another potential benefit of creating a persistent anterior flow in a body bend when metachronal paddling. After completion of the recovery stroke, the subsequent power stroke begins. This power stroke initiates as the body wave transitions from wave trough the wave crest and thus begins within the anteriorly moving flow of the wave trough (Fig. 5). As the parapodium sweeps posteriorly, it moves in opposition to the flow surrounding it. This creates a strong negative pressure region on the upstream side of the propulsor while the downstream side experiences positive pressure (Fig. 5). The location of this negative pressure region is ideally located to generate forward thrust for the animal and the magnitude of the pressure field is beyond what has been observed in other metachronal paddlers6. Given that a pressure gradient across the propulsor dictates the force created by the propulsor12, the anteriorly propagating flow created during the recovery stroke in polychaetes appears to aid in the thrust generated in the subsequent power stroke.

Daniels, et al.7, identified that the presence of a body wave also benefits later in the power stroke by increasing the parapodium power stroke angle and extending the parapodia into undisturbed water adjacent to the body, thereby enhancing thrust. In this study we find that this extension, aided by the crest of the body wave, allows swimming appendages to maintain a continuous backwards propagating jet of fluid (Figs. 2, 3), similar to that of ctenophores6. Such flows oriented horizontally to the body are not found in swimmers that use only body bending (Fig. 1)11 nor is such a flow pattern found in mechanical bending foils22 and makes it clear that the metachronal paddling overwhelms any flow that is created from body bending.

The length of the appendages in the three species investigated varied by less than threefold despite the total body length varying by nearly 30-fold. In the smallest species, P. longicirrata, parapodia length was 22% of the total body length. In the largest species, P. bicanaliculata, parapodia length was only 2% of the total body length (Table 1). Might there be an effective limit beyond which longer parapodia do not provide a net propulsive benefit? As mentioned previously, increasing body bending amplitude would likely have the negative impact of increasing pressure drag. Thus, longer parapodia would necessitate larger body bends to prevent destabilizing the flow around the swimmer during recovery strokes and this may increase pressure drag to a point where metachronal paddling with body bending becomes less effective. This may also represent an explanation for why body wave amplitude varies minimally relative to body length between species (Table 1). Given the comparatively low variability in appendage length and body wave amplitude, absolute swimming speed using the polychaete mechanism appears to depend mostly on the wave speed and the number of simultaneous body waves present.

In summary, the unique nature of polychaete swimming kinematics, which combine both a metachronal and active body bending, could represent an adaptation to allow metachronal paddling with the constraint of low flexibility in the propulsive appendages. This may have important implications for bio-inspired design. There has been recent interest in engineering metachronal paddling systems for propulsion23,24,25 but designing a system with dozens of highly flexible and dynamic appendages is inherently difficult26. As a result, many engineered metachronal systems have been rigid27 or have limited bending articulation28. While these studies have advanced our knowledge of metachronal systems, employing a traveling body wave synced to appendage stoke timing as in polychaetes may offer a solution to some of the current problems and improve efficiency of existing designs.