On the role of phase lag in multi-appendage metachronal swimming of euphausiids

Metachronal paddling is a common method of drag-based aquatic propulsion, in which a series of swimming appendages are oscillated, with the motion of each appendage phase-shifted relative to the neighboring appendages. Ecologically and economically important euphausiid species such as Antarctic krill (Euphausia superba) swim constantly by stroking their paddling appendages (pleopods), with locomotion accounting for the bulk of their metabolic expenditure. They tailor their swimming gaits for behavioral and energetic needs by changing pleopod kinematics. The functional importance of inter-pleopod phase lag (ϕ) to metachronal swimming performance and wake structure is unknown. To examine this relation, we developed a geometrically and dynamically scaled robot ('krillbot') capable of self-propulsion. Krillbot pleopods were prescribed to mimic published kinematics of fast-forward swimming (FFW) and hovering (HOV) gaits ofE. superba, and the Reynolds number and Strouhal number of the krillbot matched well with those calculated for freely-swimmingE. superba. In addition to examining published kinematics with unevenϕbetween pleopod pairs, we modifiedE. superbakinematics to uniformly varyϕfrom 0% to 50% of the cycle. Swimming speed and thrust were largest for FFW withϕbetween 15%-25%, coincident withϕrange observed in FFW gait ofE. superba. In contrast to synchronous rowing (ϕ= 0%) where distances between hinged joints of adjacent pleopods were nearly constant throughout the cycle, metachronal rowing (ϕ> 0%) brought adjacent pleopods closer together and moved them farther apart. This factor minimized body position fluctuation and augmented metachronal swimming speed. Though swimming speed was lowest for HOV, a ventrally angled downward jet was generated that can assist with weight support during feeding. In summary, our findings show that inter-appendage phase lag can drastically alter both metachronal swimming speed and the large-scale wake structure.

Metachronal Coordination of Multiple Appendages for Swimming and Pumping

As a strategy for creating fluid flow, metachronal motion is widespread across sizes and species, including a broad array of morphologies, length scales, and coordination patterns. Because of this great diversity, it has not generally been viewed holistically: the study of metachrony for swimming and pumping has historically been taxonomically siloed, in spite of many commonalities between seemingly disparate organisms. The goal of the present symposium was to bring together individuals from different backgrounds, all of whom have made substantial individual contributions to our understanding of the fluid dynamics of metachronal motion. Because these problems share a common physical-mathematical basis, intentionally connecting this community is likely to yield future collaborations and significant scientific discovery. Here, we briefly introduce the concept of metachronal motion, present the benefits of creating a research network based on the common aspects of metachrony across biological systems, and outline the contributions to the symposium.

Closer appendage spacing augments metachronal swimming speed by promoting tip vortex interactions

Numerous species of aquatic invertebrates, including crustaceans, swim by oscillating multiple closely spaced appendages. The coordinated, out-of-phase motion of these appendages, known as "metachronal paddling", has been well-established to improve swimming performance relative to synchronous paddling. Invertebrates employing this propulsion strategy cover a wide range of body sizes and shapes, but the ratio of appendage spacing (G) to the appendage length (L) has been reported to lie in a comparatively narrow range of 0.2 < G/L ≤ 0.65. The functional role of G/L on metachronal swimming performance is unknown. We hypothesized that for a given Reynolds number and stroke amplitude, hydrodynamic interactions promoted by metachronal stroke kinematics with small G/L can increase forward swimming speed. We used a dynamically scaled self-propelling robot to comparatively examine swimming performance and wake development of metachronal and synchronous paddling under varying G/L, phase lag, and stroke amplitude. G/L was varied from 0.4 to 1.5, with the expectation that when G/L is large, there should be no performance difference between metachronal and synchronous paddling due to a lack of interaction between vortices that form on the appendages. Metachronal stroking at non-zero phase lag with G/L in the biological range produced faster swimming speeds than synchronous stroking. As G/L increased and as stroke amplitude decreased, the influence of phase lag on the swimming speed of the robot was reduced. For smaller G/L, vortex interactions between adjacent appendages generated a horizontally-oriented wake and increased momentum fluxes relative to larger G/L, which contributed to increasing swimming speed. We find that while metachronal motion augments swimming performance for closely spaced appendages (G/L < 1), moderately spaced appendages (1.0 ≤ G/L ≤ 1.5) can benefit from metachronal motion only when the stroke amplitude is large.

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. Lastly, 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.

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 mm 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.

Lagrangian approach to understanding the origin of the gill-kinematics switch in mayfly nymphs

The mayfly nymph breathes under water through an oscillating array of plate-shaped tracheal gills. As the nymph grows, the kinematics of these gills change abruptly from rowing to flapping. The classical fluid dynamics approach to consider the mayfly nymph as a pumping device fails in giving clear reasons for this switch. In order to shed some light on this switch between the two distinct kinematics, we analyze the problem under a Lagrangian viewpoint. We consider that a good Lagrangian transport that effectively distributes and stirs water and dissolved oxygen between and around the gills is the main goal of the gill motion. Using this Lagrangian approach, we are able to provide possible reasons behind the observed switch from rowing to flapping. More precisely, we conduct a series of in silico mayfly nymph experiments, where body shape, as well as gill shapes, structures, and kinematics are matched to those from in vivo. In this paper, we show both qualitatively and quantitatively how the change of kinematics enables better attraction, confinement, and stirring of water charged of dissolved oxygen inside the gills area. We reveal the attracting barriers to transport, i.e., attracting Lagrangian coherent structures, that form the transport skeleton between and around the gills. In addition, we quantify how well the fluid particles are stirred inside the gills area, which by extension leads us to conclude that it will increase the proneness of molecules of dissolved oxygen to be close enough to the gills for extraction.

Dietary (periphyton) and aqueous Zn bioaccumulation dynamics in the mayfly Centroptilum triangulifer

Diet is often the predominant route of trace metal exposure in aquatic insects. In freshwater ecosystems, periphyton serves as a primary source of food to many aquatic insects and is a major sink for trace metals. We investigated the bioconcentration of the essential metal Zn by periphyton using (65)Zn as a radiotracer. At relatively low dissolved concentrations (2-20 μg L(-1)), non steady state Zn bioconcentration by periphyton averaged 6,099 ± 2,430-fold, with much of the variability determined by loading regime (number of renewals and duration of exposures). Labeled periphyton was used as a food source for dietary accumulation studies with the mayfly Centroptilum triangulifer. After 29 days, larvae concentrated Zn 19-, 16- and 17-fold relative to dietary Zn concentrations of 8.1, 43.2 and 82.3 μg g(-1) (dry weight), respectively. Adults from that same cohort only concentrated Zn 8-, 3- and 3- fold relative to those same dietary concentrations, revealing that mayflies lose significant Zn prior to reaching adulthood. Anecdotal evidence suggests that this loss occurs prior to emergence to the subimago, as negligible Zn was found in the subimago to imago exuvium. Across a range of adult tissue concentrations, maternal transfer consistently averaged 26.7 %. Uptake (k(u), 0.26 L g(-1 )d(-1)) and efflux rate constants (k(e), 0.001-0.007 d(-1)) were measured and assimilation efficiencies from dietary Zn concentrations of 4.9 and 59.7 μg Zn g(-1) were estimated to be 88 ± 4 % and 64 ± 15 %, respectively. Both life cycle and biodynamic modeling approaches point towards diet being the primary route of Zn bioaccumulation in this mayfly.