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1. Hybrid Metachronal Rowing Augments Swimming Speed and Acceleration via Increased Stroke Amplitude

   https://doi.org/10.1093/icb/icab141  

   Ford, Mitchell P; Ray, William J; DiLuca, Erika M; Patek, S N; Santhanakrishnan, Arvind (June 2021, Integrative and Comparative Biology)

   null (Ed.)

   Synopsis Numerous aquatic invertebrates use drag-based metachronal rowing for swimming, in which closely spaced appendages are oscillated starting from the posterior, with each appendage phase-shifted in time relative to its neighbor. Continuously swimming species such as Antarctic krill generally use “pure metachronal rowing” consisting of a metachronal power stroke and a metachronal recovery stroke, while burst swimming species such as many copepods and mantis shrimp typically use “hybrid metachronal rowing” consisting of a metachronal power stroke followed by a synchronous or nearly synchronous recovery stroke. Burst swimming organisms need to rapidly accelerate in order to capture prey and/or escape predation, and it is unknown whether hybrid metachronal rowing can augment acceleration and swimming speed compared to pure metachronal rowing. Simulations of rigid paddles undergoing simple harmonic motion showed that collisions between adjacent paddles restrict the maximum stroke amplitude for pure metachronal rowing. Hybrid metachronal rowing similar to that observed in mantis shrimp (Neogonodactylus bredini) permits oscillation at larger stroke amplitude while avoiding these collisions. We comparatively examined swimming speed, acceleration, and wake structure of pure and hybrid metachronal rowing strategies by using a self-propelling robot. Both swimming speed and peak acceleration of the robot increased with increasing stroke amplitude. Hybrid metachronal rowing permitted operation at larger stroke amplitude without collision of adjacent paddles on the robot, augmenting swimming speed and peak acceleration. Hybrid metachronal rowing generated a dispersed wake unlike narrower, downward-angled jets generated by pure metachronal rowing. Our findings suggest that burst swimming animals with small appendage spacing, such as copepods and mantis shrimp, can use hybrid metachronal rowing to generate large accelerations via increasing stroke amplitude without concern of appendage collision. 

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2. Hydrodynamics of Metachronal Motion: Effects of Spatial Asymmetry on the Flow Interaction Between Adjacent Appendages

   https://doi.org/10.1115/FEDSM2022-86967  

   Lou, Zhipeng; Herrera-Amaya, Adrian; Byron, Margaret L.; Li, Chengyu (August 2022, ASME 2022 Fluids Engineering Division Summer Meeting)

   Abstract Metachronal motion is a unique swimming strategy widely adopted by many small animals on the scale of microns up to several centimeters (e.g., ctenophores, copepods, krill, and shrimp). During propulsion, each evenly spaced appendage performs a propulsive stroke sequentially with a constant phaselag from its neighbor, forming a metachronal wave. To produce net thrust in the low-to-intermediate Reynolds number regime, where viscous forces are dominant, the beat cycle of a metachronal appendage must present significant spatial asymmetry between the power and recovery stroke. As the Reynolds number increases, the beat cycle is observed to change from high spatial asymmetry to lower spatial asymmetry. However, it is still unclear how the magnitude of spatial asymmetry can modify the shear layers near the tip of appendages and thus affect its associated hydrodynamic performance. In this study, ctenophores are used to investigate the hydrodynamics of multiple appendages performing a metachronal wave. Ctenophores swim using paddle-like ciliary structures (i.e., ctenes), which beat metachronally in rows circumscribing an ovoid body. Based on high-speed video recordings, we reconstruct the metachronal wave of ctenes for both a lower spatial asymmetry case and a higher spatial asymmetry case. An in-house immersed-boundary-method-based computational fluid dynamics solver is used to simulate the flow field and associated hydrodynamic performance. Our simulation results aim to provide fundamental fluid dynamic principles for guiding the design of bio-inspired miniaturized flexible robots swimming in the low-to-intermediate Reynolds number regime. 

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3. Closer Appendage Spacing Augments Metachronal Swimming Speed by Promoting Tip Vortex Interactions

   https://doi.org/10.1093/icb/icab112  

   Ford, Mitchell P; Santhanakrishnan, Arvind (May 2021, Integrative and Comparative Biology)

   null (Ed.)

   Abstract 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 nonzero 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 the metachronal motion only when the stroke amplitude is large. 

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4. Hydrodynamics of Metachronal Rowing at Intermediate Reynolds Numbers

   https://doi.org/10.1115/IMECE2023-112572  

   Lei, Menglong; Lou, Zhipeng; Wang, Junshi; Dong, Haibo; Li, Chengyu (October 2023, ASME 2023 International Mechanical Engineering Congress and Exposition)

   Abstract Metachronous rowing is a swimming mechanism widely adopted by small marine invertebrate like comb jellies, in which rows of appendages perform propulsive strokes sequentially in a coordinated manner with a fixed phase difference. To simulate metachronous rowing at intermediate Reynolds number, in this paper, a row of flexible cilia models was placed inside the flow field, with their roots stroke at a sinusoidal function of time and a fixed phase difference. A fully coupled two-way numerical solver was developed, which solves the Navier-Stokes equations for the fluid field coupled with the differential equation for the flexible cilia model. This numerical solver is applied to investigate how the row of cilia models are deformed by the hydrodynamic forces (pressure and shear) and momentum and thus impact hydrodynamic performance. Results show that the passive deformation of cilia potentially improve the hydrodynamic performance compared to the rigid cilia. With the metachronous rowing mechanism, the cilia generate the thrust to move forward. The approach used in this study presents a general way to explore the fluid dynamics of complex fluid-structure interaction problems. 

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5. Ctenophore swimming : understanding metachronal rowing at millimeter scales

   Herrera-Amaya, Adrian (June 2023, Penn State Libraries)

   The hydrodynamics of swimming at the millimeter-to-centimeter scale often present the challenge of having both viscous and inertial effects playing nontrivial roles. Inertial forces arise from the momentum of a moving fluid, while viscous forces come from friction within the flow. The non-dimensional Reynolds number (Re) compares the magnitudes of the inertial and viscous forces within a flow. At low Re (≪ 1), viscous forces dominate; at higher Re (≫ 1), inertial forces are more important. Efforts to understand the hydrodynamics of swimming have mainly focused on the extremes of fully viscous-dominated (Re ≪ 1) or inertia-dominated flow (Re ≫ 1). However, many animals swim in an intermediate regime, where inertia and viscosity are both significant. As an impactful and generalizable case study, we focus on ctenophores (comb jellies), a type of marine zooplankton. Ctenophores swim via the coordinated rowing of numerous highly flexible appendages (ctenes), with Reynolds numbers on the order of 10-100. Their locomotory dynamics present a unique opportunity to study the scaling of rowing (drag-based propulsion) across the low to intermediate Reynolds number range. With a combination of animal experiments, reduced-order analytical modeling, and physical-robotic modeling, we investigate how the kinematic and geometric variables of beating ctenes vary across Re, and how they affect swimming (including force production, speed, and maneuverability). Using animal experiments, we quantify the spatiotemporal asymmetry of beating ctenes across a wide range of animal sizes and Re. With our reduced-order model—the first to incorporate adequate formulations for the viscous-inertial nature of this regime—we explore the maneuverability and agility displayed by ctenophores, and show that by controlling the kinematics of their distributed appendages, ctenophores are capable of nearly omnidirectional swimming. Finally, we use a compliant robotic model that mimics ctenophore rowing kinematics to study rowing performance with direct calculation of thrust and lift forces distributed along the propulsor. These experiments shed new light on the relationship between motion asymmetries and thrust and lift production. This combination of animal experiments, analytical modeling, and physical modeling is the most detailed study of low to intermediate Re rowing to date, and provides a foundation for future applications in bio-inspired design. 

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