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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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Ctenophore swimming : understanding metachronal rowing at millimeter scales
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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- Award ID(s):
- 2120689
- PAR ID:
- 10638771
- Publisher / Repository:
- Penn State Libraries
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Metachronal rowing is a biological propulsion mechanism employed by many swimming invertebrates (e.g. copepods, ctenophores, krill and shrimp). Animals that swim using this mechanism feature rows of appendages that oscillate in a coordinated wave. In this study, we used observations of a swimming ctenophore (comb jelly) to examine the hydrodynamic performance and vortex dynamics associated with metachronal rowing. We first reconstructed the beating kinematics of ctenophore appendages based on a high-speed video of a metachronally coordinated row. Following the reconstruction, two numerical models were developed and simulated using an in-house immersed-boundary-method-based computational fluid dynamics solver. The two models included the original geometry (16 appendages in a row) and a sparse geometry (8 appendages, formed by removing every other appendage along the row). We found that appendage tip vortex interactions contribute to hydrodynamic performance via a vortex-weakening mechanism. Through this mechanism, appendage tip vortices are significantly weakened during the drag-producing recovery stroke. As a result, the swimming ctenophore produces less overall drag, and its thrust-to-power ratio is significantly improved (up to 55.0 % compared with the sparse model). Our parametric study indicated that such a propulsion enhancement mechanism is less effective at higher Reynolds numbers. Simulations were also used to investigate the effects of substrate curvature on the unsteady hydrodynamics. Our results illustrated that, compared with a flat substrate, arranging appendages on a curved substrate can boost the overall thrust generation by up to 29.5 %. These findings provide new insights into the fluid dynamic principles of propulsion enhancement underlying metachronal rowing.more » « less
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