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1. Swimming Through Parameter Subspaces of a Simple Anguilliform Swimmer

   https://doi.org/10.1093/icb/icaa130  

   Battista, Nicholas A (September 2020, Integrative and Comparative Biology)

   null (Ed.)

   Synopsis Computational scientists have investigated swimming performance across a multitude of different systems for decades. Most models depend on numerous model input parameters and performance is sensitive to those parameters. In this article, parameter subspaces are qualitatively identified in which there exists enhanced swimming performance for an idealized, simple swimming model that resembles a Caenorhabditis elegans, an organism that exhibits an anguilliform mode of locomotion. The computational model uses the immersed boundary method to solve the fluid-interaction system. The 1D swimmer propagates itself forward by dynamically changing its preferred body curvature. Observations indicate that the swimmer’s performance appears more sensitive to fluid scale and stroke frequency, rather than variations in the velocity and acceleration of either its upstroke or downstroke as a whole. Pareto-like optimal fronts were also identified within the data for the cost of transport and swimming speed. While this methodology allows one to locate robust parameter subspaces for desired performance in a straight-forward manner, it comes at the cost of simulating orders of magnitude more simulations than traditional fluid–structure interaction studies. 

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2. Reinforcement learning of a multi-link swimmer at low Reynolds numbers

   https://doi.org/10.1063/5.0140662  

   Qin, Ke; Zou, Zonghao; Zhu, Lailai; Pak, On Shun (March 2023, Physics of Fluids)

   The use of machine learning techniques in the development of microscopic swimmers has drawn considerable attention in recent years. In particular, reinforcement learning has been shown useful in enabling swimmers to learn effective propulsion strategies through its interactions with the surroundings. In this work, we apply a reinforcement learning approach to identify swimming gaits of a multi-link model swimmer. The swimmer consists of multiple rigid links connected serially with hinges, which can rotate freely to change the relative angles between neighboring links. Purcell [“Life at low Reynolds number,” Am. J. Phys. 45, 3 (1977)] demonstrated how the particular case of a three-link swimmer (now known as Purcell's swimmer) can perform a prescribed sequence of hinge rotation to generate self-propulsion in the absence of inertia. Here, without relying on any prior knowledge of low-Reynolds-number locomotion, we first demonstrate the use of reinforcement learning in identifying the classical swimming gaits of Purcell's swimmer for case of three links. We next examine the new swimming gaits acquired by the learning process as the number of links increases. We also consider the scenarios when only a single hinge is allowed to rotate at a time and when simultaneous rotation of multiple hinges is allowed. We contrast the difference in the locomotory gaits learned by the swimmers in these scenarios and discuss their propulsion performance. Taken together, our results demonstrate how a simple reinforcement learning technique can be applied to identify both classical and new swimming gaits at low Reynolds numbers. 

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3. Metachronal Swimming of Mantis Shrimp: Kinematics and Interpleopod Vortex Interactions

   https://doi.org/10.1093/icb/icab052  

   Garayev, Kuvvat; Murphy, David W (May 2021, Integrative and Comparative Biology)

   Abstract 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 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. 

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4. Enhanced clamshell swimming with asymmetric beating at low Reynolds number

   https://doi.org/10.1039/d2sm00292b  

   Hu, Shiyuan; Zhang, Jun; Shelley, Michael J. (May 2022, Soft Matter)

   A single flexible filament can be actuated to escape from the scallop theorem and generate net propulsion at low Reynolds number. In this work, we study the dynamics of a simple boundary-driven multi-filament swimmer, a two-arm clamshell actuated at the hinged point, using a nonlocal slender body approximation with hydrodynamic interactions. We first consider an elastic clamshell consisted of flexible filaments with intrinsic curvature, and then build segmental models consisted of rigid segments connected by different mechanical joints with different forms of response torques. The simplicity of the system allows us to fully explore the effect of various parameters on the swimming performance. Optimal included angles and elastoviscous numbers are identified. The segmental models capture the characteristic dynamics of the elastic clamshell. We further demonstrate how the swimming performance can be significantly enhanced by the asymmetric beating patterns induced by biased torques. 

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5. 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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