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Abstract Ctenophores employ flexible rows of appendages called ctenes that form the metachronal beating pattern. A complete cycle of such paddling consists of a power stroke that strokes backward to produce propulsion and a recovery stroke that allows the appendage to recover its initial position. Effective locomotion in these creatures relies on maximizing propulsion during the power stroke while minimizing drag in the recovery stroke. Unlike rigid oars, the ctenes are flexible during both the power stroke and the recovery stroke, and notably, their strokes are asymmetric, with faster movement during the power stroke. As previous research assumed uniform material properties. This assumption will eventually make the ctene deform more intensively in the power stroke than the recovery stroke due to the asymmetrical hydrodynamic forces. However, observations contradict these assumptions. One explanation posits that ctenes stiffen during the power stroke, enhancing their propulsive force, and become more flexible in the recovery stroke, reducing drag by minimizing the water-countering area. This study focusses on the influence of asymmetric stiffness on their propulsion mechanism. Inspired by nature, we conducted three-dimensional fluid-structure interaction (FSI) using an in-house immersed-boundary-method-based flow solver integrated with a nonlinear finite-element solid-mechanics solver. This integrated solver uses a two-way coupling that ensures a higher accuracy regarding the complexity due to the involvement of the multiple ctenes in a ctene row. The preliminary results show that the anisotropic stiffness of the ctene have better accuracy of deformation as compared to the deformation recorded by the high-speed camera. The asymmetric properties of the ctene material allow both the spatial and temporal asymmetry of the ctene beating pattern. Our investigation suggests that while symmetrical beating can only generate negative net thrust, a slightly asymmetrical beating can make the thrust positive. We find that power stroke period that cost 30% whole period can generates the highest thrust. As multiple ctenes involves, the interaction among ctenes can amplified the effects of the asymmetrical beating, so that the thrust generation is enhanced by 9 to 13 times because of it.
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This content will become publicly available on November 17, 2025
Fluid-Structure Interaction Analysis of Metachronal Propulsion at Intermediate Reynolds Numbers
Abstract Ctenophores swim using flexible rows of appendages called ctenes that form the metachronal paddling. To generate propulsion, each appendage operates a power stroke that strokes backward, followed by a recovery stroke that allows the appendage to readjust its position. Notably, strokes of most metachronal swimmers are asymmetric, with faster power strokes while slower recovery strokes. Previously, the material properties are assumed as isotropic. So, the faster power stoke will lead to more pronounce deformation and the slower recovery stroke will lead to less deformation. However, this contradicts with the observations that power-stroking ctenes have the least deformation and recover deforms more, indicating an anisotropic material behavior. Such anisotropic material is hard to be manufactured, but the anisotropic behavior may be achieved by making the initial structural shape curved. The pre-curved ctene, that bending towards downstream, will be straighten in power stoke while easy to bend during recovery stroke. Our study aims to demonstrate the feasibility of using pre-curved shapes to achieve anisotropic material properties during metachronal swimming. Treating it as fluid-structure interaction (FSI) problem, we integrate our in-house computational fluid dynamics (CFD) solver with a finite element method (FEM) solver, utilizing strong coupling methods for convergence. By comparing the performance of pre-curved ctenes with straight ones, which represent isotropic material properties, we found that the curved ctenes exhibited 26.05% to 65.69% higher cycle-averaged thrust compared to the straight one as stiffness is lower. However, as stiffness increased, the pre-curved ctenes produced 3.92% to 30.58% less thrust than the straight ones. Similar trends were observed in propulsive efficiency, with the pre-curved ctenes demonstrating 46.97% better efficiency at the lowest stiffness but dropping to 34.02% less efficient as stiffness rise. Thus, while the pre-curved initial shape led to better performance at lower stiffness, exceeding a certain stiffness threshold resulted in worse performance compared to straight ctenes. The thrust enhancement from pre-curve shape is due to the drag reduction during recovery stroke, where the curved shape mitigate part of force to point more downward.
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- PAR ID:
- 10613165
- Publisher / Repository:
- American Society of Mechanical Engineers
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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