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Transient motion of a swimming sheet in the inertial regime

Published online by Cambridge University Press:  13 May 2025

Gaojin Li Open the ORCID record for Gaojin Li [Opens in a new window]
Gaojin Li*
Affiliation:
State Key Laboratory of Ocean Engineering, School of Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China
*
Corresponding author: Gaojin Li, gaojinli@sjtu.edu.cn
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Abstract

Undulatory swimming is among the most common swimming forms found in nature across various length scales. In this study, we analyse the inertial effects of both the fluid and the swimmer on the transient motion of undulatory swimming using Taylor’s waving sheet model. We derive the transient velocity of the sheet for combined longitudinal and transverse waves in the Laplace domain, identifying three contributions to the velocity: the ‘slip’ velocity, fluid convection and a hydrodynamic force contribution. By numerically inverting the Laplace transform, we obtain the time history of the velocity for swimmers with varying swimming parameters and initial configurations. The acceleration performance of two types of swimmers is analysed by considering three dimensionless parameters: the acceleration rate $1/T$, sheet mass $M$, and Reynolds number $Re$, representing the effects of unsteady, convective and swimmer inertia, respectively. Under a relatively strong inertia effect, the start-up time scales as $\sim TM^2\,Re$ and $\sim TM^2$ for longitudinal and transverse waving sheets, respectively. Under weak inertia effects, the start-up time approximately reaches a constant for longitudinal waves, while it scales as $\sim T$ for transverse waves. Additionally, the transverse waving may induce a velocity overshoot, and enhances the burst swimming performance.

JFM classification

Biological Fluid Dynamics: Propulsion Biological Fluid Dynamics: Swimming/flying

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JFM Papers
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Journal of Fluid Mechanics , Volume 1011 , 25 May 2025 , A2
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© The Author(s), 2025. Published by Cambridge University Press

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