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    Fluid transport by flexible blades performing impulsive metachronal rowing

    Yu-Hang Xiong

    An-Kang Gao*

    Xi-Yun Lu

    Shaohua Chen†

    • *Contact author: ankanggao@ustc.edu.cn
    • †Contact author: shchen@bit.edu.cn

    Phys. Rev. Fluids 11, 054103 – Published 18 May, 2026

    DOI: https://doi.org/10.1103/5382-8y7t

    Abstract

    The transient flow induced by an array of wall-mounted flexible blades performing impulsive metachronal rowing, i.e., the sudden onset of coordinated oscillations of wall-mounted flexible blades with phase differences among them in an initially quiescent fluid, is numerically investigated across a wide range of the Cauchy number (Ca), which quantifies the ratio of fluid inertial to the blade elastic force. Two distinct flow regimes emerge depending on the ratio of the natural frequency (fn) to the rowing frequency (f). For stiff blades (fn>f), the mean deflection angle scales linearly with Ca, and the rescaled flow rate remains high. In contrast, for soft blades (fn<f), the deflection saturates, and the rescaled flow rate decays rapidly as Ca−2.35. The maximum fluid transport is achieved near Ca=1 and at shorter rowing wavelength (six blades per wavelength and unit spacing), where tip-shed concentrated vortices are (1) optimally positioned to reinforce the flow around power-stroke blades and (2) subsequently captured by those blades, thereby enhancing thrust. These findings provide physical insights into the hydrodynamic optimization principles underlying bio-inspired metachronal propulsion.

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