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    Wake deflection and propulsive performance of intermittently flapping foil

    Bowen Jin1,2, Jiadong Wang2, and Jian Deng2,*

    • 1Huanjiang Laboratory, Zhejiang University, Zhuji 311899, People's Republic of China
    • 2State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Mechanics, Zhejiang University, Hangzhou 310027, People's Republic of China

    • *Contact author: zjudengjian@zju.edu.cn

    Phys. Rev. Fluids 11, 034701 – Published 13 March, 2026

    DOI: https://doi.org/10.1103/wdb2-8fz1

    Abstract

    This study explores the swimming behavior and hydrodynamics of an unconstrained, intermittently pitching foil using two-dimensional numerical simulations over a broad range of kinematic parameters. In contrast to continuous swimming, intermittent motion, characterized by alternating periods of active propulsion and passive gliding, achieves higher energy efficiency, but induces substantial trajectory deflection. The swimmer develops a nonzero lateral velocity, leading to a path deviation whose direction is sensitively dependent on the pitching amplitude and duty cycle. A sharp transition in the deflection angle is observed as the amplitude increases, with a reversal in the deflection direction occurring near a critical amplitude. Linear scaling between the flapping and propulsive Reynolds numbers is identified, underscoring the dominant influence of the Strouhal number on propulsive performance. In addition, the wake structures of the intermittent swimmer vary significantly with the flapping parameters. Different vortex modes emerge during the burst and coast phases, and their alignment plays a key role in determining the stability of the trajectory direction. These findings provide insights into the hydrodynamic principles of intermittent locomotion and its advantages in propulsion efficiency.

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