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Propulsion of a flexible foil in a wavy flow: resonance, antiresonance and destructive self-interference

Published online by Cambridge University Press:  14 November 2025

Abdur Rehman Open the ORCID record for Abdur Rehman [Opens in a new window]  and
Daniel Floryan Open the ORCID record for Daniel Floryan [Opens in a new window]
Abdur Rehman*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Houston , Houston, TX 77204, USA
Daniel Floryan*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Houston , Houston, TX 77204, USA
*
Corresponding authors: Abdur Rehman, abdurrehman.92@gmail.com; Daniel Floryan, dfloryan@uh.edu
Corresponding authors: Abdur Rehman, abdurrehman.92@gmail.com; Daniel Floryan, dfloryan@uh.edu
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Abstract

Swimming and flying animals demonstrate remarkable adaptations to diverse flow conditions in their environments. In this study, we aim to advance the fundamental understanding of the interaction between flexible bodies and heterogeneous flow conditions. We develop a linear inviscid model of an elastically mounted foil that passively pitches in response to a prescribed heaving motion and an incoming flow that consists of a travelling wave disturbance superposed on a uniform flow. In addition to the well-known resonant response, the wavy flow induces an antiresonant response for non-dimensional phase velocities near unity due to the emergence of non-circulatory forces that oppose circulatory forces. We also find that the wavy flow destructively interferes with itself, effectively rendering the foil a low-pass filter. The net result is that the waviness of the flow always improves thrust and efficiency when the wavy flow is of a different frequency than the prescribed heaving motion. Such a simple statement cannot be made when the wavy flow and heaving motion have the same frequency. Depending on the wavenumber and relative phase, the two may work in concert or in opposition, but they do open the possibility of simultaneous propulsion and net energy extraction from the flow, which, according to our model, is impossible in a uniform flow.

JFM classification

Aerodynamics: Flow-structure interactions Biological Fluid Dynamics: Propulsion Biological Fluid Dynamics: Swimming/flying

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1023 , 25 November 2025 , A11
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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