TITLE:
Kinematic Characteristics and Drag Reduction of a Flexible Filament behind a Flapping Foil
AUTHORS:
Jialin Yu, Guoyi He, Jianyu Xing
KEYWORDS:
Self-Propulsion, Flexible Filament, Kármán Vortices, Strouhal Number, Drag Reduction, Fluid-Structure Interaction
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.4,
April
20,
2026
ABSTRACT: Fish self-propulsion and schooling behavior are governed by fluid-structure interaction (FSI) within vortex wakes. This study numerically investigates the kinematics of a fully free flexible filament in flapping foil-generated Kármán and reversed-Kármán vortex streets using the immersed boundary method, and explores its drag reduction effect on the upstream foil. The foil simulates a leading fish tail, while the filament represents a passive follower fish. Systematic simulations were conducted across Reynolds numbers Re = 50~300, varying flapping frequencies (f) and amplitudes (A). Results indicate that under the tested parameters, the filament could not achieve forward self-propulsion in the Kármán vortex street and instead moved backward. Re significantly modulated the filament’s motion amplitude and stability, with only Re = 150 showing clear periodicity; low flapping frequency f = 0.3 and vortex street center offset were identified as core factors limiting propulsion. Additionally, the filament exhibited a notable drag reduction effect on the flapping foil, which was negatively correlated with frequency—optimal drag reduction occurred at f = 1.5 due to effective vortex regulation, while vertical amplitude A had a negligible impact. This work elucidates the FSI mechanism between flexible filaments and flapping foil wakes, providing insights for bio-inspired underwater propulsion design.