The hydrodynamic interactions involved in the self-organisation phenomenon in biological systems are not fully understood and have attracted significant attention. A previous study (Peng et al. 2018 J. Fluid Mech. , vol. 853, pp. 587–600) found that, arranged in an unbounded fluid, the largest cluster of self-propelled bodies in tandem, capable of spontaneously forming an ordered configuration, consists of eight swimmers. Here, we numerically investigate the collective behaviour of multiple self-propelled plates in tandem within a channel of width H, confined by two parallel walls. These plates are driven by harmonic flapping motions of uniform frequency and amplitude. Results demonstrate for the first time that the channel confinement significantly enhances group cohesion, with up to 72 individuals self-organising into ordered configurations at an optimal channel width. We observe two stable configurations: a hybrid mode with subgroups (typically at smaller channel widths) and a regular mode with sparse configuration. In large regular-mode groups, the vortex fields downstream exhibit spatial periodicity, conforming to Rosenhead’s stability criterion for confined vortex streets (vortex spacing Lₕ₎ₑ 1. 419H). This theoretical alignment explains both the observed upper channel-width limit (H 4. 0-4. 5) for large-scale cohesion and the robust order in the regular mode. The plates may adopt spontaneously a ‘vortex-slalom’ path, reducing the drag force and energy consumption while maximising stability. Deviation from this path results in a spring-like restoring force, promptly returning the plate to equilibrium.
Kang et al. (Tue,) studied this question.