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Published online by Cambridge University Press: 29 August 2018
While hydrodynamic interactions for aggregates of swimmers have received significant attention in the low Reynolds number realm ($Re\ll 1$), there has been far less work at higher Reynolds numbers, in which fluid and body inertia are involved. Here we study the collective behaviour of multiple self-propelled plates in tandem configurations, which are driven by harmonic flapping motions of identical frequency and amplitude. Both fast modes with compact configurations and slow modes with sparse configurations were observed. The Lighthill conjecture that orderly configurations may emerge passively from hydrodynamic interactions was verified on a larger scale with up to eight plates. The whole group may consist of subgroups and individuals with regular separations. Hydrodynamic forces experienced by the plates near their multiple equilibrium locations are all springlike restoring forces, which stabilize the orderly formation and maintain group cohesion. For the cruising speed of the whole group, the leading subgroup or individual plays the role of ‘leading goose’.
Dynamics of the orderly formation (Fast Mode "C3+1"). The initial gap spacing is G0=1. At the equilibrium state, the whole group with N=4 consists of a compact subgroup “C3” and an individual "1" following the subgroup.
Equilibrium state of the orderly formation (Fast Mode "C3+C2+1"). The initial gap spacing is G0=1. The whole group with N=6 consists of two compact subgroups “C3”, “C2” and an individual "1" following the subgroups.
Dynamics of the orderly formation (Slow Mode "S4"). The initial gap spacing is G0=3. At the equilibrium state, the sparse configuration emerges and the four plates are equally spaced with normalized gap spacing G/λ=1.
Equilibrium state of the orderly formation (Slow Mode "S6+S2"). The initial gap spacing is G0=3. The whole group with N=8 consists of two sparse subgroups “S6” and “S2”.