Collective locomotion of two self-propelled flapping plates with different propulsive capacities.

The role of the hydrodynamic effect in the collective locomotion of several birds or fish is an interesting topic. Taking a model of a self-propelled flapping plate, we numerically investigated the collective locomotion of a pair of plates with comparable but different propulsive capacities, e.g., one long and one short plates. The longer plate is supposed to have a stronger propulsive capacity. It is found that two typical equilibrium configurations, i.e., compact and sparse configurations, may emerge, which depend mainly on initial lateral and longitudinal gap spacing, i.e., H and G0, respectively. In the compact cases, when H is small, e.g., H < 0.6, in terms of cruising speed and efficiency, hydrodynamic advantages are found for both plates. In all sparse configurations, the propulsive performance of the leading plate is identical to that of the corresponding isolated one. The following short plate in the "long-short" (the longer in the front) sparse cases always takes hydrodynamic advantages in terms of cruising speed and efficiency. In the "short-long" (the shorter in the front) sparse cases, the follower's propulsive capacity is suppressed because the cruising speed and input power decrease significantly compared to its isolated case. The analyses of hydrodynamic force and corresponding potential energy show that the staggered sparse configuration with H ∈ (0.4, 1.0) is more stable than that with other H. The "hydrodynamic drafting" analyzed here may shed some light on understanding the coordinated collective behaviors in biological and natural systems. [ABSTRACT FROM AUTHOR]