Fish schools are fascinating examples of macro-scale systems with collective behaviours. According to conventional wisdom, the establishment and maintenance of fish schools probably need very elaborate active control mechanisms. Sir James Lighthill posited that the orderly formations in fish schools may be an emergent feature of the system as a result of passive hydrodynamic interactions. Here, numerical simulations are performed to test Lighthill’s conjecture by studying the self-propelled locomotion of two, three and four fish-like swimmers. We report the emergent stable formations for a variety of configurations and examine the energy efficiency of each formation. The result of this work suggests that the presence of passive hydrodynamic interactions can significantly mitigate the control challenges in schooling. Moreover, our finding regarding energy efficiency also challenges the widespread idea in the fluid mechanics community that the diamond-shaped array is the most optimized pattern.

Numerical simulations are conducted to investigate the influences of a solid wall on the self-propelled swimming of a flexible plunging foil. It is found that the presence of a solid wall enhances the cruising speed, with the cost of increasing input power. Rigid foil can achieve high percentage increase in cruising speed when swimming near a solid wall, but the propulsive efficiency may be reduced. Foils with some flexibility can enjoy the enhancements in both cruising speed and propulsive efficiency. Another advantage of the flexible foils in near-wall swimming is that smaller averaged lateral forces are produced. The effects of wall confinement on the wake structure and the vortex dynamics are also studied in this paper. The results obtained in this study shed some light on the unsteady wall effect experienced by aquatic animals and also inform the design of bio-mimetic underwater vehicles which are capable of exploiting the wall effect.