Stable formations of self-propelled fish-like swimmers induced by hydrodynamic interactions.

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.