Numerical investigation on energetically advantageous formations and swimming modes using two self-propelled fish

Abstract

Fish schooling is a common phenomenon that is assumed to have energy advantages, and various fish schooling configurations have been observed. However, the underlying mechanism of fish schooling remains an open question. To understand the relationship between energetically advantageous formations and swimming modes, we numerically investigated two self-propelled fish at different initial spacings. Stable beneficial formations were classified into three types, based on the benefiting individuals. The analysis focused on the intrinsic mechanisms of individual benefit for the three types of energetically beneficial formations in terms of the swimming performance, velocity clouds, and vortex evolution. For the first type, both fish benefited from parallel formations as the carangiform swimming mode promoted fluid flow and reduced lateral power because of the channel effect. For the second type, the front fish gained an efficiency advantage from pressure and vortex mechanisms, while the rear fish was almost indistinguishable from the swimming-alone condition in the sinusoidal and anguilliform swimming modes. For the last type, similar to the tandem queue, the rear fish modulated the vortex and gained an energy advantage in the carangiform and anguilliform swimming modes. This study provides new insights into the appropriate configuration of fish for different swimming modes in nature.