Numerical investigation on the swimming mode and stable spacing with two self-propelled fish arranged in tandem

It is a long-held perception that fish may obtain a hydrodynamic advantage from clustering. This study attempts to determine whether all the fish in school gain the same energy advantage in different swimming modes. The numerical investigation based on two self-propelled fish arranged in tandem in carangiform, anguilliform, and sine curve swimming modes was conducted. It was found that fish could spontaneously form different steadily spaced queues, and discrete points of stable spacing were classified as proximity and wake interference points according to their swimming speed. The stable points were the result of the combined effect of wake impact and vortex modulation. From the carangiform to anguilliform to sine curve swimming modes, as the head amplitude increased, the vortex modulation of the rear fish gradually decreased, while the wake impact gradually increased. Therefore, the rear fish in carangiform swimming mode had lower energy consumption than that of the front, whereas the opposite was true in sine curve swimming mode. In addition, some interesting phenomena related to the vortex core arrangement were introduced at different stable points in these three swimming modes. The present results may enrich the scope of research on the hydrodynamic dominance of aquatic organisms in collective behaviour.