Hydrodynamics of undulatory fish schooling in lateral configurations

Abstract

The thrust benefits of lateral configurations of two-dimensional undulating fish-like bodies are investigated using high-fidelity numerical simulation. The solution of the Navier--Stokes equations is carried out with a viscous vortex particle method. Configurations of tethered pairs of fish arranged side by side are studied by varying the lateral separation distance and relative phase difference. It is shown that, in mirroring symmetry, the fish in the pair augment each other's thrust even at relatively large separations (up to ten body lengths). At small distances, this augmentation is primarily brought about by a peristaltic pumping in the gap between the fish, whereas at larger distances, the thrust is affected by subtle changes in the vortex shedding at the tail due to interactions with the other fish. In cases without symmetric undulation, one fish always draws more benefit from the interaction than the other. Finally, lateral configurations with three fish are studied with mirroring symmetry between neighboring fish. Whereas the center fish draws a net thrust benefit, this comes at the expense of a net drag on the outer two fish. Each adjacent pair in this arrangement is slightly affected by the presence of the third fish.