A Computational Study of In-Phase and Anti-Phase Interactions of Fish in a Phalanx School

Biological studies have shown that schooling behavior benefits fish's swimming performance. Particularly, side-by-side, or phalanx, formation, combined with the synchronization of undulation of the neighbors, was shown to allow the group to sustain fast incoming flow. In this work, the hydrodynamic interactions between neighbors in a phalanx school are studied through three-dimensional (3D) flow simulation. Trout-like computational models, composed of trunk (TK), caudal fin (CF), and median dorsal and anal fins (DF and AF), are used with undulatory kinematics prescribed using a traveling-wave equation. An immersed-boundary method direct numerical simulation code is used. Three trout-like models are arranged in a dense phalanx formation so that the middle fish would interact strongly with both its neighbor. The undulation of all the fish are synchronized, with the middle fish undulating either in phase or completely out of phase with its two neighbors, to examine the hydrodynamic interaction in a phalanx school in both in-phase and anti-phase modes. Results show significantly enhanced thrust though at the cost of slightly increased power consumption through anti-phase interaction, which enhanced the 3D pressure fields and momentum of the flow around neighboring CF. The wake of each fish also interacted strongly, producing expanding vortex rings and enhanced wake jets. The addition of median fins to the school additional enhanced the caudal-fin thrust through fin–fin interaction.