Unraveling hydrodynamic interactions in fish schools: A three-dimensional computational study of in-line and side-by-side configurations

We numerically investigate the hydrodynamic interactions between a pair of three-dimensional (3D) fish-like bodies arranged in both in-line and side-by-side configurations. The morphology and kinematics of these fish-like bodies are modeled on a live rainbow trout (Oncorhynchus mykiss) observed during steady swimming in the laboratory. An immersed-boundary-method-based incompressible Navier-Stokes flow solver is employed to capture the flow dynamics around the fish-like bodies accurately. Our findings indicate that hydrodynamic performance of individual fish in both arrangements is influenced by their spatial separation when in close proximity as well as by the relative phase difference between the two fish. In the case of in-phase in-line schools, the leading fish experiences up to 5.3 % increase in propulsive efficiency, attributed to the water blockage effect caused by the following fish. In comparison, the following fish experiences an increase in drag and power consumption along its body. Detailed analysis reveals that this rise in drag primarily results from an increase in friction drag ( 89 % ), driven by the amplified velocity field around the fish's body. Furthermore, altering the phase difference between the fish can help reduce pressure drag on the following fish by affecting the interaction between incoming vortex rings and its trunk. In side-by-side schools with in-phase swimming, a reduction of 6.8 % in power consumption on the caudal fin is achieved for each fish when the transverse distance is maintained at 0.25 body lengths. Flow analysis reveals that the decrease in power usage is attributed to a diminished velocity field between the caudal fins, facilitating flow separation and subsequently reducing energy expenditure required for generating comparative thrust. For the out-of-phase swimming, the side-by-side school system experiences enhanced thrust production, owing to a wake energy recapture mechanism. The degree of enhancement varies for each fish and is determined by the specific phase difference. These insights obtained from our study hold the potential to inform the design and navigation strategies of underwater robotic swarms.