Efficient Swimming in Dense Schools: Effect of Formation and Synchronization on Hydrodynamic Interactions

Fish schools, as one of the most prevalent collective systems in nature, have been thought to provide hydrodynamic benefits to individual fish, supported by many laboratory experiments and field observations. However, accurate measurement and quantitative analysis of hydrodynamic interactions in a fish school are challenging and limited by experimental and numerical techniques, especially for a three-dimensional biological fish school. The underlying physical mechanisms are thus unclear, and no widely accepted theory has been put forward for decades. The lack of understanding of hydrodynamic interactions impedes the research of fish behavior and the design and control of bio-inspired underwater robotic swarms.
Motivated by this deficiency, we first develop a narrow-band level-set-based immersed boundary (NBLS-IB) reconstruction method and a tree-topological local mesh refinement (TLMR) method coupled with parallel computing on Cartesian grids to enable fast and high-fidelity simulations. Using these advanced numerical methods, two-dimensional (2D) and three-dimensional (3D) flow simulations are performed in an incompressible Navier-Stokes in-house solver to investigate hydrodynamic interactions in fish schools.
In the case of 2D studies, a NACA foil imposed on a traveling wave kinematics is employed to mimic 2D fish-like swimming. Simulations of 2D flow past dense diamond-shaped schools suggest that body–body and vortex–body interactions significantly enhance the hydrodynamic performance of individual fish. As the lateral fish diagonally positioned in a school approach the trailing fish, their thrust and efficiency increase. This results from the wall effect elucidated by 2P vortex wakes and angled momentum jets behind the lateral fish. The fluid drained by the leading fish is obstructed by the trailing fish, improving the performance of the leading fish. In the meantime, the trailing fish captures energy from the vortex flow generated by the lateral fish and produces a high suction thrust at the head through the body–body interaction with the lateral fish. Optimal thrust production and swimming efficiency can be achieved by adjusting the phase or tail-beat frequency. Flow visualizations suggest that the wake pattern strongly depends on the phase offset and the tail-beat frequency, which bridges the gap between the wake pattern and the performance of a dense school.
Thrust enhancement, power-saving, drag reduction and their combinations have been identified through 3D simulations of flow past biological fish bodies arranged in the horizontal and vertical planes. The block effect in an in-line school increases the thrust of the leading fish and is dependent on the streamwise distance. Caudal fin power is greatly saved in an in-phase side-by-side school through flow separation on the fin surface induced by the low-speed flow between the fins. In the anti-phase side-by-side school, thrust enhancement happens because of the virtual wall effect and passive-energy-capturing mechanisms. The small gap between two in-phase fish arranged in the vertical plane speeds up the cross-stream flow between the caudal fins and strengthens and stabilizes the leading-edge vortices (LEV), increasing thrust production. However, the constructive interaction can easily be deteriorated by the out-of-phase motion. In a staggered school, vortex rings with high momentum shed by the leading fish can enhance the leading-edge vortices on the caudal fin of the following fish and significantly increase its thrust by setting the streamwise distance or phase offset at the appropriate values. In the meantime, the drag of the following fish can be significantly reduced through the interaction between its body and vortex rings shed by the leading fish. Flow analyses reveal that the vortex rings reduce the drag by decreasing the streamwise velocity around the body of the following fish, which strongly depends on the evolution and advection of these vortex rings.