Vortex dynamics in wake–body and wake-fin interactions of tuna-like staggered swimming

Fish across many species share similar schooling behavior in which abundance flow interactions occur with hydrodynamic advantages from the vortex flow shed by the conspecifics. This study investigates the mechanisms of schooling interactions in thunniform swimmers, focusing on body effects, using high-fidelity three-dimensional direct numerical simulations of a pair of closely swimming tuna-like models with realistic body morphology and swimming kinematics. An in-house immerse-boundary-method-based incompressible Navier–Stokes flow solver is employed to resolve near-body vortex topology, and the results are analyzed in detail. The interaction mechanism is evaluated by varying the streamwise distance in the stagger formation from 0 to 1 body length (BL) in increments of 0.1 BL, and by introducing tailbeat phase differences at the optimal streamwise spacing, ranging from 0 ° to 360 ° in 45 ° increments. Results identify an optimal streamwise distance of 0.5 BL, where the following fish achieve enhanced forward force production and propulsive efficiency. Notably, the following fish benefits from improved performance across all tailbeat phase differences, as the wake-fin interaction remains robust for its thrust enhancement. Flow analysis reveals that the vortex interception contributes to a 16% thrust improvement on the in-phase follower, while its drag reduction results from a combination of constructive pressure field interactions generating strong anterior suction and wake–body interactions producing forward force on the posterior body. These effects are amplified by tailbeat phase differences, with a 270 ° phase difference yielding a 19% drag reduction on the following fish and 180 ° enabling constant drag reduction throughout the motion cycle. This study highlights the enhanced swimming performance of closely paired tuna-like swimmers and identifies interaction mechanisms, offering valuable insights into the hydrodynamics of fish schooling and potential applications in underwater robotics.