How swimming style and schooling affect the hydrodynamics of two accelerating wavy hydrofoils

Fish schools can make frequent accelerations that are almost simultaneous. While schooling at constant speed is well studied, far less is known concerning accelerating fish school across various body caudal fin swimming styles. The present study investigates the effects of swimming styles and schooling on two accelerating wavy hydrofoils in a free stream flow at wavelengths λ=0.5−8, Strouhal number St=0.2−0.7, front–back distance D=0,0.25,0.5,0.75, phase difference ϕ/π=0,0.5,1,1.5, and lateral gap distance G=0.25,0.3,0.35 with fixed Reynolds number Re=5000 and maximum amplitude Amax=0.1. In total, 591 cases were simulated using open-source software IBAMR based on immersed boundary method. Low and high wavelengths correspond to advantageous propulsive efficiency and thrust, respectively. The highest group propulsive efficiency is obtained at low wavelength λ<1.2. At a side-by-side arrangement, the thrust upon the two foils can be equivalent across various wavelengths, indicating a synchronised acceleration. At staggered arrangement, the follower can take significant advantage of the leader in locomotion performance by tuning phase difference, especially at high wavelengths and close distances. Front–back distance is a key factor affecting the follower’s propulsive efficiency for short-wavelength swimmers, but not for long-wavelength ones. Various combinations of wavelength and relative distance can lead to distinct flow structures, indicating a tunable stealth capacity of the accelerating fish schools.