How wavelength affects the hydrodynamic performance of two accelerating mirror-symmetric slender swimmers

Fish schools can simultaneously accelerate during predator-prey interaction. Focusing on the representative problem, we numerically investigated how Reynolds number Re = 1000−2000, Strouhal number St = 0.2−0.7 and wavelength λ = 0.5−2 affects the mean net thrust and net propulsive efficiency of two side-by-side NACA0012 hydrofoils undulating in anti-phase. In total, 550 cases are simulated using the ConstraintIB module of the IBAMR open-source library. The thrust is strengthened by wavelength and Strouhal number, yet only slightly by the Reynolds number. We apply the symbolic regression tool PySR to formulate this relationship. We also found that mirror-symmetric schooling can achieve net thrust more than ten times that of a single swimmer, especially at low Reynolds number Re = 1000. The highest efficiency is obtained at St = 0.5 and λ = 1.1, coherently with BCF swimmers in the nature. Six distinct flow structures are identified. The highest thrust corresponds to an asymmetric flow pattern, whereas the highest efficiency occurs when the flow is symmetric with converging vortex streets.