In-phase and antiphase synchronization of undulatory swimmers in the inertial regime

Synchronized locomotion of undulatory swimmers occurs ubiquitously in nature, ranging from microorganisms such as sperms to larger aquatic animals such as eels and knifefish. To develop a unified understanding of this phenomenon, we use Taylor's two-dimensional infinitely long undulatory sheet model to study the side-by-side locomotion of two swimmers at nonzero Reynolds numbers. Our quasi-steady-state analysis of the far-field hydrodynamics demonstrates that fluid inertia causes the swimmers to reach a stable antiphase synchronized state. Numerical simulations confirm this result for two swimmers separated by a relatively large gap distance. However, when the distance falls below a critical value, the two swimmers settle into a stable in-phase state. The antiphase configuration increases the coswimming speed, the power expenditure, as well as the energy efficiency of both swimmers.