How phase synchrony affects the stable equilibrium of two free swimming pitching foils*

Aquatic animals swim efficiently in different schooling formations, with different spacing and phase synchrony. For a simplified two-dimensional pitching foil with out-of-phase synchrony, Kurt et al.(2019 JFM, 2022 Arxiv) show the existence of an equilibrium position, which can be tuned with change in reduced frequency(k) and Strouhal number(St). Following these findings and by using two free-swimming pure pitching foils, we present new simulations to examine the effect of phase synchrony on the equilibrium position and performance. We further examine how variations in Lighthill number, reduced frequency, and Strouhal number also play a role.  These results are relevant in biology and the development of bio-inspired underwater vehicles.