  We present new experiments and free-swimming simulations of a pair of
pitching hydrofoils interacting in a simple school. The hydrofoils have an
out-of-phase synchronization and their arrangement is varied from in-line to
side-by-side arrangements through a series of staggered arrangements
representing the two-dimensional interaction plane. It is discovered that there
is a two-dimensionally stable equilibrium point for a side-by-side arrangement.
In fact, this arrangement is super-stable meaning that hydrodynamic forces will
passively maintain this arrangement even under external perturbations and the
school as a whole has no net forces acting on, drifting it to one side or the
other. Moreover, previously discovered one-dimensionally stable equilibria
driven by wake vortex interactions are shown to be, in fact, two-dimensionally
unstable, at least for an out-of-phase synchronization. Additionally, the
stable equilibrium arrangement is verified for freely-swimming foils undergoing
dynamic recoil motions. When constrained, the swimmers experience a collective
thrust and efficiency increase up to 100% and 40%, respectively, in a
side-by-side arrangement. However, in a staggered arrangement where there is
direct vortex impingement on a follower, an even higher efficiency improvement
of 87% is observed, which is coupled with a 94% increase in the thrust. For
freely-swimming foils, the recoil motion attenuates the performance
improvements showing a more modest speed and efficiency enhancement of up to 9%
and 6%, respectively, when the swimmers are at their stable equilibrium. These
newfound schooling performance and stability characteristics suggest that
fluid-mediated equilibria may play a role in the control strategies of
schooling fish and fish-inspired robots.
