Experiments and computations are presented for a foil pitching about its leading edge near a planar, solid boundary. The foil is examined when it is constrained in space and when it is unconstrained or freely swimming in the cross-stream direction. It was found that the foil has stable equilibrium altitudes: the time-averaged lift is zero at certain altitudes and acts to return the foil to these equilibria. These stable equilibrium altitudes exist for both constrained and freely swimming foils and are independent of the initial conditions of the foil. In all cases, the equilibrium altitudes move farther from the ground when the Strouhal number is increased or the reduced frequency is decreased. Potential flow simulations predict the equilibrium altitudes to within 3 %–11 %, indicating that the equilibrium altitudes are primarily due to inviscid mechanisms. In fact, it is determined that stable equilibrium altitudes arise from an interplay among three time-averaged forces: a negative jet deflection circulatory force, a positive quasistatic circulatory force and a negative added mass force. At equilibrium, the foil exhibits a deflected wake and experiences a thrust enhancement of 4 %–17 % with no penalty in efficiency as compared to a pitching foil far from the ground. These newfound lateral stability characteristics suggest that unsteady ground effect may play a role in the control strategies of near-boundary fish and fish-inspired robots.

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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 onedimensionally 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.collective locomotion | hydrodynamic interactions | fish schooling | pattern formation | collective performance M. K. helped design the study, gathered and processed experimental measurements, and drafted the manuscript. A. M. helped design the study, gathered and processed the numerical data, and helped revise the manuscript. K. M. helped design the study, and helped revise the manuscript.

New experiments examine the interactions between a pair of three-dimensional (AR = 2) non-uniformly flexible pitching hydrofoils through force and efficiency measurements. It is discovered that the collective efficiency is improved when the follower foil has a nearly out-of-phase synchronization with the leader and is located directly downstream with an optimal streamwise spacing of X*=0.5. The collective efficiency is further improved when the follower operates with a nominal amplitude of motion that is 36% larger than the leader’s amplitude. A slight degradation in the collective efficiency was measured when the follower was slightly-staggered from the in-line arrangement where direct vortex impingement is expected. Operating at the optimal conditions, the measured collective efficiency and thrust are ηC=62% and CT,C=0.44, which are substantial improvements over the efficiency and thrust of ηC=29% and CT,C=0.16 of two fully-rigid foils in isolation. This demonstrates the promise of achieving high-efficiency with simple purely pitching mechanical systems and paves the way for the design of high-efficiency bio-inspired underwater vehicles.

In this paper, we investigate the effect of operating near a solid boundary on the forces produced by harmonically oscillating thrust-generating foils. A rolling and pitching foil was towed in a freshwater tank in a series of experiments with varying kinematics. Hydrodynamic forces and torques were measured in the freestream and at varying distances from a solid boundary, and changes in mean lift and thrust were found when the foil approached the boundary. The magnitude of this ground effect exhibited a strong nonlinear dependence on the distance between the foil and the boundary. Significant effects were found within three chord lengths of the boundary, and ground effect can be induced at greater distances from the boundary by biasing the tip of the foil toward the boundary. Lift coefficients changed by as much as [Formula: see text] at the closest approach to the ground, with changes [Formula: see text] [Formula: see text] for all cases across Strouhal numbers ranging from [Formula: see text] to [Formula: see text], and nominal maximum angle of attack ranging from [Formula: see text] to [Formula: see text]. The ubiquity of the ground effect in high thrust kinematics suggests that the ground effect can provide a passive obstacle avoidance capability for foil propelled vehicles. By comparison with previous experimental work, we find that the ground effect experienced by a high-aspect ratio rolling and pitching foil is a fully three-dimensional phenomenon, as it is not accurately predicted when two-dimensional flow and/or two-dimensional kinematics are enforced. While two-dimensional foil kinematics are more easily modeled for numerical studies, three-dimensional foil kinematics may be more practical for real world implementation in underwater vehicles.

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