The manta is the largest marine organism to swim by dorsoventral oscillation (flapping) of the pectoral fins. The manta has been considered to swim with a high efficiency stroke, but this assertion has not been previously examined. The oscillatory swimming strokes of the manta were examined by detailing the kinematics of the pectoral fin movements swimming over a range of speeds and by analyzing simulations based on computational fluid dynamic potential flow and viscous models. These analyses showed that the fin movements are asymmetrical up- and downstrokes with both spanwise and chordwise waves interposed into the flapping motions. These motions produce complex three-dimensional flow patterns. The net thrust for propulsion was produced from the distal half of the fins. The vortex flow pattern and high propulsive efficiency of 89% were associated with Strouhal numbers within the optimal range (0.2–0.4) for rays swimming at routine and high speeds. Analysis of the swimming pattern of the manta provided a baseline for creation of a bio-inspired underwater vehicle, MantaBot.

Inviscid computational results are presented on a self-propelled swimmer modelled as a virtual body combined with a two-dimensional hydrofoil pitching intermittently about its leading edge. Lighthill (Proc. R. Soc. Lond.B, vol. 179, 1971, pp. 125–138) originally proposed that this burst-and-coast behaviour can save fish energy during swimming by taking advantage of the viscous Bone–Lighthill boundary layer thinning mechanism. Here, an additional inviscid Garrick mechanism is discovered that allows swimmers to control the ratio of their added-mass thrust-producing forces to their circulatory drag-inducing forces by decreasing their duty cycle, $DC$ , of locomotion. This mechanism can save intermittent swimmers as much as 60 % of the energy it takes to swim continuously at the same speed. The inviscid energy savings are shown to increase with increasing amplitude of motion, increase with decreasing Lighthill number, $Li$ , and switch to an energetic cost above continuous swimming for sufficiently low $DC$ . Intermittent swimmers are observed to shed four vortices per cycle that give rise to an asymmetric time-averaged jet structure with both momentum surplus and deficit branches. In addition, previous thrust and power scaling laws of continuous self-propelled swimming are further generalized to include intermittent swimming. The key is that by averaging the thrust and power coefficients over only the bursting period then the intermittent problem can be transformed into a continuous one. Furthermore, the intermittent thrust and power scaling relations are extended to predict the mean speed and cost of transport of swimmers. By tuning a few coefficients with a handful of simulations these self-propelled relations can become predictive. In the current study, the mean speed and cost of transport are predicted to within 3 % and 18 % of their full-scale values by using these relations.

We present experiments that examine the modes of interaction, the collective performance and the role of three-dimensionality in two pitching propulsors in an in-line arrangement. Both two-dimensional foils and three-dimensional rectangular wings of AR = 2 are examined. In contrast to previous work, two interaction modes distinguished as the coherent and branched wake modes are not observed to be directly linked to the propulsive efficiency, although they are linked to peak thrust performance and minimum power consumption as previously described (Boschitsch et al 2014 Phys. Fluids 26 051901). In fact, in closely-spaced propulsors peak propulsive efficiency of the follower occurs near its minimum power and this condition reveals a branched wake mode. Alternatively, for propulsors spaced far apart peak propulsive efficiency of the follower occurs near its peak thrust and this condition reveals a coherent wake mode. By examining the collective performance, it is discovered that there is an optimal spacing between the propulsors to maximize the collective efficiency. For two-dimensional foils the optimal spacing of X * = 0.75 and the synchrony of ϕ = 2π / 3 leads to a collective efficiency and thrust enhancement of 42% and 38%, respectively, as compared to two isolated foils. In comparison, for AR = 2 wings the optimal spacing of X * = 0.25 and the synchrony of ϕ = 7 π / 6 leads to a collective efficiency and thrust enhancement of 25% and 15%, respectively. In addition, at the optimal conditions the collective lateral force coefficients in both the two- and three-dimensional cases are negligible, while operating off these conditions can lead to non-negligible lateral forces. Finally, the peak efficiency of the collective and the follower are shown to have opposite trends with increasing spacing in two- and three-dimensional flows. This is correlated to the breakdown of the impinging vortex on the follower wing in three-dimensions. These results can aid in the design of networked bio-inspired control elements that through integrated sensing can synchronize to three-dimensional flow interactions.

Scaling laws for the thrust production and energetics of self-propelled or fixed-velocity three-dimensional rigid propulsors undergoing pitching motions are presented. The scaling relations extend the two-dimensional scaling laws presented in Moored & Quinn (AIAA J., 2018, pp. 1–15) by accounting for the added mass of a finite-span propulsor, the downwash/upwash effects from the trailing vortex system of a propulsor and the elliptical topology of shedding trailing-edge vortices. The novel three-dimensional scaling laws are validated with self-propelled inviscid simulations and fixed-velocity experiments over a range of reduced frequencies, Strouhal numbers and aspect ratios relevant to bio-inspired propulsion. The scaling laws elucidate the dominant flow physics behind the thrust production and energetics of pitching bio-propulsors, and they provide guidance for the design of bio-inspired propulsive systems.

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.