Thrust-generating flapping foils are known to produce jets inclined to the free stream at high Strouhal numbers St = fA/U ∞ , where f is the frequency and A is the amplitude of flapping and U ∞ is the free-stream velocity. Our experiments, in the limiting case of St → ∞ (zero free-stream speed), show that a purely oscillatory pitching motion of a chordwise flexible foil produces a coherent jet composed of a reverse Bénard-Kármán vortex street along the centreline, albeit over a specific range of effective flap stiffnesses. We obtain flexibility by attaching a thin flap to the trailing edge of a rigid NACA0015 foil; length of flap is 0.79 c where c is rigid foil chord length. It is the time-varying deflections of the flexible flap that suppress the meandering found in the jets produced by a pitching rigid foil for zero free-stream condition. Recent experiments (Marais et al., J. Fluid Mech., vol. 710, 2012, p. 659) have also shown that the flexibility increases the St at which non-deflected jets are obtained. Analysing the near-wake vortex dynamics from flow visualization and particle image velocimetry (PIV) measurements, we identify the mechanisms by which flexibility suppresses jet deflection and meandering. A convenient characterization of flap deformation, caused by fluid-flap interaction, is through a non-dimensional 'effective stiffness', EI * = 8 EI/(ρ V 2 TE max s f c 3 f /2), representing the inverse of the flap deflection due to the fluid-dynamic loading; here, EI is the bending stiffness of flap, ρ is fluid density, V TE max is the maximum velocity of rigid foil trailing edge, s f is span and c f is chord length of the flexible flap. By varying the amplitude and frequency of pitching, we obtain a variation in EI * over nearly two orders of magnitude and show that only moderate EI * (0.1 EI * 1) generates a sustained, coherent, orderly jet. Relatively 'stiff' flaps (EI * 1), including the extreme case of no flap, produce meandering jets, whereas highly 'flexible' flaps (EI * 0.1) produce spread-out jets. Obtained from the measured mean velocity fields, we present values of thrust coefficients for the cases for which orderly jets are observed.

The flow produced by a rigid symmetric NACA0015 airfoil purely pitching at a fixed location in quiescent fluid (the limiting case of infinite Strouhal number) is studied using visualizations and particle image velocimetry. A weak jet is generated whose inclination changes continually with time. This meandering is observed to be random and independent of the initial conditions, over a wide range of pitching parameters.

Inspired by the flexible wings and fins of flying and swimming animals, we investigate the flow induced by the interaction between a flapping flexible surface and the surrounding fluid for the limiting case of Strouhal number S t → ∞ (zero free-stream speed). The model selected for this purpose is a two-dimensional sinusoidally pitching rigid symmetric foil to which is attached at the trailing edge a thin chordwise flexible surface (along the chord line). The flow so generated is a coherent jet aligned along the foil centreline, containing a reverse Bénard–Kármán vortex street and delivering a corresponding unidirectional thrust. We analyse the flow and thrust generation process. The measured velocity field suggests that the flow and thrust generation mainly occurs during the phases when the trailing edge is near the centreline. Flexibility of the surface is important in accelerating the near-wake flow and in transferring momentum and energy to the fluid. We present a detailed account of when and where the momentum and energy are added to the fluid. This study shows that the deformations of the flexible surface are responsible for generating a favourable pressure gradient along the jet direction, and for the observed unsteady actuator disc-type action.

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