Fluttering motion of a confined cylinder falling freely in fluid at rest

We investigate experimentally the planar paths displayed by cylinders falling freely in a thin-gap cell containing liquid at rest, by varying the elongation ratio and the Archimedes number of the cylinders, and the solid-to-fluid density ratio. In the investigated conditions, the oscillatory falling motion features two main characteristics: the mean fall velocity $\overline {u_v}$ does not scale with the gravitational velocity, which overestimates $\overline {u_v}$ and is unable to capture the influence of the density ratio on it; and high-amplitude oscillations of the order of $\overline {u_v}$ are observed for both translational and rotational velocities. To model the body behaviour, we propose a force balance, including proper and added inertia terms, the buoyancy force and vortical contributions accounting for the production of vorticity at the body surface and its interaction with the cell walls. Averaging the equations over a temporal period provides a mean force balance that governs the mean fall velocity of the cylinder, revealing that the coupling between the translational and rotational velocity components induces a mean upward inertial force responsible for the decrease of $\overline {u_v}$ . This mean force balance also provides a normalization for the frequency of oscillation of the cylinder in agreement with experimental measurements. We then consider the instantaneous force balance experienced by the body, and propose three contributions for the modelling of the vortical force. These can be interpreted as drag, lift and history forces, and their dependence on the control parameters is adjusted on the basis of the experimental measurements.