Marching of freely falling plates" is a fluid dynamics video submitted to the Gallery of Fluid Motion in APS-DFD 2011 at Baltimore Maryland. The problem of a freely falling plate is of interest in both fluid mechanics and nonlinear dynamics. The trajectory of the plate can be regular (Willmarth et al., 1964) or chaotic (Aref and Jones, 1993). As long as Reynolds number is high enough, regular flutter and tumble motion can be obtained for plates with small and large Froude numbers respectively. Belmonte et al. (1998) conducted experimental study on thin flat strips falling in a vertical cell. They categorized the Froude number at which the transition from flutter to tumble occurs. analyzed the transitions between fluttering and tumbling using vorticity-stream function formulation and ODE dynamic equations based on quasi-steady models. They also found that the fluid circulation is mainly generated by the plate rotation and its angular velocity. However, the correlation among the plates motion, generated vortices, and aerodynamic forces is still not fully understood yet, especially in the case of multiple bodies. The DNS (Direct Numerical Simulation, Dong et al., 2006) of freely falling plates is conducted using our in-house CFD (Computational Fluid Dynamics) solver. Showcased examples in this video are a part of DNS results in the attempt to answer the above question. arXiv:1110.3819v1 [physics.flu-dyn]

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Detailed studies are reported of the free and forced oscillation of disks and a right-circular cylinder constrained to rotate about a fixed diametrical axis passing through the centre of the body and normal to the free-stream direction. When a disk is free to rotate, it oscillates at a definite frequency with slowly varying amplitude and phase. A right-circular cylinder also oscillates at a definite frequency but with rapidly increasing amplitude. When the amplitude becomes large, after a few cycles of oscillation, the cylinder rotates steadily in one direction.Analogue computer elements, position sensors and a dynamic moment balance were used to study the static restoring moment, dynamic restoring moment, average damping moment, statistical properties of the disk motion and power spectrum of the turbulent moment. The behaviour of the disk and cylinder are explained using the measurements and the theory for random excitation of a linear system. The turbulent exciting moment is caused by the unsteady flow in the wake and can be changed by placing disks and splitter plates in the wake. A model is proposed for the unsteady flow field in the wake behind the disk. The model relates the turbulent moment to the vortex shedding process in the wake.

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