Oscillations of a Falling Slender Body in Viscous Flow
The oscillations of a falling leaf or a piece of paper in the air have been noticed for over a century dating back to J.C. Maxwell. As yet, there's no satisfactory explanation for this well-known phenomenon. Some phenomenological models are introduced to describe the behavior qualitatively. The patterns and irregular motions with chaotic attractors of the falling object have been successfully reproduced. However, these models either assume the linear relation between drag force and velocity, or ignore the viscosity and assume the flow is irrotational, or combine the results from different kinds of flows to construct models. A correct description for this question is still undetermined.
In this research, I investigate the motions of an (slender) elliptic cylinder in two-dimensional viscous flow. The dynamical system is set up by Navier-Stokes equations for the fluid and Newton's 2nd law for the object and it is the extension of the dynamics for a moving curveball. Moving coordinates methods are introduced to facilitate numerical simulations. The simulations demonstrate the flutter and tumble of this falling object and this phenomenon which has been noticed for over a century is obtained without any phenomenological model.