Chaotic dynamics of falling disks

Abstract

The study of the motion of flat bodies falling in a viscous medium dates back at least to Newton and Maxwell and is relevant to problems in meteorology, sedimentology, aerospace engineering and chemical engineering. More recent theoretical studies have emphasized the role played by deterministic chaos, although many experimental studies were performed before the development of such ideas. Here we report experimental observations of the dynamics of disks falling in water/glycerol mixtures. We find four distinct types of motion, which are mapped out in a 'phase diagram'. The apparently complex behaviour can be reduced to a series of one-dimensional maps, which display a discontinuity at the crossover from periodic to chaotic motion. This discontinuity leads to an unusual intermittency transition, not previously observed experimentally, between the two behaviours.