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(1) and Maxwell(2), and is relevant to problems in meteorology(3), sedimentology(4), aerospace engineering(1) and chemical engineering(5-8). More recent theoretical studies(9-12) have emphasized the role played by deterministic chaos, although many experimental studies(1,5-8,13,14) 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(15), not previously observed experimentally, between the two behaviours.