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Falling styles of disks

Published online by Cambridge University Press:  19 February 2013

Franck Auguste ,
Jacques Magnaudet  and
David Fabre
Franck Auguste
Affiliation:
Université de Toulouse, INPT, UPS, IMFT (Institut de Mécanique des Fluides de Toulouse), Allée Camille Soula, F-31400 Toulouse, France
Jacques Magnaudet*
Affiliation:
Université de Toulouse, INPT, UPS, IMFT (Institut de Mécanique des Fluides de Toulouse), Allée Camille Soula, F-31400 Toulouse, France CNRS, IMFT, F-31400 Toulouse, France
David Fabre
Affiliation:
Université de Toulouse, INPT, UPS, IMFT (Institut de Mécanique des Fluides de Toulouse), Allée Camille Soula, F-31400 Toulouse, France
*
†Email address for correspondence: [email protected]
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Abstract

We numerically investigate the dynamics of thin disks falling under gravity in a viscous fluid medium at rest at infinity. Varying independently the density and thickness of the disk reveals the influence of the disk aspect ratio which, contrary to previous belief, is found to be highly significant as it may completely change the route to non-vertical paths as well as the boundaries between the various path regimes. The transition from the straight vertical path to the planar fluttering regime is found to exhibit complex dynamics: a bistable behaviour of the system is detected within some parameter range and several intermediate regimes are observed in which, although the wake is unstable, the path barely deviates from vertical. By varying independently the body-to-fluid inertia ratio and the relative magnitude of inertial and viscous effects over a significant range, we set up a comprehensive map of the corresponding styles of path followed by an infinitely thin disk. We observe the four types of planar regimes already reported in experiments but also identify two additional fully three-dimensional regimes in which the body experiences a slow horizontal precession superimposed onto zigzagging or tumbling motions.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Nonlinear Dynamical Systems: Nonlinear Dynamical Systems
Type
Papers
Information
Journal of Fluid Mechanics , Volume 719 , 25 March 2013 , pp. 388 - 405
Copyright
©2013 Cambridge University Press

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Auguste et al. supplementary movie

Falling styles of discs I*=0.16; Ar=27.8 “Autorotation(=tumbling) AR regime”

Download Auguste et al. supplementary movie(Video)
Video 1.5 MB

Auguste et al. supplementary movie

Falling styles of discs I*=0.48;Ar=47.9 “Helical tumbling HA regime”

Download Auguste et al. supplementary movie(Video)
Video 1.1 MB

Auguste et al. supplementary movie

Falling styles of discs I*=0.012; Ar=47.1 “Helcial fluttering HH regime”

Download Auguste et al. supplementary movie(Video)
Video 2.2 MB

Auguste et al. supplementary movie

Falling styles of discs I*0.048; Ar=25.5 “Zigzagging (=fluttering)ZZ regime”

Download Auguste et al. supplementary movie(Video)
Video 1.5 MB

Auguste et al. supplementary movie

Falling styles of discs I*=0.0035; Ar=42.56 “Small-amplitude zigzagging A-regime(similar to regime(iii)in figure 1a)”

Download Auguste et al. supplementary movie(Video)
Video 1.9 MB

Auguste et al. supplementary movie

Falling styles of discs I*=0.0035; Ar=42.56 “Small-amplitude zigzagging A-regime(similar to regime(iii)in figure 1a)”

Download Auguste et al. supplementary movie(Video)
Video 1.6 MB