Paths of Falling Flexible Sheets

Silas Alben
School of Mathematics
Georgia Institute of Technology

Flexible sheets are released from rest and fall downward. The paths (black lines) reflect the fluttering, flapping, and circling motions of the sheets.

We have used computers to solve for the motions of flexible sheets falling in fluid. We have studied sheets with various mass densities and bending rigidities. Shown here are sheets with a single mass density and eight bending rigidities (the numbers in the upper left of the panels), released from rest at different angles. The sheet trajectories show a wide range of intricate structures as they fall. The basic behavior is a repeated series of accelerations to a critical speed at which the sheet flexes and rapidly decelerates, corresponding to sharp turns in the paths. The sheet trajectories also show persistent circling (the heavy diagonal lines in panels labeled 10, 14, and 24), periodic flapping (the zig-zag downward lines in the panel labeled 1), and more complex repeated patterns.

This work is funded by the National Science Foundation under Grant No. DMS-0810602.  

References

S. Alben, Flexible sheets falling in an inviscid fluid, Physics of Fluids, 22, 061901–1-13 (2010).  

Reporters and Editors

Reporters may freely use this image. Credit: Silas Alben and Physics of Fluids (2010).