## Van der Waals-Zeeman Colloquium

Tuesday, 19 Jun 2007, 16:00h

**All Bent Out of Shape: Periodic Buckling Instabilities
of Fluid Ropes and Sheets**

**Dr. Neil M. Ribe**

Institut de Physique du Globe de Paris,
75252 Paris cedex 05

The coiling of a thin "rope" of viscous fluid falling onto a rigid surface is an example of a buckling instability, in which a thin layer under compressional stress becomes unstable to bending disturbances. Using a combination of analytical, numerical, and experimental approaches, I and my colleagues have determined a complete "phase diagram" for the coiling of liquid ropes, comprising four distinct dynamical regimes (viscous, gravitational, inertio-gravitational, and inertial) depending on how the viscous forces that resist the bending of the rope are balanced. The most interesting behavior occurs during the gravitational-to-inertial transition, where multiple resonant modes coexist at a fixed fall height within a certain range. Similar regimes are also observed in numerical and laboratory models of folding viscous sheets. To conclude, I will show how a scaling law for the fold amplitude in a buckling sheet can explain certain striking patterns of anomalous elastic wavespeed deep in the earth's silicate mantle.