Frequency structure of the nonlinear instability of a dragged viscous thread Physical Review E, 85, 066209 (2012). Robert L. Welch, Billy Szeto and Stephen W. Morris Department of Physics, University of Toronto, 60 St. George St., Toronto, Ontario, Canada M5S 1A7.

A thread of viscous fluid falling onto a moving surface exhibits a spectacular variety of types of motion as the surface speed and nozzle height are varied. For modest nozzle heights, four clear regimes are observed. For large surface speed, the thread is dragged into a stretched centenary configuration which is confined to a plane. As the surface speed is lowered, this exhibits a supercritical Hopf bifurcation to a meandering state. At very low surface speeds, the state resembles the usual coiling motion of a viscous thread falling on a stationary surface. In between the meandering and coiling regimes, a window containing a novel multifrequency state, previously called "figures of eight" is found. We examined the longitudinal and transverse motion of the thread in all these states, using an automated apparatus that allows a detailed exploration of the parameter space. We found that the multifrequency state is characterized by a complex pattern of motion whose main frequencies are locked in a 3:2 ratio. This state appears and disappears with finite amplitude at sharp bifurcations without measurable hysteresis.

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