Patterns and instabilities at a driven fluid-air interface

Pan, Lihong (1993) Patterns and instabilities at a driven fluid-air interface. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

We have studied experimentally the dynamical behaviour of a driven fluid-air interlace in the system known as the printer's instability. The system consists of two horizontal cylinders, one mounted eccentrically inside the other, with the narrow part of the gap between them filled with a viscous oil. As one or both of the cylinders rotate, the straight oil-air interlace becomes unstable, and the inter race displays a. variety of dynamical states. These include* stationary and traveling finger patterns, solitary waves, and spatio-temporal chaos. Measurements of the onset and development of the stationary finger pattern observed when only one cylinder rotates indicate that finite-size effects delay the onset of the fingering instability. When the two cylinders counter-rotate, we observe a supercritical parity-breaking transition, at which the stationary pattern loses its reflection symmetry and begins to drift along the apparatus. From measurements of the degree of asymmetry of the drifting pattern as a function of the experimental control parameter, we find that the asymmetry increases with the square root of the control parameter, and that the drift velocity is linear in the asymmetry. This behaviour is in accord with recent theoretical predictions. At low values of the control parameter, the drifting pattern is disordered, also in agreement with theoretical results. We have also observed a nonuniform traveling pattern in which the fingers become unstable to the Kekhaiis instability, and we measure the Fekhaus stability boundary for this system.

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