Noisy and regular features in Saffman-Taylor patterns

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Abstract
Fourteen realizations of Saffman-Taylor flow at small-viscosity contrast have been measured under nearly identical flow conditions. With control-parameter fluctuations ≲0.15%, we observe fluctuations of 20% in the crudest measures of the patterns and much larger fluctuations in the strengths of individual wave numbers of a modal analysis of the patterns for this broadband instability. The initial disturbance can be observed as it propagates toward the center of the cell from the side walls. As the patterns go over from the linear to the nonlinear regime, several quantitative measures show abrupt change. In the nonlinear regime the patterns not only fail to show progress toward a single-finger steady state but the individual fingers actually show a tendency to evolve toward a narrower distribution of lengths.

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