Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1999-02-18
On 82nd Statistical Mechanics Meeting, Rutgers University, December 10-12, 1999. The announce in Journal of Statistical Physic
Nonlinear Sciences
Chaotic Dynamics
6 pages, 2 figures, RevTEX
Scientific paper
10.1023/A:1018620302081
We study the exact non-singular zero-surface tension solutions of the Saffman-Taylor problem for all times. We show that all moving logarithmic singularities a_k(t) in the complex plane \omega = e^{i\phi}, where \phi is the stream function, are repelled from the origin, attracted to the unit circle and eventually coalesce. This pole evolution describes essentially all the dynamical features of viscous fingering in the Hele-Shaw cell observed by Saffman and Taylor [Proc. R. Soc. A 245, 312 (1958)], namely tip-splitting, multi-finger competition, inverse cascade, and subsequent formation of a single Saffman-Taylor finger.
Kupervasser Oleg
Mineev-Weinstein Mark
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