Attracting manifold for a viscous topology transition

Raymond E. Goldstein, Adriana I. Pesci, Michael J. Shelley

Research output: Contribution to journalArticle

Abstract

An analytical method is developed describing the approach to a finite-time singularity associated with collapse of a narrow fluid layer in an unstable Hele-Shaw flow. Under the separation of time scales near a bifurcation point, a long-wavelength mode entrains higher-frequency modes, as described by a version of Hill's equation. In the slaved dynamics, the initial-value problem is solved explicitly, yielding the time and analytical structure of a singularity which is associated with the motion of zeros in the complex plane. This suggests a general mechanism of singularity formation in this system.

Original languageEnglish (US)
Pages (from-to)3665-3668
Number of pages4
JournalPhysical Review Letters
Volume75
Issue number20
DOIs
StatePublished - 1995

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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    Goldstein, R. E., Pesci, A. I., & Shelley, M. J. (1995). Attracting manifold for a viscous topology transition. Physical Review Letters, 75(20), 3665-3668. https://doi.org/10.1103/PhysRevLett.75.3665