Attracting manifold for a viscous topology transition

Raymond E. Goldstein, Adriana I. Pesci, Michael 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

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topology
boundary value problems
fluids
wavelengths

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Attracting manifold for a viscous topology transition. / Goldstein, Raymond E.; Pesci, Adriana I.; Shelley, Michael.

In: Physical Review Letters, Vol. 75, No. 20, 1995, p. 3665-3668.

Research output: Contribution to journalArticle

Goldstein, RE, Pesci, AI & Shelley, M 1995, 'Attracting manifold for a viscous topology transition', Physical Review Letters, vol. 75, no. 20, pp. 3665-3668. https://doi.org/10.1103/PhysRevLett.75.3665
Goldstein, Raymond E. ; Pesci, Adriana I. ; Shelley, Michael. / Attracting manifold for a viscous topology transition. In: Physical Review Letters. 1995 ; Vol. 75, No. 20. pp. 3665-3668.
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