dorsal/arxiv
View SchemaAttracting Manifold for a Viscous Topology Transition
| Authors | Raymond E. Goldstein, Adriana I. Pesci, Michael J. Shelley |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9510004 |
| URL | https://arxiv.org/abs/patt-sol/9510004 |
| DOI | 10.1103/PhysRevLett.75.3665 |
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 zeroes in the complex plane. This suggests a general mechanism of singularity formation in this system.
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"abstract": "An analytical method is developed describing the approach to a finite-time\nsingularity associated with collapse of a narrow fluid layer in an unstable\nHele-Shaw flow. Under the separation of time scales near a bifurcation point, a\nlong-wavelength mode entrains higher-frequency modes, as described by a version\nof Hill\u0027s equation. In the slaved dynamics, the initial-value problem is solved\nexplicitly, yielding the time and analytical structure of a singularity which\nis associated with the motion of zeroes in the complex plane. This suggests a\ngeneral mechanism of singularity formation in this system.",
"arxiv_id": "patt-sol/9510004",
"authors": [
"Raymond E. Goldstein",
"Adriana I. Pesci",
"Michael J. Shelley"
],
"categories": [
"patt-sol",
"cond-mat",
"nlin.PS"
],
"doi": "10.1103/PhysRevLett.75.3665",
"title": "Attracting Manifold for a Viscous Topology Transition",
"url": "https://arxiv.org/abs/patt-sol/9510004"
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