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Blow-up of unsteady two-dimensional Euler and Navier-Stokes solutions having stagnation-point formThe time-dependent form of the classic, two-dimensional stagnation-point solution of the Navier-Stokes equations is considered. If the viscosity is zero, a class of solutions of the initial-value problem can be found in closed form using Lagrangian coordinates. These solutions exhibit singular behavior in finite time, because of the infinite domain and unbounded initial vorticity. Thus, the blow-up found by Stuart in three dimensions using the stagnation-point form, also occurs in two. The singularity vanishes under a discrete, finite-dimensional 'point vortex' approximation, but is recovered as the number of vortices tends to infinity. We find that a small positive viscosity does not arrest the breakdown, but does strongly alter its form. Similar results are summarized for certain Boussinesq stratified flows.
Document ID
19890058080
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Childress, S.
(New York University NY, United States)
Ierley, G. R.
(Michigan Technological University Houghton, United States)
Spiegel, E. A.
(Columbia University New York, United States)
Young, W. R.
(California, University La Jolla, United States)
Date Acquired
August 14, 2013
Publication Date
June 1, 1989
Publication Information
Publication: Journal of Fluid Mechanics
Volume: 203
ISSN: 0022-1120
Subject Category
Fluid Mechanics And Heat Transfer
Accession Number
89A45451
Funding Number(s)
CONTRACT_GRANT: NSF PHY-80-27321
CONTRACT_GRANT: NSF DMS-83-12229
CONTRACT_GRANT: N00014-86-K-0325
CONTRACT_GRANT: NAGW-781
Distribution Limits
Public
Copyright
Other

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