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Exact and asymptotic conditions on traveling wave solutions of the Navier–Stokes equations

Phys. Fluids 21, 101703 (2009); doi:10.1063/1.3244660

Published 12 October 2009

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Y. Charles Li1 and Divakar Viswanath2
1Department of Mathematics, University of Missouri, Columbia, Missouri 65211, USA
2Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109, USA
We derive necessary conditions that traveling wave and other solutions of the Navier–Stokes equations must satisfy in the pipe, Couette, and channel flow geometries. Some conditions are exact and must hold for any traveling wave solution or periodic solution irrespective of the Reynolds number (Re). Other conditions are asymptotic in the limit Re-->[infinity]. For the pipe flow geometry, we give computations up to Re=100 000 showing the connection of our asymptotic conditions to critical layers that accompany vortex structures at high Re. ©2009 American Institute of Physics
History: Received 23 July 2009; accepted 3 September 2009; published 12 October 2009
Permalink: http://link.aip.org/link/?PHFLE6/21/101703/1
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KEYWORDS and PACS

Keywords
PACS
  • 47.10.ad
    Navier-Stokes equations
  • 47.60.Dx
    Flows in ducts and channels
  • 47.15.Rq
    Laminar flows in cavities, channels, ducts, and conduits
  • 47.27.nf
    Turbulent flows in pipes and nozzles
  • 47.27.nd
    Turbulent channel flow
  • 47.32.cb
    Vortex interactions
  • YEAR: 2009

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PUBLICATION DATA

ISSN:
1070-6631 (print)   1089-7666 (online)
Publisher:
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REFERENCES (25)
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