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

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)....

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Bibliographic Details
Published inPhysics of fluids (1994) Vol. 21; no. 10
Main Authors Li, Y. Charles, Viswanath, Divakar
Format Journal Article
LanguageEnglish
Published Melville, NY American Institute of Physics 01.10.2009
Subjects
Exact sciences and technology
Flows in ducts, channels, nozzles, and conduits
Fluid dynamics
Fundamental areas of phenomenology (including applications)
General theory
Physics
Necessary condition
Travelling waves
Pipe flow
Couette flow
Asymptotic solution
Navier-Stokes equations
Exact solution
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ISSN1070-6631
1089-7666
DOI10.1063/1.3244660

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Summary: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→∞. 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.
ISSN:1070-6631
1089-7666
DOI:10.1063/1.3244660