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Instability of plane parallel flows

  • Andrey V. BoikoEmail author
  • Alexander V. Dovgal
  • Genrih R. Grek
  • Victor V. Kozlov
Chapter
  • 1.5k Downloads
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 98)

Abstract

In this chapter the essentials of the linear-stability analysis and corresponding experimental results for such truly parallel internal flows as the plane Couette and the plane Poiseuille flow are presented. For an interested reader, a set of simple MATLAB functions and exercises are provided helping in understanding various physical and computational aspects of linear stability for shear flows.

Keywords

Reynolds Number Linear Stability Critical Reynolds Number Linear Stability Theory Neutral Stability Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

References

  1. Heisenberg W (1924) Über Stabilität und Turbulenz von Flüssigkeitsströmen. Ann Phys 74:577–627, translated as NACA TM 1291, 1951 CrossRefGoogle Scholar
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Further Reading

  1. Davies SJ, White CM (1928) An experimental study of the flow of water in pipe of rectangular section. Proc R Soc Lond A 19:92–107 ADSCrossRefGoogle Scholar
  2. Narayanan MA, Narayana T (1967) Some studies on transition from laminar to turbulent flow in a two-dimensional channel. Z Angew Math Phys 18:642–650 CrossRefGoogle Scholar
  3. Patel VC, Head MR (1969) Some observations on skin friction and velocity profiles in fully developed pipe and channel flows. J Fluid Mech 38:181–201 ADSCrossRefGoogle Scholar
  4. Sherlin GC (1960) Behaviour of isolated disturbances superimposed on laminar flow in a rectangular pipe. J Res N B S, Sec A, Phys and Chem 64A:281–289 Google Scholar
  5. Trefethen LN (2000) Spectral methods in Matlab. Society for Industrial and Applied Mathematics, Philadelphia, USA zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Andrey V. Boiko
    • 1
    Email author
  • Alexander V. Dovgal
    • 1
  • Genrih R. Grek
    • 1
  • Victor V. Kozlov
    • 1
  1. 1.Inst. Theoretical & Applied MechanicsRussian Academy of SciencesNovosibirskRussia

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