Applied Mathematics and Mechanics

, Volume 8, Issue 11, pp 1037–1044 | Cite as

Instability of hagen-poiseuille flow for axisymmetric mode

  • Wang F. M. 
  • J. T. Stuart


An investigation is described for instability problem of flow through a.pipe of circular cross section. As a disturbance motion, we consider an axisymmetric nonlinear mode. An associated amplitude or modulation equation has been derived for this perturbation. This equation belongs to the diffusion type. The coefficient of it can be negative with Reynolds number increasing, because of the complex interaction between molecular diffusion and convection. The negative diffusion, when it occurs, cause a concentration and focusing of energy within the decaying slug, acting as a role of reversing natural decays.


Reynolds Number Nonlinear Stability Poiseuille Flow Critical Reynolds Number Amplitude Function 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Cloes, D.,In Mecanique ala Turbulence, Ed. A. Favre, C.N.R.S., Paris (1962), 229–250.Google Scholar
  2. [2]
    Davey, A. and H. P. F. Nguyen, Finite-amplitude stability of pipe flow,J. Fluid Mech.,45 (1971), 701–720.MATHCrossRefGoogle Scholar
  3. [3]
    Davey, A., On Iton's finite amplitude stability theory for pipe flow,J. Fluid Mech.,82 (1978), 695–703.CrossRefGoogle Scholar
  4. [4]
    Iton, N., Nonlinear stability of parallel flows with subcritical Reynolds number, Part 1: An asymptotic theory valid for small amplitude, disturbances, Part 2: Stability of pipe Poiseuille flow to finite axisymmetric disturbances,J. Fluid Mech.,82 (1977), 455–479.CrossRefGoogle Scholar
  5. [5]
    Stuart, J.T., On the nonlinear mechanics of wave disturbance in stable and unstable parallel flow, Part 1: The basic behaviour in plane Poiseuille flow,J. Fluid Mech.,9 (1960), 353–370.MATHMathSciNetCrossRefGoogle Scholar
  6. [6]
    Stuart, J. T.,Laminar Turbulent Transition, ed. R. Eppler And H. Fasel, Springer-Verlag-Berlin-Heidelberg Press (1980).Google Scholar
  7. [7]
    Stuart, J. T., Laminar and turbulence transition in channel and pipeTransition and Turbulence, Academic Press Inc. (1981), 77–94.Google Scholar
  8. [8]
    Smith, F.T. and R.J. Bodonyi, Amplitude-dependent neutral modes in the Hagen-Poiseuille flow through a circular pipe,Proc. Roy. Soc.,A 384 (1982), 463–489.MATHGoogle Scholar
  9. [9]
    Watson, J., On the nonlinear mechanics of wave disturbance in stable and unstable parallel flow, Part 2: The development of a solution for plane Poiseuille flow and for plane Couette flow,J. Fluid Mech.,9 (1960), 371–389.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Shanghai University of Technology (SUT) 1987

Authors and Affiliations

  • Wang F. M. 
    • 1
  • J. T. Stuart
    • 2
  1. 1.Institute of Applied Math. SinicaBeijing
  2. 2.Imperial collegeU.K.

Personalised recommendations