Skip to main content
SpringerLink
Log in

Instability of hagen-poiseuille flow for axisymmetric mode

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cloes, D.,In Mecanique ala Turbulence, Ed. A. Favre, C.N.R.S., Paris (1962), 229–250.

    Google Scholar 

  2. Davey, A. and H. P. F. Nguyen, Finite-amplitude stability of pipe flow,J. Fluid Mech.,45 (1971), 701–720.

    Article  MATH  Google Scholar 

  3. Davey, A., On Iton's finite amplitude stability theory for pipe flow,J. Fluid Mech.,82 (1978), 695–703.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  6. Stuart, J. T.,Laminar Turbulent Transition, ed. R. Eppler And H. Fasel, Springer-Verlag-Berlin-Heidelberg Press (1980).

  7. Stuart, J. T., Laminar and turbulence transition in channel and pipeTransition and Turbulence, Academic Press Inc. (1981), 77–94.

  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.

    MATH  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Math. Sinica, Beijing

    Wang F. M.

  2. Imperial college, U.K.

    J. T. Stuart

Authors
  1. Wang F. M.
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. T. Stuart
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by Qin Yuan-xun

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, F.M., Stuart, J.T. Instability of hagen-poiseuille flow for axisymmetric mode. Appl Math Mech 8, 1037–1044 (1987). https://doi.org/10.1007/BF02482689

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02482689

Keywords

Search

Navigation