Hostname: page-component-68945f75b7-z7ghp Total loading time: 0 Render date: 2024-08-06T09:39:51.987Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite-amplitude stability of axisymmetric pipe flow

Published online by Cambridge University Press:  20 April 2006

Anthony T. Patera  and
Steven A. Orszag
Anthony T. Patera
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Steven A. Orszag
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Get access Rights & Permissions [Opens in a new window]

Abstract

The stability of pipe flow to axisymmetric disturbances is studied by direct numerical simulation of the incompressible Navier-Stokes equations. There is no evidence of finite-amplitude equilibria at any of the wavenumber/Reynolds number combinations investigated, with all perturbations decaying on a time scale much shorter than the diffusive (viscous) time scale. In particular, decay is obtained where amplitude-expansion perturbation techniques predict equilibria, indicating that these methods are not valid away from the neutral curve of linear stability theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 112 , November 1981 , pp. 467 - 474
Copyright
© 1981 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Davey, A. 1978 On Itoh's finite amplitude stability theory for pipe flow. J. Fluid Mech. 86, 695–703.Google Scholar
Davey, A. & Drazin, P. G. 1969 The stability of Poiseuille flow in a pipe. J. Fluid Mech. 36, 209–218.Google Scholar
Davey, A. & Nguyen, H. P. F. 1971 Finite-amplitude stability of pipe flow. J. Fluid Mech. 45, 701–720.Google Scholar
Gottlieb, D. & Orszag, S. A. 1977 Numerical Analysis of Spectral Methods: Theory and Applications. NSF-CBMS Monograph no. 26. Soc. Ind. App. Math., Philadelphia.
Herbert, T. 1977 Finite amplitude stability of plane parallel flows. In Laminar-Turbulent Transition, AGARD Conf. Proc. no. 224, 3–1–3–10.
Itoh, N. 1977 Nonlinear stability of parallel flows with subcritical Reynolds number. Part 2. Stability of pipe Poiseuille flow to finite axisymmetric disturbances. J. Fluid Mech. 82, 469–479.Google Scholar
Lessen, M., Sadler, S. G. & Liu, T. Y. 1968 Stability of pipe Poiseuille flow. Phys. Fluids 11, 1404–1409.Google Scholar
Metcalfe, R. W. & Orszag, S. A. 1973 Numerical calculation of the linear stability of pipe flows. Flow Research Rep. no. 25, Kent, Washington.Google Scholar
Orszag, S. A. 1971 Accurate solution of the Orr-Sommerfeld stability equation. J. Fluid Mech. 50, 689–703.Google Scholar
Orszag, S. A. & Kells, L. C. 1980 Transition to turbulence in plane Poiseuille and plane Couette flow. J. Fluid Mech. 96, 159–205.Google Scholar
Orszag, S. A. & Patera, A. T. 1980 Subcritical transition to turbulence in plane channel flows. Phys. Rev. Lett. 45, 989–992.Google Scholar
Patera, A. T. & Orszag, S. A. 1980 Transition and turbulence in planar channel flows. In Proc. 7th Int. Conf. on Numerical Methods in Fluid Dynamics (ed. W. C. Reynolds & R. W. MacCormack), pp. 329–335. Springer.
Salwen, H., Cotton, F. W. & Grosch, C. E. 1980 Linear stability of Poiseuille flow in a circular pipe. J. Fluid Mech. 98, 273–284.Google Scholar
Sexl, T. 1927 Zur Stabilitätsfrage der Poiseuilleschen und Couetteschen Strömüng. Ann. Physik 83, 835–848.Google Scholar