Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 22
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Zammert, Stefan and Eckhardt, Bruno 2015. Crisis bifurcations in plane Poiseuille flow. Physical Review E, Vol. 91, Issue. 4,


    Hagan, Jonathan and Priede, Jānis 2014. Two-dimensional nonlinear travelling waves in magnetohydrodynamic channel flow. Journal of Fluid Mechanics, Vol. 760, p. 387.


    Deguchi, K. and Altmeyer, S. 2013. Fully nonlinear mode competitions of nearly bicritical spiral or Taylor vortices in Taylor-Couette flow. Physical Review E, Vol. 87, Issue. 4,


    Casas, Pablo S. and Jorba, Àngel 2012. Hopf bifurcations to quasi-periodic solutions for the two-dimensional plane Poiseuille flow. Communications in Nonlinear Science and Numerical Simulation, Vol. 17, Issue. 7, p. 2864.


    Cousin-Rittemard, N.M.M. and Gruais, I. 2009. On the connection of isolated branches of a bifurcation diagram: the truss arch system. Dynamical Systems, Vol. 24, Issue. 3, p. 315.


    Fujimura, K. 2006. Nonlinear Evolution of Two-Dimensional Tollmien–Schlichting Waves Triggered by a Linearly Damping Eigenmode. Journal of the Physical Society of Japan, Vol. 75, Issue. 6, p. 064401.


    Wu, Xuesong and Luo, Jisheng 2006. Influence of small imperfections on the stability of plane Poiseuille flow and the limitation of Squire’s theorem. Physics of Fluids, Vol. 18, Issue. 4, p. 044104.


    Mercader, I. Batiste, O. Ramírez-Piscina, L. Ruiz, X. Rüdiger, S. and Casademunt, J. 2005. Bifurcations and chaos in single-roll natural convection with low Prandtl number. Physics of Fluids, Vol. 17, Issue. 10, p. 104108.


    Casas, Pablo S. and Jorba, Àngel 2004. Unstable manifold computations for the two-dimensional plane Poiseuille flow. Theoretical and Computational Fluid Dynamics, Vol. 18, Issue. 2-4, p. 285.


    Luo, Jisheng and Wu, Xuesong 2004. Influence of small imperfections on the stability of plane Poiseuille flow: A theoretical model and direct numerical simulation. Physics of Fluids, Vol. 16, Issue. 8, p. 2852.


    Mehta, Prashant G. 2004. A unified well-posed computational approach for the 2D Orr–Sommerfeld problem. Journal of Computational Physics, Vol. 199, Issue. 2, p. 541.


    Pino, D. Net, M. Sánchez, J. and Mercader, I. 2001. Thermal Rossby waves in a rotating annulus. Their stability. Physical Review E, Vol. 63, Issue. 5,


    Drissi, A. Net, M. and Mercader, I. 1999. Subharmonic instabilities of Tollmien-Schlichting waves in two-dimensional Poiseuille flow. Physical Review E, Vol. 60, Issue. 2, p. 1781.


    Li, Hsi-Shang and Fujimura, Kaoru 1999. Nonlinear equilibrium solutions in stratified plane Poiseuille flow. Physics of Fluids, Vol. 11, Issue. 11, p. 3322.


    Li, H.-S. and Fujimura, K. 1996. Nonlinear critical Reynolds number of a stratified plane Poiseuille flow. Physics of Fluids, Vol. 8, Issue. 5, p. 1127.


    Rauh, A. Zachrau, T. and Zoller, J. 1995. Nonlinear stability analysis of plane poiseuille flow by normal forms. Physica D: Nonlinear Phenomena, Vol. 86, Issue. 4, p. 603.


    Sangalli, M. Gallagher, C. T. Leighton, D. T. Chang, H.-C. and McCready, M. J. 1995. Finite-Amplitude Waves at the Interface between Fluids with Different Viscosity: Theory and Experiments. Physical Review Letters, Vol. 75, Issue. 1, p. 77.


    Schatz, Michael F. Barkley, Dwight and Swinney, Harry L. 1995. Instability in a spatially periodic open flow. Physics of Fluids, Vol. 7, Issue. 2, p. 344.


    Umeki, Makoto 1994. Numerical simulation of plane Poiseuille turbulence. Fluid Dynamics Research, Vol. 13, Issue. 2, p. 67.


    Rotenberry, James M. 1993. Finite amplitude steady waves in the Blasius boundary layer. Physics of Fluids A: Fluid Dynamics, Vol. 5, Issue. 7, p. 1840.


    ×
  • Journal of Fluid Mechanics, Volume 229
  • August 1991, pp. 389-416

Finite-amplitude bifurcations in plane Poiseuille flow: two-dimensional Hopf bifurcation

  • Israel Soibelman (a1) and Daniel I. Meiron (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112091003075
  • Published online: 01 April 2006
Abstract

We examine the stability to superharmonic disturbances of finite-amplitude two-dimensional travelling waves of permanent form in plane Poiseuille flow. The stability characteristics of these flows depend on whether the flux or pressure gradient are held constant. For both conditions we find several Hopf bifurcations on the upper branch of the solution surface of these two-dimensional waves. We calculate the periodic orbits which emanate from these bifurcations and find that there exist no solutions of this type at Reynolds numbers lower than the critical value for existence of two-dimensional waves (≈2900). We confirm the results of Jiménez (1987) who first detected a stable branch of these solutions by integrating the two-dimensional equations of motion numerically.

Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax