Multiple bifurcation of rotating pipe flow

Alex Mahalov, Sidney Leibovich

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Viscous rotating Hagen-Poiseuille flow is shown to contain a multiple bifurcation point at which two Hopf bifurcations coalesce. The double Hopf bifurcation has nonsemisimple 1:1 resonance. The full problem in the neighborhood of this point may be reduced to a four-dimensional system of weakly nonlinear amplitude equations using an expansion of the center manifold type. An efficient numerical procedure to find the coupling coefficients in the amplitude equations is employed which avoids the explicit need to compute adjoint eigenfunctions. Numerical investigation of the amplitude equations has lead to the discovery of several new states of the fluid motion in this system, including stable rotating traveling and modulated traveling waves, a Feigenbaum period-doubling cascade, and chaotic trajectories. Homoclinic loops are found leading to dynamics which may be associated with "bursting" events in the physical problem under consideration.

Original languageEnglish (US)
Pages (from-to)61-77
Number of pages17
JournalTheoretical and Computational Fluid Dynamics
Issue number2
StatePublished - Nov 1991
Externally publishedYes

ASJC Scopus subject areas

  • Computational Mechanics
  • Condensed Matter Physics
  • General Engineering
  • Fluid Flow and Transfer Processes


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