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Double Hopf bifurcation in corotating spiral Poiseuille flow Marc Avila,a

Summary: Double Hopf bifurcation in corotating spiral Poiseuille flow
Marc Avila,a
Alvaro Meseguer,b
and Francisco Marquesc
Departament de Física Aplicada, Univ. Politècnica de Catalunya, C/ Jordi Girona 1-3,
Mod. B5, 08034 Barcelona, Spain
Received 17 January 2006; accepted 10 April 2006; published online 1 June 2006
Nonlinear dynamics of the spiral Poiseuille problem for moderate axial through flow is investigated
numerically within the corotating regime for medium gap geometry. The neighborhood of a double
Hopf bifurcation point of the linear stability boundary, where spiral waves of opposite axial phase
propagation compete, is explored by accurately solving time-dependent Navier-Stokes equations
with a solenoidal spectral method. The mode interaction generates a quasiperiodic stable regime of
interpenetrating spirals, which coexists with stable limit cycles associated with the aforementioned
spiral waves of opposite helicoidal orientation. The spatiotemporal properties of the computed
solutions are explained and discussed in terms of equivariant bifurcation and normal form theories.
Similar flows have also been observed experimentally in the past within the corotating region.
© 2006 American Institute of Physics. DOI: 10.1063/1.2204967
The spiral Poiseuille problem deals with the behavior of
an incompressible viscous fluid confined between two co-


Source: Avila, Marc - Complex Dynamics and Turbulence Group, Max-Planck-Institut für Dynamik und Selbstorganisation, Göttingen


Collections: Physics