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dc.contributor.authorMellibovsky Elstein, Fernando
dc.contributor.authorEckhardt, Bruno
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Física Aplicada
dc.identifier.citationMellibovsky, F.; Eckhardt, B. Takens–Bogdanov bifurcation of travelling-wave solutions in pipe flow. "Journal of fluid mechanics", Febrer 2011, vol. 670, p. 96-129.
dc.description.abstractThe appearance of travelling-wave-type solutions in pipe Poiseuille flow that are disconnected from the basic parabolic profile is numerically studied in detail. We focus on solutions in the twofold azimuthally-periodic subspace because of their special stability properties, but relate our findings to other solutions as well. Using time-stepping, an adapted Krylov–Newton method and Arnoldi iteration for the computation and stability analysis of relative equilibria, and a robust pseudo-arclength continuation scheme, we unfold a double-zero (Takens–Bogdanov) bifurcating scenario as a function of Reynolds number (Re) and wavenumber (κ). This scenario is extended, by the inclusion of higher-order terms in the normal form, to account for the appearance of supercritical modulated waves emanating from the upper branch of solutions at a degenerate Hopf bifurcation. We provide evidence that these modulated waves undergo a fold-of-cycles and compute some solutions on the unstable branch. These waves are shown to disappear in saddle-loop bifurcations upon collision with lower-branch solutions, in accordance with the bifurcation scenario proposed. The travelling-wave upper-branch solutions are stable within the subspace of twofold periodic flows, and their subsequent secondary bifurcations could contribute to the formation of the phase space structures that are required for turbulent dynamics at higher Re.
dc.format.extent34 p.
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.subjectÀrees temàtiques de la UPC::Física
dc.subject.lcshBifurcation theory
dc.titleTakens–Bogdanov bifurcation of travelling-wave solutions in pipe flow
dc.subject.lemacBifurcació, Teoria de la
dc.contributor.groupUniversitat Politècnica de Catalunya. DF - Dinàmica No Lineal de Fluids
dc.rights.accessOpen Access
dc.description.versionPostprint (published version)
local.citation.authorMellibovsky, F.; Eckhardt, B.
local.citation.publicationNameJournal of fluid mechanics

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