title: Tangent double Hopf bifurcation in a differentially rotating cylinder flow.
abstract: A tangent double Hopf bifurcation has been found in a rotating cylinder flow driven by the counter-rotation of the top endwall. The codimension-3 tangent double Hopf point has been located using linear stability analysis. The nonlinear analysis of the multiple solutions in a neighborhood of this bifurcation point is performed by numerical solutions of the three-dimensional Navier-Stokes equations. At the tangent double Hopf point, two rotating waves and an unstable modulated rotating wave bifurcate simultaneously. A center manifold/normal form analysis is also performed, which is in very good agreement with both the linear and nonlinear computations. By a detailed exploration of the nonlinear flow, we have unraveled the complex dynamics generated by the mode competition, which is organized by the codimension-3 tangent double Hopf bifurcation.
authors.affiliation: Departament de Física Aplicada, Universitat Politècnica de Catalunya, Jordi Girona Salgado s/n, Mòdul B4 Campus Nord, 08034 Barcelona, Spain. marques@fa.upc.es
authors.forename: F
authors.initials: F
authors.lastname: Marques
authors.forename: A Yu
authors.initials: AY
authors.lastname: Gelfgat
authors.forename: J M
authors.initials: JM
authors.lastname: Lopez