Axisymmetric Hopf bifurcation in a free-surface rotating cylinder flow

Stuart James Cogan, Gregory J Sheard, Kris Ryan


Using highly resolved simulations of the axisymmetric Navier--Stokes equations and a truncated Landau model we investigate the behavior of the flow in the vicinity of the axisymmetric Hopf-type transition in an open cylinder of height-to-radius aspect ratio of~$3/2$. Rotating flows in open cylinders have many practical applications for which the knowledge of the different flow states encountered is of value. We report on the location and non-linear evolution characteristics of the bifurcation and present, for the first time, evidence that confirms that transition occurs via a non hysteretic supercritical Hopf bifurcation, and visualisations of the mode to fully define the transition.

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