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T. B. Benjamin, “Bifurcation Phenomena in Steady Flows of a Viscous Fluid. I. Theory,” Proceedings of the Royal Society A, Vol. 356, No. 1696, 1978, pp. 1-26. doi:10.1098/rspa.1978.0028

has been cited by the following article:

• TITLE: Time-Dependent Ferrofluid Dynamics in Symmetry Breaking Transverse

  AUTHORS: Sebastian Altmeyer

  KEYWORDS: Taylor-Couette Flow; Ferrofluids; Reynolds Number; Symmetry Breaking; Rotating System and Boundary Layer

  JOURNAL NAME: Open Journal of Fluid Dynamics, Vol.3 No.2, June 26, 2013

  ABSTRACT: We investigate the Taylor-Couette flow of a rotating ferrofluid under the influence of symmetry breaking transverse magnetic field in counter-rotating small-aspect-ratio setup. We find only changing the magnetic field strength can drive the dynamics from time-periodic limit-cycle solution to time-independent steady fixed-point solution and vice versa. Thereby both solutions exist in symmetry related offering mode-two symmetry with left-or right-winding characteristics due to finite transverse magnetic field. Furthermore the time-periodic limit-cycle solutions offer alternately stroboscoping both helical left-and right-winding contributions of mode-two symmetry. The Navier-Stokes equations are solved with a second order time splitting method combined with spatial discretization of hybrid finite difference and Galerkin method.