Bifurcations of Taylor-Couette Flow Subject to a Nonaxisymmetric Coriolis Force
Taylor-Couette flow, the flow between concentric rotating cylinders, subject to a nonaxisymmetric Coriolis force was studied experimentally. The system consists of the Taylor-Couette apparatus placed on a turntable so that the rotation axis of the inner-cylinder is orthogonal to the axis of the turntable. The outer-cylinder does not rotate about its axis. The system is thus controlled by two dimensionless parameters: the Reynolds number, Re, which scales the inner-cylinder frequency; and Omega, which scales the turntable frequency. The Coriolis force is induced by the interaction between the flow velocity field and the rotational field of the turntable. The orthogonal relation between the inner-cylinder rotation axis and the turntable axis creates a nonaxisymmetric Coriolis force. To first order in Omega, the Coriolis force induces an axial flow, whose amplitude varies sinusoidally about the azimuth, on the base flow. The system was studied by seeding the flow with reflective platelets. A time series of the reflectance was statistically analyzed to determine the location of bifurcations in the flow as Omega and Re were varied. The first set of experiments was the "scan" in which a broad region of Omega -Re space was explored. The scan revealed the general location of the bifurcation boundaries and motivated the second group of experiments. These experiments, designed to determine the boundaries more precisely, yielded a bifurcation map of the system. The bifurcation map revealed that the Coriolis force alters the ordinary Taylor-Couette system: as Re is increased, the first two flow bifurcations are delayed as a function of Omega. For low Omega there is a region of disordered flow within the time-periodic state. The flow thus displays re-emergent order as a function of either Re or Omega. As Omega is increased, the bifurcation boundaries converge and the disordered state becomes more turbulent. The flow displays turbulence at an order of magnitude lower in Re than that for the ordinary system. Beyond the convergence of the boundaries, the flow bifurcates directly to turbulence from the base flow state. The dynamics are attributed to broken axisymmetry and competition between the axial and azimuthal modes.
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- FLOW STABILITY;
- Physics: Radiation