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C. Leclercq, B. Pier and J. Scott
Laboratoire de mécanique des fluides et d'acoustique, École centrale de Lyon – CNRS – Université Claude-Bernard Lyon 1 – INSA, 36 avenue Guy-de-Collongue, 69134 Écully cedex, France
Journal of Fluid Mechanics 733, 68–99 (2013)
The combined effects of axial flow and eccentricity on the temporal stability properties of the Taylor–Couette system are investigated using a pseudospectral method. Eccentricity is found to stabilize the Couette flow regardless of axial advection intensity. As the axial Reynolds number Re_z is increased for any fixed eccentricity e≤0.7, the critical mode switches from deformed toroidal Taylor vortices to helical structures with an increasing number of waves, and with helicity opposed to the inner-cylinder rotation. For a wide-gap configuration of radius ratio η=0.5, increasing axial advection has a stabilizing effect for low Re_z, then a weak destabilizing effect for high enough Re_z. Centrifugal effects are always destabilizing, but axial shear is responsible for the dominance of helical modes of increasing azimuthal complexity. The modes localize in the converging gap region, and the energy concentrates increasingly into axial motion for larger Re_z. Critical quantities are also computed for a small-gap case, and similar trends are observed, even though no destabilizing effect of advection is observed within the range of Re_z considered. Comparison with the experiment of Coney & Mobbs (Proc. Inst. Mech. Engrs, vol. 184 Pt 3L, 1969–70, pp. 10–17) for η=0.89, shows good agreement, despite small discrepancies attributed to finite length effects.
hal-00865631
2013c_leclercq_jfm.pdf