Temporal stability of eccentric Taylor–Couette–Poiseuille flow

Abstract

AbstractThe 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 ${\mathit{Re}}_{z} $ is increased for any fixed eccentricity $e\leq 0. 7$, 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 $\eta = 0. 5$, increasing axial advection has a stabilizing effect for low ${\mathit{Re}}_{z} $, then a weak destabilizing effect for high enough ${\mathit{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 ${\mathit{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 ${\mathit{Re}}_{z} $ considered. Comparison with the experiment of Coney & Mobbs (Proc. Inst. Mech. Engrs, vol. 184 Pt 3L, 1969–70, pp. 10–17) for $\eta = 0. 89$ shows good agreement, despite small discrepancies attributed to finite length effects.