Effect of a time-periodic axial shear flow upon the onset of Taylor vortices.

Abstract

The onset of instability in the presence of an oscillatory axial flow between concentric rotating cylinders to both axisymmetric and nonaxisymmetric disturbances is investigated on a linear basis for a narrow-gap geometry. We consider two types of axial oscillation: one is due to an oscillatory pressure gradient, and the other is due to an oscillation of the inner cylinder. For small Reynolds numbers, the results are obtained for axisymmetric disturbances by expansion in terms of the amplitude of the oscillatory flow. For finite Reynolds numbers (Re\ensuremath{\le}100), the governing equations are solved for general disturbances by a Galerkin expansion with time-dependent coefficients, and the stability boundaries of the system are determined by use of Floquet theory. The time-modulated axial flow, in general, stabilizes significantly axisymmetric disturbances except for some cases of counter-rotation with an oscillation of the inner cylinder. No subharmonic critical solutions appear for Re\ensuremath{\le}100. For Re\ensuremath{\le}100, axisymmetric disturbances are found to be more unstable than nonaxisymmetric ones when the outer cylinder is stationary, in contrast to the steady Poiseuille flow case for Re\ensuremath{\gtrsim}30. Nonaxisymmetric disturbances exhibit phase locking and jumps in the response frequency.