State selection in Taylor-vortex flow reached with an accelerated inner cylinder

Abstract

The selection of the axial wavelength in axisymmetric Taylor-vortex flow was studied by numerical experiments where the inner cylinder speed was linearly increased from subcritical to supercritical values over a finite ramp time to values not far above $\hbox{\it Re}_c$. For impulsive increases of the inner cylinder speed (zero ramp time) the preferred axial wavelength was less than the critical wavelength. As the ramp time was increased, the preferred axial wavelength increased and approached the critical wavelength, so that for very slow increases of the inner cylinder speed the preferred axial wavelength was equal to the critical wavelength. A linear model was developed which revealed that a linearly increased inner cylinder speed resulted in a delayed growth for each of the amplitudes of the modes. When the ramp time was sufficiently large, the amplitude of the mode with the critical wavelength was delayed the least from growing to high amplitudes. This mode then self-interacted and saturated resulting in steady Taylor-vortex flow. Finally, nonlinear effects and state selection are discussed from the point of view of nonlinear dynamics.