Time scales for transition in Taylor-Couette flow

The time scale for onset and decay of vortices in a Taylor-Couette system cannot be predicted from linear stability analysis, yet it is important from a practical standpoint. A two-dimensional pseudospectral direct numerical simulation was used to examine the time scales for subcritical-to-supercritical transition and supercritical-to-subcritical transition for a variety of aspect ratios (Γ = H/d = 8,16,24,32,40,∞) and radius ratios (η = 0.5, 0.7, and 0.9). A viscous time scale incorporating both the gap width, d, and the distance between the endwalls of the system, H, is most appropriate for the onset of Taylor vortices, although no time scale collapses the data for all aspect ratios and radius ratios. For decay, a viscous time scale using the gap width as the length scale collapses the data as the aspect ratio gets large. These results indicate that the onset of vortices is a consequence of the propagation of vortical structures related to the endwalls, while decay is related to viscous dissipation from the sidewalls.