A study of thin-walled Taylor column under the influence of rotation

An extended study of thin-walled Taylor column under the influence of rotating cylinder is presented with very consistent results in numerical simulations and laboratory experiments. In the previous set-up, the Taylor column effect is produced under the influence of protruded cylinder from the top lid, and the thin-walled Taylor column is formed by draining of the fluid at the bottom. The primary interest of this study is to investigate the influence to thin-walled Taylor column when the cylinder is exerted with a relative rotation rate under very small Rossby number (\textit{Ro}$=U/$\textit{fR}) and Ekman number (\textit{Ek}$=\nu /$\textit{fR}$^{2})$. The flow patterns are performed with different cylinder height ratios ($h$/$H)$ along with varying relative rotation ratio of cylinder to the background $\alpha =\omega /\Omega $. Steady-state solutions being solved numerically in the rotating frame are shown to have good agreements with experimental flow visualizations on the resulting appearance of deformed thin-walled Taylor columns. As a result, the thin-walled Taylor column is observed to strengthen up with increasing $\alpha $, and weakens with decreasing $\alpha $. In addition, the weakening thin-walled Taylor column is observed to experience a break through transition near the bottom, which penetration diverged the recirculating region into two portions.