A Bathtub Vortex under the Influence of a Taylor Column in a Rotating Tank

Numerical simulations and laboratory experiments were conducted to investigate a bathtub vortex under the influence of a Taylor column in a rotating tank. A central drain hole is placed at the bottom of the tank and a top-down cylinder is suspended from the rigid lid. We examine the effects of the Rossby number, \textit{Ro} and the Ekman number, \textit{Ek}. Steady-state solutions are shown to have good agreements with flow visualizations and PTV measurements. It is found that at \textit{Ro}$\sim $10$^{-2}$, a bottom Ekman pumping forms a classic one-celled structure for the case of no suspended cylinder $h/H$=0, while for various $h/H\ne $0, the strong interaction of the bathtub vortex and Taylor column results in a two-celled structure with an inner Ekman pumping and an outer Taylor column induced upwelling. In $h/H\ne $0, the Taylor wall separates the vortex into an inner and an outer region, but allows the outer fluid to flow into the inner region through a top and a bottom gap which can be classified into two and three flow paths, respectively. Moreover, the individual flow rate of each path and the weaker influence of the Taylor column at \textit{Ro}$\sim $1 and $\sim $10$^{2}$ are also discussed. Finally, we observe that the vorticity strength of the vortex exhibits the relationship with a dimensionless group$\sqrt {fQ/gH^2(1-h/H)} $.