Numerical Study on the Motion of Azimuthal Vortices in Axisymmetric Rotating Flows

A rich phenomenon in the dynamics of azimuthal vortices in a circular cylinder caused by the inertial oscillation is investigated numerically at high Reynolds numbers and moderate Rossby numbers. In the actual spin-up flow where both the Ekman circulation and the bottom friction effects are included, the first appearance of a seed vortex is generated by the Ekman boundary-layer on the bottom wall and the subsequent roll-up near the corner bounded by the side wall. The existence of the small vortex then rapidly propagates toward the inviscid region and induces a complicated pattern in the distribution of azimuthal vorticity, i.e. inertial oscillation. The inertial oscillation however does not deteriorate the classical Ekman-pumping model in the time scale larger than that of the oscillatory motion. Motions of single vortex and a pair of vortices are further investigated under a slip boundary-condition on the solid walls. For the case of single vortex, repeated change of the vorticity sign is observed together with typical propagation of inertial waves. For the case of a pair of vortices with a two-step profile in the initial azimuthal velocity, the vortices' movement toward the outer region is resisted by the crescent-shape vortices surrounding the pair. After touching the border between the core and outer regions, the pair vortices weaken very fast.