Near-axis asymptote of the bathtub-type inviscid vortical flows (Q5942676)

The author investigates the asymptotic behavior of a bathtub-type vortical flow near the axis. The most interesting case is that when the intensity of axial vorticity in the flow is high, and this case is specially studied by the author. The asymptotic analysis focuses on the vorticity evolution in the vicinity of axis without extending the strong vortex approximation to the drain. The analysis involves higher-order terms and indicates that the streamfunction \(\psi\) of strong vortex flow behaves as \(\psi\sim r^{4/3}z\) near the axis. This is confirmed by numerical results obtained for the bathtub flow. It is assumed that the Reynolds number is high, so that the vortex remains inviscid except, possibly, for thin boundary layers which are not specially considered in the paper.