Anatomy of a Bathtub Vortex

Abstract

We present experiments and theory for the "bathtub vortex," which forms when a fluid drains out of a rotating cylindrical container through a small drain hole. The fast down-flow is found to be confined to a narrow and rapidly rotating "drainpipe" from the free surface down to the drain hole. Surrounding this drainpipe is a region with slow upward flow generated by the Ekman layer at the bottom of the container. This flow structure leads us to a theoretical model similar to one obtained earlier by Lundgren [J. Fluid Mech. 155, 381 (1985)]], but here including surface tension and Ekman upwelling, comparing favorably with our measurements. At the tip of the needlelike surface depression, we observe a bubble-forming instability at high rotation rates.