The bathtub vortex forms when water drains out of a container through a small drain-hole at the bottom and a dip in the water surface is formed which makes the vortex beautifully visible. This everyday phenomenon is the prototype fluid vortex and it has features in common with many flows in nature and technology.
We have worked on theory of the flow-structure and the surface shape of the bathtub vortex, and we have performed experiments, including the following surface photographs and flow-visualisations.
The free surface of a time-independent bathtub vortex in a rotating cylindrical container with a drain-hole at the bottom. The rotation rate of the container is 6 rpm (left), 12 rpm (center), and 18 rpm (right). The water in the central region is spinning fast and the depth of the surface dip increases when the rotation rate is increased.
An overlay of two flow visualisations made at 12 rpm by using a vertical light sheet through the axis of symmetry and adding fluorescent dye at the surface (red) and at the bottom inlet (green), respectively. The red dye is flowing in a thin surface layer to the central vortex core where it is diverted down-wards to the drain-hole. The free surface dip is seen above the central red region (the red pattern above the surface is due to reflections). The green dye spirals inward in the thin Ekman boundary layer at the bottom, then up-wards around the central drain-pipe forming the layered structure, and finally down the drain.
The bathtub vortex was discussed in a radio interview with BBC 4 for the science magazine program Leading Edge in October 2003, and our work was published in Physical Review Letters and Journal of Fluid Mechanics.
A. Andersen, T. Bohr, B. Stenum, J. Juul Rasmussen, and B. Lautrup, Anatomy of a Bathtub Vortex, Physical Review Letters 91, 104502 (2003) (pdf)
A. Andersen, B. Lautrup, and T. Bohr, An averaging method for nonlinear laminar Ekman layers, Journal of Fluid Mechanics 487, 81-90 (2003) (pdf)
A. Andersen, T. Bohr, B. Stenum, J. Juul Rasmussen, and B. Lautrup, The bathtub vortex in a rotating container, Journal of Fluid Mechanics 556
, 121-146 (2006) (pdf