Bathtub vortices

Anders Andersen (DTU and Risø), Tomas Bohr (DTU),
Jens Juul Rasmussen (Risø), and Bjarne Stenum (Risø).

Risø: Department of Optics and Fluid Dynamics, Risø National Laboratory, DK-4000 Roskilde, Denmark

DTU: Department of Physics, Technical University of Denmark, 2800 Kongens Lyngby, Denmark.

Abstract: Bathtub vortices, i.e., swirling flows with a free surface which may extend down to the outlet of the fluid container are well known. The properties of such flows are, however, to our knowledge not described in detail neither experimentally nor theoretically. The free surface appears with a very sharp tip for some parameter values, and the flow field around the tip is strongly singular. We present experimentally measured free surface profiles, flow visualisations, and measured velocity profiles for a steady bathtub vortex flow. We describe the flow theoretically, and at a distance away from the vortex center we find that the observed flow agrees with results from boundary layer theory and the theory of rotating flows. We describe how to extend the theoretical predictions to the vortex region close to the axis of rotation where standard boundary layer theory is not valid and discuss how to model the free surface shape.