Asymptotic theory for a bathtub vortex in a rotating tank

Abstract

AbstractFluid entering the periphery of a cylindrical tank mounted on a rotating table is pumped inwards toward a central, floor drain by a potential vortex that is established in the fluid interior. We present here an asymptotic theory for small Rossby and Ekman numbers, including detailed solutions in the vortex core. Results for azimuthal velocity variation with radius agree quite well with the experiments of Andersen et al. (J. Fluid Mech., vol. 556, 2006, pp. 121–146), in spite of their free upper boundary. Modifications of the flow are presented in the instance that a short cylinder is place on the tank axis as in the work of Chen et al. (J. Fluid Mech., vol. 733, 2013, pp. 134–157). The overall flow structure found here is exactly that noted by both Andersen et al. and Chen et al.