Anatomy of a bathtub vortex

Area of Science:

• Fluid Dynamics
• Physics of Rotating Fluids

Background:

• The "bathtub vortex" is a common phenomenon observed when draining rotating fluids.
• Previous models, like Lundgren's, did not fully account for surface tension or Ekman upwelling.

Purpose of the Study:

• To experimentally and theoretically investigate the fluid dynamics of the bathtub vortex.
• To develop an improved theoretical model incorporating surface tension and Ekman upwelling.
• To analyze the bubble-forming instability at the vortex tip.

Main Methods:

• Conducted experiments on fluid draining from a rotating cylindrical container.
• Developed a theoretical model based on fluid flow observations.
• Compared experimental measurements with theoretical predictions.

Main Results:

• Identified a narrow, rapidly rotating "drainpipe" of downward flow from the surface to the drain.
• Observed slow upward flow in the surrounding region due to the Ekman layer.
• The new theoretical model, including surface tension and Ekman upwelling, showed good agreement with experimental data.
• A bubble-forming instability was observed at the needlelike surface depression tip at high rotation rates.

Conclusions:

• The study provides a comprehensive understanding of the bathtub vortex flow structure.
• The developed theoretical model accurately captures key physical phenomena, including surface tension and Ekman upwelling.
• The observed instability at the vortex tip warrants further investigation.