Bathtub vortex
Water draining through a hole in a circular basin creates a whirlpool — a vortex that forms not from the Coriolis effect (negligible at this scale) but from conservation of angular momentum. As water spirals inward, even the tiniest initial rotation gets amplified. The result: a free vortex where velocity grows as 1/r. Click and drag to add angular momentum.
vθ = Γ / 2πr (free vortex) Γ = const (Kelvin’s theorem)
Why whirlpools form
A popular myth says bathtub water drains in opposite directions in the Northern and Southern hemispheres due to the Coriolis effect. In reality, the Coriolis force is far too weak to influence water at bathtub scale. What actually creates the vortex is conservation of angular momentum. Any tiny initial rotation in the water — from how you filled the tub, a slight asymmetry in the drain, or even a gentle air current — gets amplified enormously as the water converges toward the drain.
The free vortex
In an ideal free (irrotational) vortex, the tangential velocity follows vθ = Γ/(2πr), where Γ is the circulation and r is the distance from the center. The velocity increases without bound as r approaches zero — which is why the water spins so fast near the drain. In reality, viscosity creates a small forced-vortex core where the water rotates as a solid body, preventing infinite velocities.
The funnel depression
The characteristic funnel shape at the center of a whirlpool arises from a balance between centrifugal force (pushing water outward) and gravity (pulling it down). The faster the rotation, the deeper the funnel. In the simulation, you can see this as a dark depression at the center that deepens as circulation increases.
Angular momentum amplification
Angular momentum L = mvr is conserved for each fluid parcel. As a parcel moves from radius R to radius r, its tangential velocity increases by a factor of R/r. Water starting at the edge of a 30 cm basin with a barely perceptible 1 mm/s tangential speed will be spinning at 30 cm/s — 300 times faster — when it reaches 1 mm from the drain. This dramatic amplification is why even the tiniest initial rotation creates a visible vortex.