This is a Rankine combined vortex: a solid-body core of radius r₀ (v = Ω·r, spinning like a rigid disk) surrounded by a potential (free) vortex outside it, where angular momentum is conserved along a streamline: v·r ≈ const = Ω·r₀². That's why the classic 1/r velocity law only holds outside the core — right at the center r→0 would send v to infinity, which real viscous fluid can't do, so it rotates as a rigid body instead.
The free-surface shape comes from balancing centrifugal acceleration against gravity along the surface: dz/dr = v(r)²/(g·r). Integrating this numerically from the center outward gives a shallow parabolic bowl inside the core and a much steeper, near-1/r² funnel wall just outside it — the visible "hole" of a whirlpool sits right at the core boundary.
Floating tracers drift inward under mass-conservation radial inflow (v_r ∝ 1/r, since the same volume flux crosses ever-smaller circles) while spinning per the Rankine profile — so they visibly speed up as they approach the core, exactly as debris does above a bathtub drain.
- Raise outlet flow to strengthen circulation Γ and deepen the funnel.
- Distinct from a tornado: this is a liquid free-surface vortex driven by drain-induced angular momentum conservation, not an atmospheric pressure-driven vortex.