Do baths and oceans both have swirling water?
Yes, and both hemispheres have it. Water in a bath may already have a little rotation. As it gathers toward the drain, that swirl often becomes more noticeable. Follow a white marker as it circles and moves inward.
Large ocean eddies circle too, but have no drain at the center. Their size and long duration make Earth’s rotation important. Hemisphere alone cannot predict every direction: both clockwise and counterclockwise eddies occur in each.
Try two small comparisons
- Choose the bath and change only the initial swirl direction. Can both directions drain?
- Choose the ocean. Keep the center low and switch hemispheres; then keep the hemisphere fixed and compare a low and high center.
More to explore
Look closer: observations and controls
What happens when already-turning water approaches a drain?
Removing a plug draws water inward, but does not always create a visible vortex. A little existing rotation can become more noticeable during convergence. Stirring the other way can change direction; the drain does not choose it from nothing.
Follow an outer white marker. It circles while moving inward. When outside torques are negligible, its rotation follows a conservation rule: halving radius approximately doubles sideways speed. That applies to the model’s outer region, not every point near the center.
Speed cannot grow without limit. We approximate the center with a core turning like one solid disc. Inside it, tangential speed decreases toward the axis and is zero at the center. Speed peaks at the core edge, while pressure is lowest near the axis. Those are different locations.
Rotation lowers the surface toward the center. The picture compares simplified model states; it does not solve the full formation of a real vortex from still water.
Is an ocean eddy a giant drain?
Ocean eddies occur in both hemispheres, and either hemisphere can have clockwise and counterclockwise eddies. Currents can bend and shed rings tens to hundreds of kilometers wide. Some persist for weeks or months, transporting water, heat and salt. There is no hole draining water from the center.
Our comparison uses a slow, large, mid-latitude ocean eddy. Its sea surface can be a little lower or higher at the center. Pressure differences associated with that slope act on the water. Earth’s rotation also deflects its motion. In approximate balance, the water circles along the sea-level contours. The vertical section exaggerates a very gentle real slope.
Change only the hemisphere first. For our low-centered eddies, the north turns counterclockwise and the south clockwise. Change to a new high-centered trial and both directions reverse. The hemisphere and the kind of eddy both matter. This comparison concerns ideal balanced eddies, not every current, river whirlpool or small swirl.
Change one condition at a time
- Choose the bathtub, keep its drain size fixed and reverse the initial swirl. Both directions can drain.
- Choose the ocean, keep a low center and switch hemispheres. Follow the same white marker.
- Keep the hemisphere and change the center from low to high. Why does the direction reverse again?
- For a real observation, float a small leaf in a shallow bowl, stir gently and watch the water slow down. Repeat with the opposite initial swirl.
A bath is small and drains quickly, so leftover currents and basin shape usually dominate its direction. Large ocean eddies move over long distances and times, making Earth’s rotation important. Scale relative to speed matters; entering the ocean does not force all water to turn one way.
Open: the mathematics of Rankine’s combined vortex
The circulation Γ is the line integral of velocity around the axis. Outside the core, v_t · r = Γ / 2π at every radius and the vorticity is zero; inside, the fluid rotates like a solid at the angular rate Γ / (2πR²) with uniform vorticity. Both formulas give the same speed Γ / (2πR) at r = R, so speed is continuous, though its derivative changes there, and peaks exactly there. For a bathtub-scale example: Γ ≈ 0.12 m²/s with a 2.4 cm drain radius puts R near 5.8 cm and the peak speed near 33 cm/s — enough to press the funnel about a centimetre deep.
Open: deriving the funnel surface
Radial equilibrium asks the pressure gradient to supply the centripetal acceleration, ∂p/∂r = ρ · v_t² / r, while vertically the pressure is hydrostatic, ∂p/∂z = −ρg. Dividing the two gives the free-surface slope dz/dr = v_t² / (g·r): where the spin is fastest the surface climbs steepest. Substituting the 1/r speed and integrating yields z(r) = −(v_R²/2g)(R/r)² outside the core, with a total centre dip of v_R²/g. The side view in the film exaggerates the vertical scale by a labelled factor; the shape of the curve itself comes from this integral, not from a hand-drawn bowl.
Open: the hemisphere draining legend
The story says drains turn anticlockwise in the north and clockwise in the south. Earth’s deflecting term is real, but at mid latitudes its size is only f = 2Ω·sinφ ≈ one part in ten thousand per second: over a minute of draining it deflects the flow by under one percent of its speed — far less than leftover swirl or the asymmetry of the basin. Carefully prepared symmetric containers and long settling times can reveal Earth’s weak rotational influence. Ordinary sinks are usually dominated by residual flow and geometry, so hemisphere alone cannot determine direction.
Limits of the model
The model here is steady and axisymmetric: the circulation Γ is a given parameter, and stays fixed in the angular-momentum tracking chapter. Changing its value in the side-view chapter compares separate steady solutions, not unforced growth from an unsteady flow solver. The core radius is a fixed multiple of the drain radius (a real core radius is set by the flow, viscosity and entrainment together); the drain’s volume flow is a deliberately strong teaching value so the spiral is visible within seconds; viscous diffusion, the three-dimensional flow near the drain and air entrainment are not modelled. One boundary matters especially: the model is exactly symmetric between the two spin directions.
Zero circulation is supported: water can drain radially without a rotational funnel. Markers leaving the drain are replenished at the outside as new tracer water, not teleported parcels. The bathtub display clock runs at 2.2 times physical model time; changing settings starts a new steady-field trial. The angular-momentum chapter holds circulation fixed. Varying it in the funnel chapter compares steady states, not an unforced growth of circulation. We do not lower the whole basin level or conserve finite-basin water volume; surface height references a distant level. If the predicted dip reaches the bottom, the picture reports a model limit instead of inventing an air core. See the Library of Congress on drain direction.
Open: the separate ocean-eddy model
The prescribed sea-level anomaly is η(r)=A·exp[−r²/(2L²)]. The same profile determines geostrophic tangential velocity, vθ=(g/f)·dη/dr, with f=2Ω·sinφ. Positive velocity means counterclockwise viewed from above. A low center has A<0, giving counterclockwise motion for positive northern f and clockwise motion in the south. A high center reverses both. Tracers remain at fixed radius; there is no radial drain flow.
The example uses latitudes ±35 degrees, L=50 kilometers and central anomalies of ±25 centimeters. Peak speed is about 0.36 m/s and the Rossby number about 0.085. Geostrophic balance is an approximation that neglects smaller centripetal corrections. This does not simulate eddy detachment or vertical pumping and does not apply near the equator. Parameter changes compare different balanced trials. One film second represents six ocean hours; vertical sea-level sections are greatly exaggerated relative to horizontal distance.
Sources: NOAA: What is an eddy?, NASA: The Hunt for the Right Eddy, NASA: The Eddy and the Plankton.