Three Hours of Stillness

The Coriolis formula, in numbers

The effect is named after Gaspard-Gustave de Coriolis, who described it mathematically in 1835 to explain why an object moving across a rotating surface appears to curve off its path. For water moving at Earth's surface, the quantity that matters is the Coriolis parameter, written f = 2Ω·sin(φ), where Ω is Earth's angular rotation rate — 7.2921159 × 10⁻⁵ radians per second — and φ is the latitude of the place. The formula says something simple: the effect is zero at the equator, where the sine of the latitude is zero, grows as you move toward the poles, and flips sign between the northern and southern hemispheres. That sign flip is exactly where the reversed-drain myth comes from.

The trouble is that the speed the formula gives is small. At 44.43 degrees north, f comes out to just over a hundred-thousandth per second — a number so small that its effect only becomes visible after water has sat motionless for hours. Physicists compare how fast water is already moving to how fast Earth's rotation would move it through a quantity called the Rossby number: Ro = U/(f·L), where U is the water's residual velocity and L is the basin's size. When Ro is far above 1, the water's existing motion wins decisively over Earth's rotation. In an ordinary sink, with a radius of a few tens of centimeters and a drain speed on the order of twenty centimeters per second, Ro comes out at several thousand — Coriolis stands no chance against the currents left by the tap or the basin's own shape.

What the two labs did differently

For the Coriolis effect to actually show, someone had to strip away everything that normally hides it. Ascher Shapiro, at MIT, published the first successful experiment in Nature in 1962: a circular, symmetric basin with a small central drain, left standing still for twenty-four to forty-eight hours before draining, so any current left over from filling it would fully die out. Only then did the drain show a consistent rotation in the direction given by the northern hemisphere — a rotation so faint that Shapiro needed a stopwatch and floating tracer particles to detect it, not the naked eye.

Three years later, a team led by Lloyd Trefethen repeated the experiment in Sydney, in the southern hemisphere, publishing the result in Nature in 1965. With the same protocol of extended stillness and the same symmetric basin, the drain vortex rotated consistently the opposite way from the one measured at MIT — independent confirmation that the sign change in Coriolis's formula corresponds to something real, not just something on paper. Neither experiment resembles an ordinary bath: both needed hours of absolute stillness, a basin built specifically for symmetry, and fine instruments to measure a rotation the naked eye cannot distinguish from the noise of residual currents.

Where it actually matters

Coriolis isn't a laboratory curiosity — at large scale it becomes the dominant force. Hurricanes rotate consistently in opposite directions in the two hemispheres for exactly this mathematical reason, because they span hundreds of kilometers and last for days, not seconds; at that scale, the Rossby number drops well below 1, and Earth's rotation wins decisively. Major ocean currents follow the same rule. The physical principle stays the same in a storm and in a sink; what separates them is scale — L and the time the motion acts over are millions of times larger in a storm, and those are exactly the terms that decide the winner in the Rossby number.

Sources

• A. Shapiro, "Bath-Tub Vortex", Nature 196, 1080–1081 (1962).
• L. M. Trefethen, R. W. Bilger, P. T. Fink, R. E. Luxton, R. I. Tanner, "The Bath-Tub Vortex in the Southern Hemisphere", Nature 207, 1084–1085 (1965).

The Coriolis parameter, stillness time, and Rossby number shown above are recomputed live from the standard formulas of geophysical fluid dynamics for whatever latitude the reader chooses — they are not values from a fixed table.