I didn’t actually write this…

In physics, the Coriolis effect is an apparent deflection of moving objects when they are viewed from a rotating reference frame.

Newton’s laws of motion govern the motion of an object in an inertial frame of reference. When transforming Newton’s laws to a rotating frame of reference, the Coriolis force appears, along with the centrifugal force. If the rotation speed of the frame is not constant, the Euler force will also appear. All three forces are proportional to the mass of the object. The Coriolis force is proportional to the speed of rotation and the centrifugal force is proportional to its square. The Coriolis force acts in a direction perpendicular to the rotation axis and to the velocity of the body in the rotating frame and is proportional to the object’s speed in the rotating frame. The centrifugal force acts outwards in the radial direction and is proportional to the distance of the body from the axis of the rotating frame.

These three additional forces are termed either inertial forces, fictitious forces or pseudo forces. These names are used in a technical sense, to mean simply that these forces vanish in an inertial frame of reference.

The mathematical expression for the Coriolis force appeared in an 1835 paper by a French scientist Gaspard-Gustave Coriolis in connection with hydrodynamics, and also in the tidal equations of Pierre-Simon Laplace in 1778. Early in the 20th century, the term Coriolis force began to be used in connection with meteorology.

Perhaps the most commonly encountered rotating reference frame is the Earth. Moving objects on the surface of the Earth experience a Coriolis force, and appear to veer to the right in the northern hemisphere, and to the left in the southern. Exactly on the equator, motion east or west, remains (precariously) along the line of the equator. Initial motion of a pendulum in any other direction will lead to a motion in a loop. Movements of air in the atmosphere and water in the ocean are notable examples of this behavior: rather than flowing directly from areas of high pressure to low pressure, as they would on a non-rotating planet, winds and currents tend to flow to the right of this direction north of the equator, and to the left of this direction south of the equator. This effect is responsible for the rotation of large cyclones.

In a very carefully controlled experiment to remove all other forces from the system, rotation could conceivably play a role on scales as small as a bathtub. An article in the British Journal of Fluid Mechanics in the 1930s described an early attempt to do so. A few drops of ink were put into the bathtub water. It was claimed that if one observed when the ink stopped swirling, meaning the viscosity of the water had dissipated its initial vorticity (or curl; i.e.\nabla \times U = 0) then, if the plug was extracted ever so slowly so as not to introduce any additional vorticity, the tub would empty with a counterclockwise swirl in the northern hemisphere.

In reality the Coriolis effect is a few orders of magnitude smaller than various random influences on drain direction, such as the geometry of the container and the direction in which water was initially added to it. Most toilets flush in only one direction, because the toilet water flows into the bowl at an angle.  If water shot into the basin from the opposite direction, the water would spin in the opposite direction.

So popular culture is incorrect in stating that water in bathtubs or toilets always drains in one direction in the Northern Hemisphere, and in the other direction in the Southern Hemisphere as a consequence of the Coriolis effect. This idea has been perpetuated by several television programs, including an episode of The Simpsons and one of The X-Files.  In addition, several science broadcasts and publications (including at least one college-level physics textbook) have made this incorrect statement.

The Rossby number can also tell us about the bathtub. If the length scale of the tub is about L = 1 m, and the water moves towards the drain at about U = 60 cm/s, then the Rossby number is about 6 000. Thus, the bathtub is, in terms of scales, much like a game of catch, and rotation is unlikely to be important.

Some sources that incorrectly attribute draining direction to the Coriolis force also get the direction wrong. If the Coriolis force were the dominant factor, drain vortices would spin counterclockwise in the northern hemisphere and clockwise in the southern.

When the water is being drawn towards the drain, the radius of its rotation around the drain decreases, so its rate of rotation increases from the low background level to a noticeable spin in order to conserve its angular momentum (the same effect as ice skaters bringing their arms in to cause them to spin faster). As shown by Ascher Shapiro in a 1961 educational video called Vorticity, Part I, this effect can indeed reveal the influence of the Coriolis force on drain direction, but only under carefully controlled laboratory conditions. In a large, circular, symmetrical container (ideally over 1m in diameter and conical), still water (whose motion is so little that over the course of a day, displacements are small compared to the size of the container) escaping through a very small hole, will drain in a cyclonic fashion: counterclockwise in the Northern hemisphere and clockwise in the Southern hemisphere — the same direction as the Earth rotates with respect to the corresponding poles.

So the Kryptos whirlpool is symbolic of a toilet.  Dont’ argue with me, it’s science!