Confusion about Coriolis

July 2000
by Robert Novella

You might think that the popularity of the weather channel would result in a much higher public saviness for meteorological concepts. While more people than ever are aware of cold fronts, dew points, jet streams, and high-pressure systems, many meteorological misconceptions are still deeply entrenched in the public consciousness. So pervasive are these misconceptions that they are propagated by people who should know better, like teachers, forecasters, professors, and even textbook authors.

How many times have you heard the myth that water in a container like a toilet or sink swirls in different directions down the drain depending on which side of the equator you are on? (supposedly, counterclockwise for those in the north and clockwise in the south) Some people even know the name of the force that is supposed to be responsible for this phenomenon, the coriolis force. The effects of this force are real, however draining toilets are essentially immune from its effects.

The coriolis force is actually a fictitious force (like the centrifugal force) since it is a byproduct of movement in an accelerating reference frame (the spinning earth). It is not a force in its own right like gravity, the electro-weak or color force. It manifests itself as a deflection of movement for objects not attached to the surface of the earth. The classic example is the counterclockwise rotation of low-pressure weather systems in the northern hemisphere. Every hurricane that plagues North America during each summer and fall are characterized by this rotation. Southern hemisphere storms also exhibit rotational movement but are clockwise. This movement is a byproduct of motion on a surface that rotates, and has been well understood since 1835 when French mathematician Gaspard Gustave de Coriolis laid out the laws of mechanics for a rotating reference frame (wouldn’t you love to have a fictitious force named after you).

Imagine a rocket firing from the equator aimed precisely at New York. Since the earth rotates once every twenty four hours and the circumference at the equator is about 24,000 miles, it is rotating at 1,000 miles-per-hour. Since New York is further north and the circumference at its latitude is less, it travels less than 1,000 mph in the course of a day (approximately 800 mph) Since the rocket has an initial eastward velocity of 1,000 mph, it maintains that speed even though the ground underneath moves progressively slower as it travels further north. This disparity between the rocket’s eastward movement and the ground’s eastward movement manifests itself as a diagonal north/east trajectory of the rocket causing it to land somewhere in New England or possibly the Atlantic ocean.

So how does this apply to rotating storms and flushing toilets? Imagine a low-pressure system. If the earth were not rotating, nearby sections of the atmosphere would be drawn directly towards it. In a rotating frame of reference, a cloud to the south of the low pressure would move north but slightly to the east of the low-pressure system due to the coriolis force. A cloud that was initially north would do the opposite. This is what creates the counterclockwise rotation in the northern hemisphere.

Since the direction of rotating large-scale air currents depends on the location relative to the equator, it has long been assumed that the same must be true for the rotation of other fluids such as flushing toilet water or draining sink water. This myth is so pervasive and taken for granted that we never consider verifying it. All it would take is a casual look down after a flush. If we did we would notice that sometimes it works, as it should, but other times it doesn’t. So what’s going on here?

The key differences between hurricanes and swirling water in the home are velocity and time. Ocean currents and weather patterns typically move much faster than water in a drain. Since the coriolis force increases with velocity, the effect in the home is greatly reduced. Furthermore, cyclonic storms and large vortices in the ocean persist for many days. Water swishing down a drain, by contrast, is a very short-lived phenomenon. The coriolis force is very feeble (1969, Adair). It is only because large weather systems are very long lived that the weak yet cumulative coriolis force can produce a noticeable effect. Draining household water simply does not persist long enough with a sufficient velocity for the coriolis force to have an impact on the direction of flow. Add to this the predominance of other much stronger forces and coriolis never really had a chance.

Ok, so what does determine the direction of rotation for draining water in the home? Primarily it is the rotation inadvertently induced in the water before it is drained. The way the sink is filled can be the determining factor as well as the eddies and vortices created by washing. For a toilet it can be the direction of the jets of water under the rim. For both cases the shape of the sink or bowl itself can have a dominating influence. For a draining pool the determining factor can be as simple as the direction the wind blows or even how the last swimmer exited the pool. Then again, if no antecedent spin was introduced or if the water has been undisturbed for a suitable period of time there might not be any visible rotation at all.

Can the coriolis force have a noticeable effect in the home? Yes, but it takes an effort very few would have the patience for or interest in. First you have to remove all sources of noise. Thermal currents and vibrations would have to be kept to a bare minimum since they can easily overwhelm any contribution by the coriolis force. The water would need to be left undisturbed for many hours to remove any trace of motion caused by filling the container. Also, the drain hole would need to be very small so the force would have enough time to build up and reveal itself. Experiments such as this have been carried out and they do indeed reveal the coriolis force. Until household sinks and toilets undergo radical structural and usage changes the myth of the coriolis effect in the home will continue to be just that, a myth.

The second most prevalent misconception about the weather I’ve come across deals with prediction. While people still bemoan the accuracy of their local weather forecasters, weather prediction has seen vast improvements over the past several decades. Satellites, computer modeling, and the science of meteorology have all conspired to produce unparalleled accuracy in short-term weather forecasting. The key phrase here, however, is “short-term.” Many people assume that long-term predictions will eventually see similar improvements. Is it not unreasonable to believe that in the future, new technology and new insights into the intricacies of Earth’s weather will allow us to make accurate predictions weeks and months in advance? Well, no. Let me be more blunt. Regardless of the technology, regardless of the new powers at our command, long-term weather prediction is inherently and forever beyond our grasp.

The key aspect about the weather that precludes long-term weather prediction is its chaotic nature. Chaotic systems in nature do not evolve in a predictable and deterministic fashion like a planet orbiting a star. If a planets velocity and distance, relative to the sun, are known, then the planet’s position can be determined decades in the future or past with near 100% accuracy. A small error in the initial conditions, like velocity, will result only in a minor error in the prediction of its orbit. Chaotic systems like the weather, human heartbeats or even the stock exchange, on the other hand, are characterized by sensitive dependence on initial conditions. Small errors introduced in measuring its initial state cause the predicted system to quickly diverge from the real one. The inevitable result is that long-term predictions for such systems are doomed to fail.

The idea that dynamic systems can be so chaotic may not sound too revolutionary but for centuries the philosophy of determinism colored our perception of how the universe works. Everything was perceived as cogs in a big machine that, given precise initial conditions, could be predicted far into the future and retrodicted far into the past with near perfect accuracy. Isaac Newton’s laws of motion produced scientific support for determinism with its unprecendentedly accurate description of planetary motions. Small errors in determining planetary motion or distance resulted in small errors in predictions even if they were years in the future (planetary motions are in fact chaotic but it takes millions of years for this to be expressed). It is thus natural to assume that similarly small errors in the initial conditions of other dynamic systems will not have a deleterious effect on the accuracy of long-term predictions. This is where sensitive dependence to initial conditions comes into play. Truly chaotic dynamic systems are so unstable, with so many variables interacting unpredictably, that the slightest inaccuracy in measurements produce errors that grow exponentially. In a brief period of time the initial uncertainty, no matter how small, expands producing errors that are as big as the phenomenon being measured.

Physicist Edward Lorenz discovered this inherently unpredictable nature of weather in 1960. Lorenz devised a rudimentary computer program to model the Earth’s atmosphere using different variables to represent pressure, humidity, and many other factors that are crucial to atmospheric dynamics. As the program ran, Lorenz could see the manifestations of the equations unfold into simple but realistic weather patterns. Lorenz stopped one run of his program prematurely to leave and upon returning started it up again at a point halfway through the previous run. To do this he manually entered the values of the various variables expecting the output to be identical to the previous run up to the point he had stopped it earlier. What he found, however, was that the program quickly diverged from the previous pattern, eventually becoming completely unrecognizable from before. At first Lorenz was puzzled; his equations were completely deterministic; the same initial conditions should produce identical results every time. He quickly realized, however, that the initial conditions were not identical. The numbers he entered were rounded versions of the numbers the program had previously been manipulating. For example, if on the first run, the value for humidity was .694233, Lorenz entered .694 for the subsequent run. At most he would be off by one part in one thousand, but such an insignificant difference between the two starting conditions produced wildly varying results. This minute
difference amounted to such a minor atmospheric disturbance that it was compared to a butterfly flapping its wings. This phenomenon soon became known as the Butterfly Effect; a concept that is embodied in the following centuries-old poem:

“For want of a nail, the shoe was lost; For want of a shoe, the horse was lost; For want of a horse, the rider was lost; For want of a rider, the battle was lost; For want of a battle, the kingdom was lost!”

The Butterfly Effect sounded the death knell for long-term weather prediction. If a measurement error as insignificant as the disturbance caused by a butterfly flapping its wings could cause a storm weeks later, then weather prediction would forever be limited. You might ask why we couldn’t just increase the precision of our measurements. Unfortunately, the relationship between measurement accuracy and predictability is not linear, it’s logarithmic (Meiss, ‘95). This means that a huge increase in precision does not produce a concomitant increase in the accuracy of prediction. For example, suppose an order of magnitude (ten times) increase in measurement precision allowed us to make quality predictions 6 days further in the future than we were capable of before. A hundred-fold increase in precision would not give us 60 days but only a 12 day improvement. Therefore great technological leaps in measurement would not buy us much. The slightest measurement errors, no matter how vanishingly small they were, would continually snowball, making predictions completely worthless very quickly. Imagine miniscule weather nanobots, numbering in the quintillions, scattered throughout our atmosphere, constantly measuring wind, temperature, humidity, pressure etc. Even this fantastic scenario would not dramatically increase our predictive powers. Every measurement made would still be an average of the tiny parcel of atmosphere in which the nanobot floated. Even the tiny errors involved in this incredible precision would ultimately doom our predictions. Clearly what we would need is infinite precision. If we knew with absolute precision the location and momentum of every particle in our atmosphere (barring any influence from outer space) we could indeed predict the weather far into the future (with a suitably powerful computer, of course). Unfortunately, this level of precision would not merely be hideously difficult or unimaginably expensive or even wildly impractical. It would be fundamentally impossible by definition, similar to exceeding the speed of light in a vacuum, going below absolute zero or getting your food exactly as you ordered it at a McDonalds drive through window.

Let’s drill down one more level to find out why infinite precision is impossible. During the development of quantum theory in the 1920’s, physicist Werner Heisenberg codified his famous principle of indeterminacy; better know as the uncertainty principle. This principle forever limited what we can know about the universe. It states that it is impossible to determine at the same time and with arbitrary accuracy pairs of physical properties dealing with space-time and energy. The classic example of these so-called “conjugate variables” are position and momentum, although many more exist. The more accurately position is determined, the less accurately momentum can be determined. The act itself of measuring one variable makes measuring the other variable increasingly inaccurate. Both values can be resolved at the same time but not with a high degree of accuracy. If position is determined precisely then nothing can be known about momentum and vice versa. This is not due to the inadequacy of the instruments at our disposal nor is it because we haven’t figured out a way to do it yet; it is a fundamental aspect of nature. Therefore, if a particle’s position and momentum can never be resolved together beyond an absolute minimum, then there will forever be an uncertainty in our measurements making long-term prediction of any chaotic system inherently impossible.

Imagine our distant descendants millions of years from now. Their technology and intellects are inconceivably advanced, virtually godlike. Even they will have no hope of accurate long-term weather predictions, and must be content to sit around and complain to each other about the poor weather forecasts.

1) Concepts in Physics: Robert K. Adair (New York: Academic Press, 1969), p. 155
2) Sci.Nonlinear Faq: James D. Meiss,
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