The Coriolis Force

I am often asked by students whether their toilet bowl will flush clockwise or counterclockwise in the southern hemisphere, or whether it will flush straight down in Ecuador. This would, of course, be important information if you were ever kidnapped and blindfolded and dropped off in a strange land. If we assume a commode of conventional size, then this “toilet bowl test” will fail because the answer lies in the manufacturer’s design. But if your northern hemisphere toilet bowl were a few hundred miles in diameter then the Coriolis force of the rotating Earth would easily overcome the random water currents, and force the bowl to empty its contents in a counter clockwise swirl. If you have southern hemisphere friends with an equally large toilet, then theirs would indeed empty in the opposite (clockwise) direction.

The circulation within oversized flush toilets is a natural consequence of motion on the surface of an object that rotates. We owe our detailed understanding of the effect to the work of Gaspard Gustave de Coriolis who, in 1831, presented details of the laws of mechanics in a rotating reference frame to the Academie des Sciences in Paris. Earth’s surface provides an excellent place to demonstrate why the origin of the Coriolis force is relatively simple. Our planet rotates on its axis approximately once every 24 hours. In that 24 hour period, objects on Earth’s equator travel a circle with a circumference of nearly 25,000 miles, which corresponds to a speed of a more than 1,000 miles per hour. By 41° north, the latitude of New York City and the American Museum of Natural History, the circumference traveled is only about 19,000 miles. The west-to-east speed is now approximately 800 miles per hour. As you continue to increase in Earth latitude (north or south of the equator) your west-to-east speed decreases until it hits exactly zero miles per hour at the poles. (For this reason, most satellites are launched as close to the equator as possible, which enables them to get a good “running start” in their eastward orbits.

Imagine a puffy cloud in the northern hemisphere and a meteorological low pressure system directly to its north. The cloud will tend to move toward the low. But during the journey its greater eastward speed will enable the cloud to overtake the low, which is itself in motion, and end up east of its destination. Another puffy cloud that is north of the low will also tend to move toward the low, but will naturally lag behind and end up west of its destination. To an unsuspecting person on Earth’s surface, these curved north-south paths would appear to be the effects of a mysterious force (the Coriolis force) yet no true force was ever at work.

When many puffy clouds approach a low pressure system from all directions you get a merry-go-round of counter-clockwise motion, which is better known as a cyclone. In extreme cases you get a monstrous hurricane with wind speeds upwards of a hundred miles per hour. For the southern hemisphere the same arguments will create a cyclone that spirals clockwise. The military normally knows all about the Coriolis force and thus introduces the appropriate correction to all missile trajectories. But in 1914, from the annals of embarrassing military moments, there was a World War I naval battle between the English and the Germans near the Falklands Islands off Argentina (52° south latitude). The English battle cruisers Invincible and Inflexible engaged the German war ships Gneisenau and Scharnhorst at a range of nearly ten miles. Among other gunnery problems encountered, the English forgot to reverse the direction of their Coriolis correction. Their tables had been calculated for northern hemisphere projectiles, so they missed their targets by even more than if no correction had been applied. They ultimately won the battle against the Germans with about sixty direct hits, but it was not before over a thousand missile shells had fallen in the ocean.

In high school I knew all about the Coriolis force, but I never had the opportunity to test it on something as large as a swimming pool until the summer after my junior year when I worked as a lifeguard. At the mid-summer cleaning, I opened the drain valve to the pool and carefully observed the circulation. The water funneled in the “wrong” direction—clockwise. The last I had checked, I was life-guarding in Earth’s northern hemisphere so I was tempted to declare Coriolis forces to be a hoax. But a fast “back of the envelope” calculation verified that the difference in Coriolis velocity across the pool was a mere ½ inch per minute. This is slow. The water currents from somebody just climbing out of the pool, or even a gentle breeze across the water’s surface would easily swamp the effect and I would end up with clockwise one half the time and counterclockwise the other half of the time. A proper experiment to demonstrate the insignificance of the Coriolis forces would require that I empty and refill the pool dozens of times. But each try would dump 15,000 cubic feet of water and diminish my job security. So I didn’t.

The air circulation near a high pressure systems, which are inelegantly known as anticyclones, is a reverse picture of our cyclone. On Earth, these high pressure systems are the astronomer’s best friend because they are typically devoid of clouds. The surrounding air still circulates, but it does so without the benefit of clouds as tracers of the air flow. The circulation around low and high pressure systems, known as geostrophic winds, presents us with the paradox that Coriolis forces tend to move air along lines of constant pressure (isobars) rather than across them.

Now imagine, if you will, a place that is not only fourteen hundred times larger than Earth, but has an equatorial speed that is about twenty-five times as fast, and has a deep, thick, colorful atmosphere. That place is the planet Jupiter, where a day lasts just 9 hours and 56 minutes. It is a cosmic garden of atmospheric dynamics where all rotationally induced cloud and weather patterns are correspondingly enhanced. In the most striking display of the Coriolis force in the entire solar system, Jupiter lays claim to the largest, most energetic, and longest-lived storm ever observed. It is an anticyclone that looks like a great red spot in Jupiter’s upper atmosphere. We call it Jupiter’s Great Red Spot. Discovered in the mid 1660s by the English physicist Robert Hooke and separately by the Italian astronomer Giovanni Cassini, the feature has persisted for over 300 years. It was not until the twentieth century when the Dutch-born, American astronomer Gerard Kuiper was the first to supply the modern interpretation of the Spot as a raging storm.

The Great Red Spot, by the way, is bigger than Earth, although its size and shape has varied over the years. It lives in Jupiter’s southern hemisphere and rotates counterclockwise, which immediately tells us we have a high pressure system. The coloration, from orange-red to a barely visible pale cream, is generally attributed to various concentrations of phosphorus and sulfur compounds. Close-up images from the Voyager flyby missions of the late 1970s revealed a maelstrom of colorful curlicues at the interface of the Great Red Spot and the surrounding atmosphere. There were also strikingly resolved horizontal belts and zones interlaced with countless smaller cyclones and anticyclones that give Jupiter the appearance of an archaeological cross section of a Big Mac hamburger from McDonald’s, bun included. Above all else, however, the Voyager data posed renewed theoretical challenges. It resolved Jovian features down to twenty miles in diameter—astonishingly small when one remembers Jupiter’s size relative to Earth. Models of cosmic phenomena are often clean and tidy until they are tested outside of the limits in which they were formulated. Higher image resolution is one such example. When this happens, many models are discarded, others are modified, while some are freshly invented, but jumps in resolution have always been followed by a deeper understanding of the universe.

Whatever else a model of Jupiter’s atmosphere is designed to explain, it should as a minimum, account for basic properties of the Great Red Spot such as its longevity, and perhaps its distinguished size, and that it is an anticyclone. An ideal model would be able to account for all atmospheric motion on Jupiter. The tools available to the theorist are Newton’s laws of motion as adapted to the properties of gases and liquids—otherwise known as fluid mechanics.

Contemporary models do capture the basic features of the Great Red Spot, but very little is known about the structure of Jupiter’s under-layers. Jupiter radiates more heat than it receives from the Sun, and there are enormous thermal reservoirs in Jupiter’s interior that can drive atmospheric flow patterns. One source is the radioactive decay of trace elements while another is the leftover heat form Jupiter’s initial contraction from a proto-planetary cloud to a planet in the early solar system. The sustaining source of energy for the Spot could also (or instead) be tapped from other sources. On Earth, hurricanes are partially driven by the latent heat released to the atmosphere when rain drops condenses out of the air. A similar mechanism may dominate in Jupiter’s atmosphere as its gases condense toward its liquid interior. The Spot has also been observed (and successfully modeled) to dine upon smaller turbulent eddies in its vicinity. This cannibalistic behavior is yet another source of energy. Clues to the deeper cloud layers will almost certainly be gained when the spacecraft Galileo passes Jupiter (in December 1995) and parachutes a mini-probe that will measure temperature, density, composition, wind speeds, and lightning events as it descends through the outer atmosphere.

For now, there is no reasonable hope of describing every one of Jupiter’s surface features in detail. A more realistic approach is to construct an atmospheric model that provides a statistically equivalent picture of Jupiter’s surface features. In other words, a model of a Big Mac can approximate all Big Macs even though it may not look like any one in particular.

One nagging problem with models that always produce a single, sustained anticyclone is the blunt reality that Jupiter’s northern hemisphere is devoid of a twin Great Red Spot. Clearly, if models show that big spots are inevitable, then the north ought to have one too. Elsewhere in the solar system, the Coriolis force has given rise to a great dark spot on Neptune. We call it Neptune’s Great Dark Spot. Like Jupiter’s Great Red Spot, it is an anticyclone of epic proportions in Neptune’s southern hemisphere that appears without a twin in the north. This is a problem that may require an as yet unexplored north-south asymmetry in both Jupiter’s and Neptune’s internal structure. One way to induce such an asymmetry would be to survive a cosmic collision in one of your two hemispheres. The July 1994 encounter between Jupiter and the dozens of crumbled comet parts from Shoemaker-Levy 9 left visible and sustained scars on Jupiter’s outer gaseous surface. The long-term effects of this impulse of deposited energy remains to be seen. Will the scars form stable new structures among the cloud-tops? Or will the scars dissipate completely into the atmosphere? For the moment, feel free to consider the new blemishes to be extra ingredients in your hamburger.