Prioritize...
At the completion of this section, you should be able to discuss the meaning of an "apparent force" and how they are created. You should also be able to talk more specifically about the Coriolis force: what causes it, what are its effects, and the time/space scales on which its effects are visible (and not visible).
Read...
If you've ever been in a car that has taken a curve a bit too fast, you know that there is a definite sensation of force that pulls your body toward the outside of the curve. Have you ever thought about why you experience this sensation? There certainly is nothing actually pushing on you or the car. To set the scientific record straight, we need to start with a brief review of velocity and acceleration.
The velocity of an object is defined a vector. Remember that a vector has both a magnitude (in this case: speed) and it has direction. Acceleration, on the other hand, is a change in velocity over time, So, because velocity is a vector, acceleration must also be a vector. That means that there are two ways for your car to accelerate: 1) by changing speed; and/or, 2) by changing direction. The bottom line here is that when your car rounds the curve, there's an acceleration resulting from a continuous change in direction (even if you round the corner at a constant speed). In the spirit of Newton's Second Law of motion, the sensation that you feel pulling you outward provides evidence of a net force and acceleration at work.
But the net force and acceleration do not act outward. To unravel this apparent paradox, let's first suppose that you approach the curve determined to drive at a constant velocity. Such an attempt is ill-advised. To drive at a constant velocity means that your speed and direction cannot vary. In order for your car to safely negotiate the sharp curve in the road, the direction of his car must change continually around the bend, thus qualifying as an acceleration. In the spirit of Newton's Second Law, there must be continual acceleration towards the center of the curve. The acceleration into the curve arises from a real force between you tires and the road. If there weren't such an inward-directed force, your car would surely run straight off the road and crash. Try rounding the an ice-covered curve at the same speed to see how important this force is!
Now, you may intellectually appreciate that his car accelerates toward the center of the curve in response to this inwardly directed force between his tires and the road, but you still feel as if you were accelerating outward! As far as you are concerned, the only force of any real consequence is the force that your seat belt exerts, preventing you from sliding all the way out of the seat. This presents a quandary. You don't sense the inward acceleration, but you feel the outward force.
Centrifugal Force
The apparent outward acceleration that you perceive can be traced to your "frame of reference." By frame of reference, I mean the part of your immediate surroundings that you sense is not accelerating (the interior of your car, in this case). Indeed, you perceive that your car is not accelerating as it negotiates the curve at constant speed (even though there really is an acceleration toward the center of the curve). This perception leads you to falsely sense that some force, which acts to accelerate your body outward, is the "real" force at work. But it's not, of course. This outward-accelerating force, called the centrifugal force, is only an "apparent" force that arises from the false impression that the car's interior is not accelerating.
The key point I'm trying to make here is that our human sense of what is accelerated and what is not accelerated sometimes depends on our frame of reference. The earth revolves around the sun, yet we have absolutely no sense that we earthlings are speeding through space at about 10,000 miles an hour.
To "drive" home my point that the perception of unaccelerated surroundings can lead to false perceptions, consider that we perceive the sun "moving" across the sky on a daily basis (a false perception, of course). So, by merely standing on this planet and monitoring the sun's position during the day, you harbor the same sort of mistaken idea about what is accelerated and what is not accelerated -- just as you do when you drive around a sharp curve and your body slides outward.
There is another consequence that arises from the false sense that our earthly surroundings are unaccelerated, and it has a real impact on our observations of the direction of the wind.
Coriolis Force
Remember that I demonstrated the consequences of the pressure gradient force using a two-compartment water tank. In that experiment water flowed directly from high to low pressure over a short period of time. Air behaves much the same way on small time and spatial scales (for example, letting the air out of a balloon).
On the much longer time scales and much larger spatial scales of high and low pressure systems, air does not flow directly toward low pressure. For example, check out the 18Z surface analysis on September 8, 2011 (below). Focus your attention on the closed, circular isobars and the wind barbs around Tropical Storm Lee (its center was just off the central coast of Louisiana at this time). Note that the winds don't blow directly toward the lowest pressure located at the center. There must be another force at work. If there wasn't, the wind would all be blowing directly towards the center of the low pressure.
What is this mysterious force that prevents air from moving directly inward toward the center of lowest pressure? It's the Coriolis force, which, like the centrifugal force, falls into the category of an "apparent" force. Indeed, the Coriolis force arises simply as a consequence of the eastward rotation of our spherical earth. The Coriolis force is named after the French engineer and mathematician, Gustave Coriolis. Though Gustave is credited with the discovery of the Coriolis force as it relates to motion in the atmosphere, he was a tinkering kind of guy, studying rotating parts on machines (mid-19th century). He apparently never delved into what might happen to airborne objects moving over the rotating earth.
So, how does the Coriolis force come into play? Let's consider two points at the same longitude, one at latitude 40 degrees north (we'll call Point N) and the other at 20 degrees north (Point S). Because the latitude circle at 40 degrees north is noticeably smaller than the latitude circle at 20 degrees north, Point S must move eastward faster than Point N because it must travel a greater distance around the equatorial circle during one 24-hour revolution of the earth. Indeed, the posted speed limit for Point S is approximately 900 miles an hour, while, at 40 degrees North latitude, the eastward speed of Point N (and all other points at 40 degrees north) is about 800 miles an hour. For sake of reference, the eastward speed at the North Pole is zero.
Peculiar things happen when points on the earth's surface move at different speeds as the planet rotates on its axis. Suppose a projectile is launched northward from the equator toward latitude 40 degrees north. The projectile retains its great eastward speed as it starts its northward journey. Meteorologists refer to the projectile essentially retaining its original eastward speed as "the conservation of rotational kinetic energy." That's a mouthful, I admit, so I'll leave out the jargon to explain what's really happening. With each passing moment, the northward-moving projectile moves over ground that has an eastward speed less than its own. In effect, the projectile surges east ahead of the lagging ground below. To an observer on the launching pad, the projectile appears to swerve to the right (relative to an observer at the launching site). Please be aware that there was no error in the flight telemetry of the projectile. The apparent deflection to the observer's right was a natural consequence of our spherical, rotating earth.
Launching the projectile from north to south results in a similarly rightward deflection relative to the observer on the launching pad at 40 degrees north. The projectile, by retaining much of its original eastward speed of about 800 miles an hour, moves progressively over ground with faster eastward speed. In effect, the projectile falls behind the ground below, lagging increasingly to the west. To the observer on the launching pad at latitude 40 degrees north, the projectile again appears to deflect to the right.
Most elementary texts in meteorology try to teach the Coriolis force by simply launching a projectile from the North Pole, where the eastward speed of the ground is zero! But this case can be misleading because the "earth simply rotates underneath the southward-moving projectile," making it appear to the observer at the North Pole that the projectile deflected to the right. But such an explanation breaks down at other launch points in the northern hemisphere because the eastward speed of the ground is not zero. So the general explanation of the Coriolis force is a bit more complicated than the special case of launching a projectile from the North Pole.
No matter what direction the observer launches the projectile, the deflection will always be to his or her right in the Northern Hemisphere (check out "Explore Further..." for more on deflection of east-west moving projectiles). I can make similar arguments for the Southern Hemisphere by first noting that if an observer in space looks "up" at the South Pole, the sense of the Earth's rotation appears to be clockwise (opposite the counterclockwise sense an observer gets while looking "down" at the North Pole). Thus, deflections due to the Coriolis force in the Southern Hemisphere are to the left of the observer.
Coriolis Force Effects (and Myths)
I emphasize that the Coriolis force is not a true force in the tradition of gravity, friction, and the pressure gradient forces. It cannot cause motion. Rather, it is an apparent effect that simply results from an object moving over our spherical, rotating planet. And the Coriolis force does not discriminate. Indeed, no free-moving object, including wind and water, is exempt from its influence. However, the magnitude of the Coriolis deflection depends on a number of factors. These factors depend on 1) the latitude of the moving object, 2) the object's velocity, and 3) the object's flight time. So the question is... Does the Coriolis force have a noticeable effect on the water swirling in your drain? Or a baseball thrown from the pitcher's mound to home plate? Let's explore these questions in a bit more detail.
To begin to answer these questions, let's start with the idea that: the Coriolis force depends on the latitude of the moving object. We have already discussed that since the Earth is spherical, different latitudes are traveling at different speeds as the Earth rotates. The Coriolis deflection arises because of the difference in the velocities of these different reference frames. It turns out that near the equator these differences are small, while at the pole, the reference frame differences are large. Therefore, Coriolis deflections are largest near the Earth's poles, while near the equator they are very small. In fact, right on the equator, the deflection due to the Coriolis force is zero!
Next, let's explore the idea that the Coriolis force increases as the velocity of the object increases. To understand this claim, focus, by way of example, on south-to-north motion. Let's suppose there are two parcels of air (or projectiles) that start to move directly northward from the same latitude at the same time. Let's assume that one travels much faster than the other (remember, however, that both parcels have identical eastward speeds because they start at the same latitude). After say, seven hours of "flight time," the speedy parcel has moved much farther northward than the slower parcel. Because the ground beneath the faster parcel moves much more slowly to the east than the ground below the slower parcel, it appears that the rightward deflection of the faster parcel is greater than the deflection of the slower parcel. North-to-south motions yield the same result: as the speed of any air parcel (or projectile) increases, so does the magnitude of the acting Coriolis force (and vice verse). Similar arguments yield the same result for east-west motion.
Finally, let's think about the Coriolis deflection as a function of the object's flight time. It turns out that for typical velocities observed in nature, the time needed to observe deflection due to the Coriolis force is on the order of minutes to hours. This means that you cannot observe the Coriolis deflection of water emptying from a drain (the speed is too slow and the time is too short). This goes double for the water swirling in your toilet bowl. In such cases, water circulates in a certain direction because the basin is designed to move water in that direction (as the case for toilets) or the swirling water is simply residual motion left-over from filling the basin. I point to these specific examples because they are often misunderstood by the general population (and even some scientists!). There are many videos on the Internet that claim to show the Coriolis Effect in this manner. For example, check out this video taken in Equatorial Kenya. First off, given what you have just learned, what are the problems (there are several) with this demonstration? Second, if it is not the Coriolis force at work here, how is the water made to spin in different directions? Give it a try at home and see if you can duplicate the results.
What about objects that move faster? Let's do an actual calculation (although I'll spare you the math) for a 100 mph fast ball thrown from the pitcher's mound to home plate at Citizen's Bank Park in Philadelphia, Pennsylvania. The latitude of Philadelphia is about 40 degrees North, the speed of the baseball is 45 m/s, and the time that it takes reach home plate is approximately 0.4 seconds. Using these values, I calculate a Coriolis deflection of only 0.39 millimeters (0.015 inches)! Hardly a major-league curve ball. How about a bullet? Does a competition rifle shooter have to compensate for the Coriolis deflection when shooting at 1000 yards? For our calculation let's use a .308 caliber bullet fired at 800 m/s, and we'll assume the same latitude (40N). The flight time for the bullet is 1.14 seconds. The deflection of the bullet due to the Coriolis effect is 56.5mm (2.22 inches). For comparison, the "drop" of the bullet due to gravity at this distance is over 250 inches!
The "take away" point here is that although the Coriolis force affects all free-moving objects, these affects can be small, unless the speeds are very great or the travel time is long. The atmosphere has the advantage when it comes to the latter. Travel times for air parcels can exceed 10,000 seconds, resulting in significant Coriolis deflection. So, when estimating wind direction we will need to consider both real forces (pressure gradient and friction) as well as apparent forces (Coriolis and occasionally centrifugal). We'll cover this in the next section.
Explore Further...
Suppose that a projectile is now launched due eastward from a high tower on a platform floating over the Pacific Ocean (in the figure below, the projectile with its point toward you is the one moving eastward).
To understand what happens to the projectile, let's go back to our example of driving around a sharp curve in the road. If you negotiate the curve at the speed limit of 25 miles an hour, you feel a small outward pull in response to the centrifugal force, but it's no big deal. However, the next time you take the same route and drive around the curve, let's say your speed is a more reckless 40 miles an hour. Now you will feel a much stronger outward pull as you struggle to keep you body in proper position to steer (your tires might also squeal). Lesson learned: driving too fast around a curve throws your body outward with more force.
The eastward-launched projectile doesn't have a tightly fastened seat belt as it starts to round the latitude curve at breakneck speed. Indeed, because the projectile moves faster to the east than the Pacific Ocean on the latitude circle underneath it, it gets thrown outward from the earth's axis of rotation at a right angle (the solid arrow on the figure to your left points the way to the projectile's new position marked by the dashed circle). Such a right-angled path away from the earth's axis of rotation causes the projectile to gain altitude, of course, but it also takes it south of its original latitude (check out the figure on your left again, and note that the dashed line drawn directly downward from the projectile's new position toward the center of the earth intersects the earth's surface at a latitude south of its original launch latitude). The projectile stops its outward fling as gravity reasserts its presence, exerting a pull on the projectile in the direction back toward the exact center of the earth (once again, along the dashed line). Clearly, from the perspective of an observer on the launching platform, the projectile appears to have deflected to the right.
If a projectile is launched westward from another ocean platform floating in the Pacific, its overall eastward speed is now less than the ocean on the latitude circle below it. To understand what I mean, let's assume that the eastward speed of the earth's surface at the launching site is 500 miles an hour. Suppose the projectile is fired westward at 400 miles an hour. Thus, the overall eastward speed of the projectile is only 100 miles an hour, much lower than the eastward speed of the earth's surface on the latitude circle underneath the projectile. If you're still not convinced, think of riding on a train moving eastward at 40 miles an hour and you decide to walk to the back of the passenger car (toward the west). If you walk at a pace of three miles an hour to the west, you're overall eastward speed is 37 miles an hour. It's the same deal with the westward-moving projectile.
At any rate, with the projectile moving at an overall lesser speed, the centrifugal force weakens and the projectile moves toward the earth's axis of rotation at a right angle. In so doing, it loses altitude, of course, and it also moves northward. In other words, a dashed line drawn directly downward toward the center of the earth hits the planet's surface at an altitude north of the projectile's original launch latitude. From the perspective of an observer on the launching platform, there is an apparent deflection to the right.
If you want to read a more detailed description of the Coriolis Effect (including the mathematics) see: http://en.wikipedia.org/wiki/Coriolis_effect