THE CORiOLiS FORCE

Another apparent force is caused by Earth's rotation, one that only arises when bodies are in motion relative to the rotating Earth, and this force is known as the Coriolis force after the French engineer and scientist Gaspard-Gustave Coriolis (1792-1843). It turns out to be much more important than the centrifugal force for currents and winds, although its effects are rather subtle. The sphericity of Earth is not important in the coriolis force itself, and until we get to the section on differential rotation and Earth's sphericity in this chapter, we can imagine Earth to be a rotating disk, with the rotation axis through the North Pole at the center of the disk.

To gain an intuitive idea of what the coriolis force is, consider the (hopefully fanciful) situation in which a missile is launched from the North Pole toward the equator, as illustrated in figure 3.I.1 Once launched and above Earth's atmosphere, the missile is uninfluenced by the fact that Earth is rotating beneath it. Suppose the missile is initially aimed at Africa and that it takes about six hours for the missile to reach the equator. When the missile reaches the equator, Earth has rotated a quarter turn, but the missile has not and so it will land in South America! From the perspective of someone tracking the missile from the surface of Earth, the missile has not gone in a straight line but has veered to the right.

If a missile is fired from the equator toward the North Pole, it begins its flight with a large eastward velocity, equal to that of the surface of Earth at the equator. As the missile moves poleward, it maintains an eastward velocity (in fact, it conserves its angular momentum), which soon exceeds that of Earth beneath it. From the point of view of an observer on Earth's surface, the missile again appears to veer to the right. From the point of view of an observer on Earth, it seems that the missile has experienced a force—the coriolis force—that causes it to veer to the right. Just as with the centrifugal force, the coriolis force is something that we introduce to be able to use Newton's laws in a rotating frame of reference. It is not a real force in the sense that no other body causes it;

a brief introduction to dynamics a) Missile leaves pole aimed at Africa b) Missile goes in straight line, but Earth rotates beneath it a) Missile leaves pole aimed at Africa

b) Missile goes in straight line, but Earth rotates beneath it

c) From Earth's point of view, missile is deflected to its right
Figure 3.1. A missile launched from the North Pole toward Africa. Earth rotates beneath the missile, and the missile lands in South America. From the point of view of an observer on Earth, the missile has been deflected to its right, and the force causing that deflection is the Coriolis force.

rather, it is a manifestation of the inertial tendency of a body to go in a straight line while Earth rotates.

Let us now imagine that a missile is fired along a line of latitude, neither toward the equator nor away from it. First consider the situation in which the missile is fired in the direction of Earth's rotation. The missile is now rotating around Earth's axis of rotation faster than Earth beneath it, and so the outward centrifugal force on the missile exceeds that of an object stationary relative to Earth. Thus, the missile veers outward from the axis of rotation and so to the right of its original path. Similarly, if the missile is fired in a direction opposite to Earth's rotation, it rotates more slowly than a stationary object and so experiences a weaker centrifugal force than when it was sitting stationary on the ground. It is thus drawn inward toward the axis of rotation, and again appears to be deflected to the right relative to its direction of travel. Indeed, no matter what the missile's initial orientation, when it is in the Northern Hemisphere, it will always veer to the right; similarly, in the Southern Hemisphere, the deflection and the apparent force is always to the left of the direction of motion. Thus, in both hemispheres, a body moving away from the equator veers eastward and a body moving eastward veers toward the equator.

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