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Westward Movement of Tropical Cyclones Upon their Initial Inception |
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The tropical cyclones commonly known as hurricanes form off the west coast of Africa at a latitude band of 14±6 degrees north. They form as a result of pools of warm moist air at the ocean surface. When one of these pools begins to drain to a higher altitude a vortex is formed. The winds at its latitude are flowing westward so the vortex moves westward. But in addition to this wind flow there is another effect involved having to do with the angular momentum of the vortex with respect to Earth's axis.
Consider a mass of air at the Earth's surface. The radius of the Earth at the equator is 3963 miles. At an altitude of 10 miles the distance to the center of the Earth is 3973 miles. The important distance is to the Earth's axis of rotation. At 14° latitude at the Earth's surface that distance is (3963)cos(14°)=3845.3 miles. At an altitude of 10 miles that distance is (3973)cos(14°)=3855.0 miles. The ratio of these two distances is 1.002523.
At the Earth's surface a point at 14° latitude is traveling east with the Earth at a velocity of about 1006 miles per hour.
The angular momentum L of a mass m rotating about a center a distance R away with a tangential velocity v is
If a mass moves from a distance R_{0} from the center of rotation to a distance R_{1} and angular momentum is maintained then
Thus the velocity of an air mass at the surface at 14° traveling east at 1006 miles per hour falls to an eastward velocity of 1003.5 MPH. Thus it appears to be moving westward at a speed of 2.5 MPH.
Thus a newborn hurricane traveling westward with the wind at 10 MPH would accelerate to a westward speed of 12.5 MPH.
(To be continued.)
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