Cyclone Consequences
A curious meteorological application of this theorem involves considering the wind as a vector defined at every point continuously over the surface of a planet with an atmosphere. As an idealisation, take wind to be a two-dimensional vector: suppose that relative to the planetary diameter of the Earth, its vertical (i.e., non-tangential) motion is negligible.
One scenario, in which there is absolutely no wind (air movement), corresponds to a field of zero-vectors. This scenario is uninteresting from the point of view of this theorem, and physically unrealistic (there will always be wind). In the case where there is at least some wind, the Hairy Ball Theorem dictates that at all times there must be at least one point on a planet with no wind at all and therefore a tuft. This corresponds to the above statement that there will always be p such that f(p) = 0.
In a physical sense, this zero-wind point will be the eye of a cyclone or anticyclone. (Like the swirled hairs on the tennis ball, the wind will spiral around this zero-wind point - under our assumptions it cannot flow into or out of the point.) In brief, then, the Hairy Ball Theorem dictates that, given at least some wind on Earth, there must at all times be a cyclone somewhere. Note that the eye can be arbitrarily large or small and the magnitude of the wind surrounding it is irrelevant.
This is not strictly true as the air above the earth has multiple layers, but for each layer there must be a point with zero horizontal windspeed.
Read more about this topic: Hairy Ball Theorem
Famous quotes containing the word consequences:
“The middle years are ones in which children increasingly face conflicts on their own,... One of the truths to be faced by parents during this period is that they cannot do the work of living and relating for their children. They can be sounding boards and they can probe with the children the consequences of alternative actions.”
—Dorothy H. Cohen (20th century)