## Wednesday, May 13, 2015

### The Hairy Ball Theorem: Guaranteeing a bad hair day somewhere

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(This week's post was inspired by a small bit in one of Dan Lewis's excellent "Now I Know" daily trivia pieces. Head on over there and sign up for his free newsletter!)

There will be weather for approximately 1 billion more years from next Thursday. Since you will have probably stopped renewing your medical certificate by then, that means you'll have to deal with weather for as long as you fly.

Why will there be weather for a billion years? Simple: the Sun is what causes weather. Through the unequal heating of the Earth's surface by sunlight, air masses are warmed at different rates, causing warm air at the equator to try to flow to the colder area at the poles and vice versa. On its voyage, it runs into a bunch of different processes that combine to create the crazy dance that is the weather (and which prevent it from ever actually completing its journey). Bill Nye, someone else whose name happens to also fit the "[Name] the [noun] Guy" pattern, has the most awesome demonstration of this flow I've ever seen, and in less than two minutes:

Why only a billion more years and not forever? Simple: the Sun will eventually make it impossible for weather to exist. Like most of us, as it ages, it expands around the waistline. Eventually, it will expand so much on its way to becoming a red giant that it will engulf the Earth. Before then, it will strip the Earth of its water and atmosphere as it boils everything off the planet. This will make the California drought look like the Amazonian rainforest, and being below the surface of the Sun will make density altitude calculations even harder for student pilots to figure out than they already are.

The Sun guarantees there will always be weather, but it doesn't say whether that weather will be bad or good. That's where the Hairy Ball Theorem kicks in.

The Hairy Ball Theorem may sound like something best not solved with an Epilator (perhaps Occam's Razor would be more help), but it's really a simple idea with profound consequences. It's actually why it is a mathematical certainty that there will be somewhere on the planet with absolutely no wind at all. Watch this video by the brilliant guys at Minute Physics to get a quick grasp on it:

What's the significance of having no wind somewhere? Besides, doesn't that happen all the time? When it's really nice out and the skies are a beautiful shade of blue, there usually isn't much of a breeze at all. That's because there's a nice high pressure system parked over top of you, and you're at the center of its circulation, where there is little to no wind. Take a look at this picture from Wunderground and note how the nice weather over the middle of the country is being brought by some high-pressure systems (like the one by north Texas and the Oklahoma panhandle and the one in northwest Nebraska):

 The blue Hs are high-pressure systems, and the red Ls are low-pressure systems.
There are two sides to every coin, and if there are places with high pressure, there must be places with low pressure. By the same token, if high pressure brings nice weather, we can expect low pressure to bring bad weather. By looking at that map, we can also see that that is generally true: most of the bad weather and rain is accompanied by big red Ls.

There's more to that map, though. Look to the center right, and notice there's a L off the coast of Virginia. It doesn't look like much now, but here's what it looked like less than one day earlier:

 Photo from NASA via Wikipedia.
That looks like an awfully angry low pressure system, and it is. It happens to be 2015's first named storm, Tropical Storm Ana, as it made its way over North Carolina. Unfortunately, Ana doesn't have a well-developed eye, but that's what is at the core of the most intense form of low-pressure systems: a hurricane.

While hurricanes are known popularly by their destructive winds covering thousands of square miles, at their core is a small area called the eye. In the wall of that eye, conveniently called the "eyewall", the most intense winds are found. And at the center of the eye is... no wind. (Or hardly any wind, at least.) It's a major cowlick on the planet that—unlike the one on top of your head—moves around. The Hairy Ball Theorem says that "every cow must have at least one cowlick," and that's an enormous one.

 Hurricane Andrew barreling toward Florida in 1992 on its way to becoming one of the most destructive hurricanes in United States history. Note the well-defined eye at the center.
The Hairy Ball Theorem is not—I repeat NOT—why there is no wind at the center of a hurricane. In fact, in the big bucket of meteorology, it isn't even a drop as far as importance. There are many, many complex reasons why storms are the way they are, and the Coriolis Effect is the major one that makes Hs cycle clockwise and Ls go counter-clockwise. The Hairy Ball Theorem says nothing about the "cowlick" or where it will be; its relevance is only that it guarantees that there will be at least one place like this somewhere on Earth.

Well, actually, it doesn't limit itself to Earth. We've found tornadoes on Mars, the Great Red Spot on Jupiter, and here's a picture of a storm on Saturn taken by NASA's Cassini spacecraft:

And a cowlick on the head of Uranus is even visible on the left side of this picture taken by the Hubble Space Telescope:
 There is a neat 2-minute movie also available for free at NASA's Hubble site.

But after all that, do not tell your flight instructor, science teacher, the person who administered your private pilot written, or anybody else that cyclonic rotation happens because of the Hairy Ball Theorem, because it doesn't. The Coriolis Effect does that, so keep your fuzzy balls to yourself. The Hairy Ball Theorem is good for two things: 1. Guaranteeing there will be a spot with no wind and 2. Making topologists giggle. That's all.

Now I'm off to eat read about the Ham Sandwich Theorem before the No Free Lunch Theorem gets in my way. See you next Wednesday!

The author is an airline pilot, flight instructor, and adjunct college professor teaching aviation ground schools. He holds an ATP certificate with a DHC-8 type rating, as well as CFI, CFII, MEI, AGI, and IGI certificates, and is a FAASafety Team representative and Master-level participant in the FAA's WINGS program. He is on Facebook as Larry the Flying Guy, has a Larry the Flying Guy YouTube channel, and is on Twitter as @Lairspeed.

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