Math in the News: Issue 88


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In this issue of Math in the News we examine the Polar Vortex. We examine the physics of the cyclonic winds that make up the Polar Vortex and under what conditions the current expansion of Arctic weather affects a large part of the United States.

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Math in the News: Issue 88

  1. 1. Examining the Polar Vortex Math in the News Issue 88
  2. 2. Polar Vortex The bitterly cold winter of 2014 that has affected much of the U.S. is due in part to the Polar Vortex. To learn more about this weather phenomenon, click on the video.
  3. 3. Polar Vortex A Polar Vortex is a swirling mass of wind that circulates around the polar regions of the Earth. To better understand the forces at work in this swirling mass, let’s look at a simpler example of circular motion.
  4. 4. Polar Vortex Imagine a ball of mass m circling around a center point. The radius of the circle is r and the speed of the ball is v. Its centripetal force, which keeps the ball going in a circular motion, is shown in this equation.
  5. 5. Polar Vortex Let’s rewrite the equation to isolate the speed of the swirling air mass. The result is a radical function. It tells us that the speed of a Polar Vortex is, among other things, a function of its mass. m•v F= r ¯ v= 2 F •r m
  6. 6. Polar Vortex The mass of the swirling winds is not an isolated object, as in the ball rotating around a center point. But the column of air does have mass.
  7. 7. Polar Vortex The mass is based on the air density. The product of air density and the volume of air results in the mass of the Polar Vortex. Mass = Density • Volume m = r •V
  8. 8. Polar Vortex When the air density increases, so does the mass of the column of air. Going back to our velocity equation, you can see that the graph of the velocity-versusmass equation results in a decreasing velocity for an increasing mass. m = r •V
  9. 9. Polar Vortex The result of a highpressure system is that the speed of the Polar Vortex decreases. There is less force containing the Polar Vortex.
  10. 10. Polar Vortex With a decreased force containing the Vortex, there is a greater likelihood of the polar winds seeping out beyond the Arctic. And this is what has happened.
  11. 11. Polar Vortex In fact, because the air pressure isn’t uniform, the result is a wobbly Polar Vortex that spreads beyond its usual limits.
  12. 12. Polar Vortex This isn’t just wind that’s moving into the U.S. It’s Arctic weather that’s seeping in. This is why temperatures have dropped so dramatically.
  13. 13. Polar Vortex Eventually the air pressure will normalize and the Polar Vortex will return to its usual size and expanse.