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Basic Physics and Dynamics of a Tornado

Posted on Monday, July 8, 2013 at 5:00 PM MST

Ever wonder what goes on inside a tornado? If you cut it all down to just basics, it's pretty simple. A tornado is just a column of air violently rotating around an area of low pressure (how they form will be discussed at some future date). They work in the exact same way as the carnival ride where you spin around really fast and the floor drops out.

As you probably know, any fluid will flow from an area of high pressure to an area of low pressure. In a tornado, all of the air, dirt, dust, debris, etc. is being pulled toward the low pressure at the center of the tornado by a force called the Pressure Gradient Force, or just PGF for short. Whatever the tornado happens to be carrying very rarely reaches the center because its velocity is so fast (just like why satellites orbiting the earth never come crashing down). Things will want to travel in a straight line, so forces are needed to change their direction. In a tornado, it's the PGF that pulls an air parcel in towards the center, and when combined with another force, effectively puts air/debris into orbit around the low pressure at the center.

As I just mentioned, a tornado does need a second force pushing out to balance the PGF. Otherwise the PGF would pull everything into the center and the tornado would collapse in on itself. Any guesses as to what that force might be? It is a force that you encounter every day in your daily lives: Centripetal Acceleration (also sometimes called the Centrifugal Force). If you're wondering where you encounter it in daily life, whenever you go around a corner in your car, centripetal acceleration is what pushes you in the opposite direction you're turning. On the carnival ride I mentioned above, centripetal acceleration is what pushes you against the wall and holds you there when the floor drops out. Centripetal acceleration in a tornado works the exact same way: it pushes air parcels out towards the edge of the circulation.

Before I go any further, I should mention that like many measurements and calculations in meteorology, these forces that I am talking about here are actually forces per unit mass (Newtons per kilogram), or accelerations (remember Newton's second law: F = ma), typically given in meters per second per second. Remember that accelerations can change the direction of an object in motion, as well as its speed. Now, let's get on to some graphics.

To throw some fancy weather terms around, a healthy tornado is said to be in Cyclostrophic Balance, which is where the PGF and Centripital Acceleration balance each other. In other words, if you add the two forces together, you will get zero. Here's what the basic force diagram of a tornado looks like:

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It is important to note that for a system in cyclostrophic balance, the Coriolis Force (force due to Earth's rotation) is so small compared to the other forces that we neglect it because it would hardly change the velocity of the air parcel at all. For tornadoes in Oklahoma, it would change the PGF and CA by about 0.0001 m/s2

For those of you who are more mathematically inclined, the equation to model a system in cyclostrophic balance is very simple and is given in polar coordinates as:

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Where V is the wind speed, R is the radius of the tornado, and the right hand side is the PGF. If you are unfamiliar with physics, the left hand side is the centripetal acceleration

We use polar coordinates instead of Cartesian coordinates because the pressure gradient and centripetal acceleration are only in the r-direction (there are no major forces in the θ-direction). In Cartesian coordinates we would have to consider the PGF and centripetal acceleration in both the x and y directions and the equation gets much uglier. This equation can also be converted very easily to natural coordinates, but most people are much more familiar with polar coordinates. This model can also be applied to eyes of hurricanes, but they don't maintain cyclostrophic balance nearly as well as tornadoes do.


Posted In: Education

Tagged: Thunderstorm, Tornado, Physics