The Cyclostrophic Wind Equation

Cyclostrophic flow is a fairly common flow in the atmosphere. This balance involves two forces in the n equation of motion, those being the following:

The centrifugal force: The pressure gradient force:

With the balance between the pressure gradient force in the n equation of motion and the centrifugal force, this constricts the possible types of flow to two types. The flow can be either cyclonic or anti-cyclonic with a circular motion as a result of the centrifugal force. However, the pressure gradient force always points inward, making the center of circulation an area of low pressure. Since only two forces are considered, there are certain assumptions the also have to be made. The flow must be frictionless, always parallel to the height contours, and the scale of the flow is either small in scale or near the equator, where the coriolis force is essentially zero. The following picture illustrates cyclostrophic flow:

rT > 0 < 0 rT < 0 > 0

When we assume that a flow is cyclostrophic in nature, the coriolis force is defined as being zero. Therefore, a method must exist to determine if the coriolis force can be neglected. If the ratio of the centrifugal force to the coriolis force is large, then the cyclostrophic assumption can be made. This ratio, called the Rossby number is defined below:

Ro is the Rossby number

There are some real world applications to cyclostrophic flow. Small scale circulations, such as tornados, waterspouts, and dust devils are small enough so that the coriolis force can be neglected. However, tornados typically have a cyclonic circulation associated with them, because the rotation of the mesocyclone that spawns the tornado is cyclonic. However, waterspouts and dust devils are not as constrained to the weather systems that spawn them. Both of these circulations have been observed to be both cyclonic and anti-cyclonic.

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