stylistic:style_transfer, information:classification, information:extraction
Length scales and the Rossby number

The time, space, and velocity scales are important in determining the importance of the Coriolis force. Whether rotation is important in a system can be determined by its Rossby number, which is the ratio of the velocity, U, of a system to the product of the Coriolis parameter, f = 2 ω sin φ {\displaystyle f=2\omega \sin \varphi \,}, and the length scale, L, of the motion:

Hence, it is the ratio of inertial to Coriolis forces; a small Rossby number indicates a system is strongly affected by Coriolis forces, and a large Rossby number indicates a system in which inertial forces dominate. For example, in tornadoes, the Rossby number is large, so in them the Coriolis force is negligible, and balance is between pressure and centrifugal forces. In low-pressure systems the Rossby number is low, as the centrifugal force is negligible; there, the balance is between Coriolis and pressure forces. In oceanic systems the Rossby number is often around 1, with all three forces comparable.

An atmospheric system moving at U = 10 m/s (22 mph) occupying a spatial distance of L = 1,000 km (621 mi), has a Rossby number of approximately 0.1.

A baseball pitcher may throw the ball at U = 45 m/s (100 mph) for a distance of L = 18.3 m (60 ft). The Rossby number in this case would be 32,000 (at latitude 31°47'46.382").

Baseball players don't care about which hemisphere they're playing in. However, an unguided missile obeys exactly the same physics as a baseball, but can travel far enough and be in the air long enough to experience the effect of Coriolis force. Long-range shells in the Northern Hemisphere landed close to, but to the right of, where they were aimed until this was noted. (Those fired in the Southern Hemisphere landed to the left.) In fact, it was this effect that first drew the attention of Coriolis himself.