Rossby number
The Rossby number named for Carl-Gustav Arvid Rossby, is a dimensionless number used in describing fluid flow. The Rossby number is the ratio of inertial force to Coriolis force, terms and in the Navier–Stokes equations respectively. It is commonly used in geophysical phenomena in the oceans and atmosphere, where it characterizes the importance of Coriolis accelerations arising from planetary rotation. It is also known as the Kibel number.
The Rossby number is defined as
where U and L are respectively characteristic velocity and length scales of the phenomenon, and is the Coriolis frequency, with being the angular frequency of planetary rotation, and the latitude.
A small Rossby number signifies a system strongly affected by Coriolis forces, and a large Rossby number signifies a system, in which inertial and centrifugal forces dominate. For example, in tornadoes, the Rossby number is large, in low-pressure systems it is low, and in oceanic systems it is of the order of unity, but depending on the phenomena can range over several orders of magnitude. As a result, in tornadoes the Coriolis force is negligible, and balance is between pressure and centrifugal forces. Cyclostrophic balance also commonly occurs in the inner core of a tropical cyclone. In low-pressure systems, centrifugal force is negligible, and balance is between Coriolis and pressure forces. In the oceans all three forces are comparable. For a figure showing spatial and temporal scales of motions in the atmosphere and oceans, see Kantha and Clayson.
When the Rossby number is large, the effects of planetary rotation are unimportant and can be neglected. When the Rossby number is small, then the effects of planetary rotation are large, and the net acceleration is comparably small, allowing the use of the geostrophic approximation.
