From AMS Glossary
A dimensionless number relating the ratio of inertial to Coriolis forces for a given flow of a rotating fluid.
Explicitly, the Rossby number is
where U is the velocity scale, f is the Coriolis parameter, and L is the horizontal length scale. This number plays a fundamental role in defining the regime of large-scale geophysical fluid dynamics. Large-scale flows are defined as those that are significantly influenced by the earth's rotation and with sufficiently large L for Ro to be order one or less (e.g., flows with sufficiently small Rossby number are in geostrophic balance).