# Rossby number

From AMS Glossary

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## Rossby number

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).