Rossby number

The Rossby number (Ro), named for

, terms ${\displaystyle |\mathbf {v} \cdot \nabla \mathbf {v} |\sim U^{2}/L}$ and ${\displaystyle \Omega \times \mathbf {v} \sim U\Omega }$ in the

where U and L are respectively characteristic velocity and length scales of the phenomenon, and ${\displaystyle f=2\Omega \sin \phi }$ is the Coriolis frequency, with ${\displaystyle \Omega }$ being the angular frequency of planetary rotation, and ${\displaystyle \phi }$ 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

When the Rossby number is large (either because f is small, such as in the tropics and at lower latitudes; or because L is small, that is, for small-scale motions such as flow in a bathtub; or for large speeds), 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.^[9]

See also

• Coriolis force – Apparent force in a rotating reference frame
• Centrifugal force – Type of inertial force

References and notes