Rossby number

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The Rossby number, named for Carl-Gustav Arvid Rossby, is a dimensionless number used in describing fluid flow, usually in geophysical phenomena in the oceans and atmosphere. It characterises the ratio of the net acceleration in a fluid to the Coriolis accelerations arising from planetary rotation. It is also known as the Kibel number.

It is defined as:

where U and L are, respectively, characteristic velocity and length scales of the phenomenon and f = 2 Ω sin φ is the Coriolis frequency, where Ω is the angular velocity of planetary rotation and φ the latitude.

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, ie 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.

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