Rossby number

 ( Atmospheric Dynamics ) 

The Rossby number ( Ro), 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 $|\backslash mathbf\{v\}\; \backslash cdot\; \backslash nabla\; \backslash mathbf\{v\}|\; \backslash sim\; U^2\; /\; L$ and $\backslash Omega\; \backslash times\; \backslash mathbf\{v\}\; \backslash sim\; U\backslash Omega$ in the Navier–Stokes equations respectively.

Pronab K Banerjee (2025). 9788177646535, Allied Publishers Pvt. Ltd.. . ISBN 9788177646535

It is commonly used in geophysics phenomena in the oceans and atmosphere, where it characterizes the importance of Coriolis effect arising from rotation. It is also known as the Kibel number.

B. M. Boubnov, G. S. Golitsyn (1995). 9780792333715, Springer. . ISBN 9780792333715

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Definition and theory The Rossby number (Ro, not R_o) is defined as

$\backslash text\{Ro\}\; =\; \backslash frac\{U\}\{Lf\},$

where U and L are respectively characteristic velocity and length scales of the phenomenon, and $f\; =\; 2\backslash Omega\; \backslash sin\; \backslash phi$ is the Coriolis frequency, with $\backslash Omega$ being the angular frequency of rotation, and $\backslash phi$ the latitude.

A small Rossby number signifies a system strongly affected by , and a large Rossby number signifies a system in which inertial and centrifugal forces dominate. For example, in , the Rossby number is large (≈ 10³), in low-pressure systems it is low (≈ 0.1–1), and in oceanic systems it is of the order of unity, but depending on the phenomena can range over several orders of magnitude (≈ 10⁻²–10²).

As a result, in tornadoes the Coriolis force is negligible, and balance is between pressure and centrifugal forces (called cyclostrophic balance).

James R. Holton (2025). 9780123540157, Academic Press. . ISBN 9780123540157

Cyclostrophic balance also commonly occurs in the inner core of a tropical cyclone.

John A. Adam (2025). 9780691114293, Princeton University Press. . ISBN 9780691114293

In low-pressure systems, centrifugal force is negligible, and balance is between Coriolis and pressure forces (called geostrophic balance). In the oceans all three forces are comparable (called cyclogeostrophic balance).

(2025). 9780124340688, Elsevier. . ISBN 9780124340688

For a figure showing spatial and temporal scales of motions in the atmosphere and oceans, see Kantha and Clayson.

Lakshmi H. Kantha (2025). 9780124340688, Elsevier. . ISBN 9780124340688

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 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 wind.

Roger Graham Barry & Richard J. Chorley (2025). 9780415271714, Routledge. . ISBN 9780415271714

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See also

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References and notes

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Further reading For more on numerical analysis and the role of the Rossby number, see:

• Dale B. Haidvogel & Aike Beckmann (1998). 9781860941146, Imperial College Press. . ISBN 9781860941146
• Zygmunt Kowalik & T. S. Murty (1993). 9789810213343, World Scientific. . ISBN 9789810213343

For an historical account of Rossby's reception in the United States, see

• Jeffery Rosenfeld (2025). 9780738208916, Basic Books. . ISBN 9780738208916

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