Rossby number

Builds on Dimensionless numbers in fluid mechanics

Definition

Consider a flow in a frame that rotates with angular speed $\Omega$ , and let $f$ be the Coriolis parameter. On a planet at latitude $\varphi$ , $f = 2 \Omega \sin \varphi$ . Let $U$ be a characteristic speed and $L$ a characteristic horizontal length of the flow. The Rossby number is $\mathrm{Ro} = \frac{U}{f L}.$

Remarks

It is a dimensionless number: $[f L] = \mathsf{T}^{-1} \mathsf{L} = [U]$ . Example: a mid-latitude weather system with $U = 10\ \mathrm{m/s}$ , $L = 10^6\ \mathrm{m}$ and $f = 10^{-4}\ \mathrm{s}^{-1}$ has $\mathrm{Ro} = 0.1$ , so rotation dominates. Non-example: $U / f$ alone is not a Rossby number; it has dimension $\mathsf{L}$ . The Rossby number is the ratio of the advective acceleration $U^2 / L$ to the Coriolis acceleration $f U$ .

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Dimensionless numbers in fluid mechanics concept
Rossby number definition

Tag	`AVSSJ9X2JN`
URI	`m2://AVSSJ9X2JN`
Kind	definition
Writing	W0 stub
MSC	76U05, 76M55, 86A10
Defines	Rossby number
Uses	Dimensionless numbers in fluid mechanics
Changed	3 November 2026

Rossby number

Definition

Remarks

Reading path

Further reading

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