# Rossby number

Physical key figure
Surname Rossby number
Formula symbol ${\ displaystyle {\ mathit {Ro}}}$
dimension dimensionless
definition ${\ displaystyle {\ mathit {Ro}} = {\ frac {U} {L \ cdot f _ {\ mathrm {C}}}}}$
 ${\ displaystyle U}$ characteristic speed ${\ displaystyle L}$ characteristic length ${\ displaystyle f _ {\ mathrm {C}}}$ Coriolis parameters
Named after Carl-Gustaf Rossby
scope of application geophysics

The Rossby number (after Carl-Gustaf Rossby ; not ) is a dimensionless number that is mainly used in geophysics for oceanographic and atmospheric phenomena. It can be used to assess the influence of the Coriolis effect on a rotating movement. The Rossby number describes the ratio of inertial force to Coriolis force : ${\ displaystyle {\ mathit {Ro}}}$ ${\ displaystyle R_ {0}}$

${\ displaystyle {\ mathit {Ro}} = {\ frac {F_ {traeg}} {F_ {c}}}}$

It is defined as:

${\ displaystyle {\ mathit {Ro}} = {\ frac {U} {L \ cdot f _ {\ mathrm {C}}}}}$

in dependence of

• the characteristic speed ${\ displaystyle U}$
• the characteristic length over which the observed phenomenon takes place on the earth's surface${\ displaystyle L}$
• the Coriolis parameter ,${\ displaystyle \ textstyle f _ {\ mathrm {C}} = 2 \ cdot \ omega \ cdot \ sin \ phi}$

where is the latitude. ${\ displaystyle \ phi}$

Depending on the phenomenon under consideration, the Rossby number can differ by several orders of magnitude. A small Rossby number means that the Coriolis force has a large influence on the system under consideration, while other forces predominate when the value is larger. For example, the value of the Rossby number in tornadoes is large (≈ 10 3 ), in low pressure areas it is small (≈ 0.1 to 1). The earth's rotation can be neglected for large Rossby numbers ( ). ${\ displaystyle {\ mathit {Ro}} \ gg 1}$

## literature

• Helmut Kraus: The Rossby number similarity . In: Ders .: Basics of boundary layer meteorology. Introduction to the physics of the atmospheric boundary layer and micrometeorology . Springer, Berlin 2008, ISBN 978-3-540-75980-5 , pp. 97-102.
• Horst Kurz: Turbulent diffusion in an atmospheric boundary layer with a Rossby number similarity . Dissertation, Technical University Darmstadt 1978.

## Individual evidence

1. Lakshmi H. Kantha & Carol Anne Clayson: Numerical Models of Oceans and Oceanic Processes . Academic Press, 2000, ISBN 0-12-434068-7 , Table 1.5.1, pp. 56 ( limited preview in Google Book search).