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).