Editing Rossby number (section)

== Definition and theory ==
The Rossby number (Ro, not R<sub>o</sub>) is defined as

: <math>\text{Ro} = \frac{U}{Lf},</math>

where ''U'' and ''L'' are respectively characteristic velocity and length scales of the phenomenon, and <math>f = 2\Omega \sin \phi</math> is the [[Coriolis frequency]], with <math>\Omega</math> being the [[angular frequency]] of [[planet]]ary [[rotation]], and <math>\phi</math> the [[latitude]].

A small Rossby number signifies a system strongly affected by [[Coriolis force]]s, and a large Rossby number signifies a system in which inertial and [[centrifugal force]]s dominate. For example, in [[tornado]]es, the Rossby number is large (≈ 10<sup>3</sup>), in [[low-pressure system]]s 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<sup>−2</sup>–10<sup>2</sup>).<ref name=Kantha1>{{cite book |title=Numerical Models of Oceans and Oceanic Processes |author1=Lakshmi H. Kantha |author2= Carol Anne Clayson|author2-link=Carol Anne Clayson |publisher=Academic Press |isbn=0-12-434068-7 |year=2000 |page=56 (Table 1.5.1) |url=https://books.google.com/books?id=Gps9JXtd3owC&dq=tornado+rossby&pg=PA56}}</ref> As a result, in tornadoes the Coriolis force is negligible, and balance is between pressure and centrifugal forces (called ''cyclostrophic balance'').<ref name=Holton>{{cite book |title=An Introduction to Dynamic Meteorology |year=2004 |author=James R. Holton |url=https://books.google.com/books?id=fhW5oDv3EPsC&dq=tornado+rossby&pg=PA64
|page= 64 |isbn=0-12-354015-1 |publisher=Academic Press}}</ref><ref name=Kantha2/> Cyclostrophic balance also commonly occurs in the inner core of a [[tropical cyclone]].<ref name=Adam>{{cite book |title=Mathematics in Nature: Modeling Patterns in the Natural World |author=John A. Adam |isbn=0-691-11429-3 |publisher=Princeton University Press |url=https://books.google.com/books?id=2gO2sBp4ipQC&dq=Coriolis+cyclostrophic+%22low+pressure+%22&pg=PA134 |page=135 |year=2003}}</ref> 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]]'').<ref name=Kantha2>{{cite book |title=Numerical Models of Oceans and Oceanic Processes |page=103 |author1=Lakshmi H. Kantha |author2= Carol Anne Clayson|author2-link=Carol Anne Clayson |isbn=0-12-434068-7 |year=2000 |publisher=Elsevier |url=https://books.google.com/books?id=Gps9JXtd3owC&dq=Coriolis+cyclostrophic+%22low+pressure+%22&pg=PA103}}</ref> For a figure showing spatial and temporal scales of motions in the atmosphere and oceans, see Kantha and Clayson.<ref Name=Kantha3>{{cite book |author=Lakshmi H. Kantha |author2= Carol Anne Clayson |author2-link=Carol Anne Clayson|isbn=0-12-434068-7 |year=2000 |title=Numerical Models of Oceans and Oceanic Processes |page=55 (Figure 1.5.1) |publisher=Elsevier |url=https://books.google.com/books?id=Gps9JXtd3owC&dq=tornado+rossby&pg=PA56}}</ref> 

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 [[Coriolis_force#Draining_in_bathtubs_and_toilets|flow in a bathtub]]; or for large speeds), the effects of [[planet]]ary [[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|geostrophic approximation]].<ref name=Barry>{{cite book |title=Atmosphere, Weather and Climate |author=Roger Graham Barry & Richard J. Chorley |url=https://books.google.com/books?id=MUQOAAAAQAAJ&dq=Coriolis++%22low+pressure%22&pg=PA115 |page=115 |isbn=0-415-27171-1 |year=2003 |publisher=Routledge}}</ref>