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The Coriolis frequency ''ƒ'', also called the Coriolis parameter or Coriolis coefficient, is equal to twice the rotation rate ''Ω'' of the Earth multiplied by the sine of the
latitude In geography, latitude is a coordinate that specifies the north–south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pole ...
\varphi. :f = 2 \Omega \sin \varphi.\, The rotation rate of the Earth (''Ω'' = 7.2921 × 10−5 rad/s) can be calculated as 2''π'' / ''T'' radians per second, where ''T'' is the rotation
period Period may refer to: Common uses * Era, a length or span of time * Full stop (or period), a punctuation mark Arts, entertainment, and media * Period (music), a concept in musical composition * Periodic sentence (or rhetorical period), a concept ...
of the Earth which is one ''sidereal'' day (23 h 56 min 4.1 s). In the midlatitudes, the typical value for f is about 10−4 rad/s. Inertial oscillations on the surface of the earth have this frequency. These oscillations are the result of the Coriolis effect.


Explanation

Consider a body (for example a fixed volume of atmosphere) moving along at a given latitude \varphi at velocity v in the earth's rotating reference frame. In the local reference frame of the body, the vertical direction is parallel to the radial vector pointing from the center of the earth to the location of the body and the horizontal direction is perpendicular to this vertical direction and in the meridional direction. The Coriolis force (proportional to 2 \, \boldsymbol), however, is perpendicular to the plane containing both the earth's angular velocity vector \boldsymbol (where , \boldsymbol, = \Omega ) and the body's own velocity in the rotating reference frame v. Thus, the Coriolis force is always at an angle \varphi with the local vertical direction. The local horizontal direction of the Coriolis force is thus \Omega \sin \varphi. This force acts to move the body along
longitudes Longitude (, ) is a geographic coordinate that specifies the east– west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek lette ...
or in the meridional directions.


Equilibrium

Suppose the body is moving with a velocity v such that the centripetal and Coriolis (due to \boldsymbol ) forces on it are balanced. We then have : v^2/r= 2 (\Omega \sin \varphi) v where r is the radius of curvature of the path of object (defined by v). Replacing v = r\omega , where \omega is the magnitude of the spin rate of the Earth, we obtain :f = \omega = 2 \Omega \sin \varphi. Thus the Coriolis parameter, f , is the angular velocity or frequency required to maintain a body at a fixed circle of latitude or zonal region. If the Coriolis parameter is large, the effect of the earth's rotation on the body is significant since it will need a larger angular frequency to stay in equilibrium with the Coriolis forces. Alternatively, if the Coriolis parameter is small, the effect of the earth's rotation is small since only a small fraction of the centripetal force on the body is canceled by the Coriolis force. Thus the magnitude of f strongly affects the relevant dynamics contributing to the body's motion. These considerations are captured in the nondimensionalized
Rossby number 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 , \mathbf \cdot \nabla \mathbf, \sim U^2 / L and \Omega ...
.


Rossby parameter

In stability calculations, the rate of change of f along the meridional direction becomes significant. This is called the
Rossby parameter The Rossby parameter (or simply beta \beta) is a number used in geophysics and meteorology which arises due to the meridional variation of the Coriolis force caused by the spherical shape of the Earth. It is important in the generation of Rossby wa ...
and is usually denoted : \beta = \frac where y is the in the local direction of increasing meridian. This parameter becomes important, for example, in calculations involving
Rossby waves Rossby waves, also known as planetary waves, are a type of inertial wave naturally occurring in rotating fluids. They were first identified by Sweden-born American meteorologist Carl-Gustaf Arvid Rossby. They are observed in the atmospheres and ...
.


See also

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Beta plane In geophysical fluid dynamics, an approximation whereby the Coriolis parameter, ''f'', is set to vary linearly in space is called a beta plane approximation. On a rotating sphere such as the Earth, ''f'' varies with the sine of latitude; in the s ...
*
Earth's rotation Earth's rotation or Earth's spin is the rotation of planet Earth around its own axis, as well as changes in the orientation of the rotation axis in space. Earth rotates eastward, in prograde motion. As viewed from the northern polar star Polari ...
*
Rossby-gravity waves Rossby-gravity waves are equatorially trapped waves (much like Kelvin waves), meaning that they rapidly decay as their distance increases away from the equator (so long as the Brunt–Vaisala frequency does not remain constant). These waves have ...


References

{{DEFAULTSORT:Coriolis Frequency Atmospheric dynamics Oceanography fr:Force de Coriolis#Paramètre de Coriolis