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 pol ...
.
:
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
is about 10
−4 rad/s.
Inertial oscillations on the surface of the earth have this
frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
. These
oscillation
Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...
s are the result of the
Coriolis effect
In physics, the Coriolis force is an inertial or fictitious force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the ...
.
Explanation
Consider a body (for example a fixed volume of atmosphere) moving along at a given latitude
at velocity
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
), however, is perpendicular to the plane containing both the earth's angular velocity vector
(where
) and the body's own velocity in the rotating reference frame
. Thus, the Coriolis force is always at an angle
with the local vertical direction. The local horizontal direction of the Coriolis force is thus
. 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 letter ...
or in the meridional directions.
Equilibrium
Suppose the body is moving with a velocity
such that the centripetal and Coriolis (due to
) forces on it are balanced. We then have
:
where
is the radius of curvature of the path of object (defined by
). Replacing
, where
is the magnitude of the spin rate of the Earth, we obtain
:
Thus the Coriolis parameter,
, 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
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 \Omeg ...
.
Rossby parameter
In stability calculations, the rate of change of
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
:
where
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
*
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 so ...
*
Earth's rotation
*
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