Coriolis frequency

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 φ.

The rotation rate of the Earth (Ω = 7.2921 × 10⁻⁵ rad/s) can be calculated as 2π / T radians per second, where T is the rotation period of the Earth which is one sidereal day (23 hr 56 m 4.1 s). In the midlatitudes, the typical value for ${\displaystyle f}$ 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.

Consider a body (for example a fixed volume of atmosphere) at latitude ${\displaystyle \varphi }$ moving at velocity ${\displaystyle v}$ 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 hence in the meridional direction). The Coriolis force (proportional to ${\displaystyle 2\,{\boldsymbol {\Omega \times v}}}$), however, is perpendicular to the plane containing both the earth's angular velocity vector ${\displaystyle {\boldsymbol {\Omega }}}$ (where ${\displaystyle |{\boldsymbol {\Omega }}|=\Omega }$) and the body's own velocity in the rotating reference frame ${\displaystyle v}$. Thus, the Coriolis force is always at an angle ${\displaystyle \varphi }$ with the local vertical direction. The local horizontal direction of the Coriolis force is thus ${\displaystyle \Omega \sin \varphi }$. This force acts to move the body along longitudes or in the meridional directions.

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