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 formula_1. The rotation rate of the Earth ("Ω" = 7.2921 × 10 rad/s) can be calculated as 2"π" / "T" radians per second, where "T" is the rotation period of the Earth which is one "sidereal" day (23 h 56 min 4.1 s). In the midlatitudes, the typical value for formula_3 is about 10 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 formula_1 at velocity formula_5 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 formula_6), however, is perpendicular to the plane containing both the earth's angular velocity  vector formula_7 (where formula_8) and the body's own velocity in the rotating reference frame formula_9. Thus, the Coriolis force is always at an angle formula_1 with the local vertical direction. The local horizontal direction of the Coriolis force is thus formula_11. This force acts to move the body along longitudes or in the meridional directions. Equilibrium. Suppose the body is moving with a velocity formula_5 such that the centripetal and Coriolis (due to formula_13) forces on it are balanced. We then have where formula_15 is the radius of curvature of the path of object (defined by formula_16). Replacing formula_17 , where formula_18 is the magnitude of the spin rate of the Earth, we obtain Thus the Coriolis parameter, formula_20, 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 formula_20 strongly affects the relevant dynamics contributing to the body's motion. These considerations are captured in the nondimensionalized Rossby number. Rossby parameter. In stability calculations, the rate of change of formula_20 along the meridional direction becomes significant. This is called the Rossby parameter and is usually denoted where formula_24 is the in the local direction of increasing meridian. This parameter becomes important, for example, in calculations involving Rossby waves.