From AMS Glossary
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Flow in the absence of external forces; in meteorology, frictionless flow in a geopotential surface in which there is no pressure gradient.
The centrifugal and Coriolis accelerations must therefore be equal and opposite, and the constant inertial wind speed Vi is given by
where f is the Coriolis parameter and R the radius of curvature of the path. The inertial path is anticyclonic in both hemispheres, more strongly curved near the poles than near the equator, resembling a series of similar loops called inertial circles. The inertial frequency with which these loops are described by the parcel is approximately equal to f/2π = 2 sinφ per sidereal day, where φ is the latitude. All the loops are bounded on the north and south by the same parallels of latitude, but the parcel has a net longitudinal movement as it describes them. The inertial period (the reciprocal of inertial frequency) is just one-half pendulum day.