Long Atmospheric Waves and the Polar-Plane Approximation to the Earth’s Spherical Geometry

Abstract

The spherical geometry of the earth is replaced by polar cylindrical geometry, with a plane tangential to the earth at the pole. The resulting frequency and structure of free motions in an isothermal, adiabatic atmosphere with a resting basic state is studied in both geometries. The solutions for ? (meridional wind) may be written as a single Bessel function if certain approximations are made. For positive equivalent depths, the geometrical approximation is best when the Lamb parameter ?? 10, so that Rossby waves are well modeled, while fast moving gravity waves are not well approximated. The impact of setting f to a constant value when undifferentiated, as in the usual midlatitude beta-plane approximation, is examined. It is found that the value of f is as important in determining how well the model behaves as are the geometrical and other approximations.