Abstract
Abstract The prognostic equations for the total angular momentum vector M are derived for f- and β-plane geometries and compared to those of spherical models. It is shown that the omission of the centrifugal effects and the corresponding adjustment of gravity in atmospheric f- (β-) plane models imply that a torque is exerted in analogy to the spherical case where this torque is caused by the nonspherical shape of the earth. For hydrostatic flow on the f- (β-) plane, it is only for the vertical component Mz of angular momentum that a prognostic equation can be derived. If the traditional approximation is introduced, Mz becomes a conserved quantity on the f plane in the absence of orographic and frictional torques while the corresponding component Mz on the sphere is not conserved. The prognostic equation for Mz on the β plane is an approximation to that on the sphere at least for nondivergent flow. The f- (β-) plane equations for the horizontal components of M deviate substantially from those valid on the...
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