Abstract
The problem of linearized oscillations of the gaseous envelope of a rotating sphere (with periods in excess of a day) is considered using the β-plane approximation. Two particular β-planes are used—one centered at the equator, the other at a middle latitude. Both forced and free oscillations are considered. With both β-planes it is possible to approximate known solutions on a sphere. The use of either β-plane alone, however, results in an inadequate description. In particular it is shown that the equatorial β-plane provides good approximations to the positive equivalent depths of the solar diurnal oscillation, while the midlatitude β-plane provides good approximations to the negative equivalent depths. The two β-planes are also used to describe Rossby-Haurwitz waves on rapidly rotating planets, and the vertical propagatability of planetary waves with periods of a day or longer.
