PLANETARY WAVES ON BETA-PLANES

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 ?-plane approximation. Two particular ?-planes are used?one centered at the equator, the other at a middle latitude. Both forced and free oscillations are considered. With both ?-planes it is possible to approximate known solutions on a sphere. The use of either ?-plane alone, however, results in an inadequate description. In particular it is shown that the equatorial ?-plane provides good approximations to the positive equivalent depths of the solar diurnal oscillation, while the midlatitude ?-plane provides good approximations to the negative equivalent depths. The two ?-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.