Thermal and gravitational excitation of atmospheric oscillations

Previous work on the excitation of large-scale oscillations in an atmosphere on a rotating globe is extended to include a unified treatment for both gravitational and thermal forcing functions and is applied to the solar and lunar semi-diurnal pressure variation, that is, S2 and L2, respectively. It is assumed that the heating is applied only at the base of the atmosphere and that the temperature gradient is constant in this region as in the actual troposphere. The solution of the problem consists of the usual Bessel's functions characteristic of a purely gravitational forcing function found by Pekeris [see 1 of “References” at end of paper], plus a particular integral found by the method of variation of parameters. The total resonant amplification is obtained for the various atmospheric models used by Jacchia and Kopal [2]. The hitherto neglected phase of the dynamical tidal oscillation is included in a treatment where complex variables are systematically employed to represent the magnitude and phase of observables. It is found that current atmospheric models favor the conclusion that thermal effects are far more important than the gravitational in producing the S2 variation (≃15) as compared with Chapman's [3] 1924 conclusion that they are of nearly equal importance. However, if one assumes, as did Chapman, that eddy motion at the ground is the only heating source, then our conclusion is at odds with observed values of eddy conductivity found by Eiffel Tower measurements. A possible resolution of this paradox is the consideration of other heating sources. Balloon observations by Riehl and the analysis of Haurwitz [4] are cited in support of this possibility.