Gravitational and thermal oscillations in the Earth's upper atmosphere

Abstract

The recent work of Sen and White [1] on the excitation of large-scale oscillations in an atmosphere on a rotating globe by gravitational and thermally induced forces is extended to include heating in any portion of the atmosphere. The region where the heating occurs is unrestricted regarding temperature profile. The solution χ(z) of the radial differential equation of motion consists of (1) a complementary function yex/2, and (2) a particular solution q(z)/γH(z) + ex/2 I(x) where I is obtained by integrating the heat source function (with appropriate weight factor) from the top of the atmosphere to the level in question, γ is the ratio of specific heats, H(z) is the scale height, x = ∫dz/H where z is the altitude, q is the heat source function, and χ(z) is the divergence of the velocities. With this representation of the wave function, one recovers the expressions for the velocity components and pressure variations of Pekeris [2] and of Weekes and Wilkes [3] for the purely gravitational case, provided the wave function y is replaced by [y + I]. General expressions are also obtained for the vertical and horizontal displacements and for the amplification over equilibrium tide at any level. The latter expression is useful for establishing the so-called solar control of the dynamics of a given layer by radiation absorbed in any other layer. The boundary conditions of Weekes and Wilkes [3] are shown valid for a "top" with constant positive temperature gradient, believed to be the case above 100 km. Finally, the solar and lunar semi-diurnal winds as collected by Briggs and Spencer [4] for the E region when tested by present theory are found to have the same azimuthal dependence as exists at the ground. This is consistent with the original assumption of “variables separable.”