Attenuation of Evanescent Acoustic-Gravitational Modes in the Earth’s Thermosphere

Abstract

The attenuation of the acoustic-gravitational nondivergent f-mode and inelastic γ-mode in the Earth’s upper atmosphere due to viscosity and thermal conductivity is studied. To analyze the attenuation, a system of hydrodynamic equations is used, including the modified Navier–Stokes and heat transfer equations. These modified equations take into account the contribution of the background density gradient to the transfer of energy and momentum by waves. Dispersion equations are obtained for f- and γ-modes in an isothermal dissipative atmosphere. It is shown that viscosity and thermal conductivity have little effect on the frequency of these modes under typical conditions in the thermosphere. Expressions are obtained for the damping decrements of the f- and γ-modes. It was established that the decrement of the γ-mode attenuation is almost an order of magnitude higher in the Earth’s thermosphere than the corresponding decrement of the f-mode. It is also found that the attenuation of the f-mode does not depend on the thermal conductivity but is due only to the dynamic viscosity and increases with an increase in the relative contribution of the bulk viscosity. The dissipation of the γ-mode is caused by dynamic viscosity and thermal conductivity and does not depend on the bulk viscosity. The time variation of the perturbation amplitudes for the f- and γ-modes at different heights of the thermosphere is considered. The characteristic attenuation times of the f- and γ-modes at different heights depending on the wavelength, as well as at different levels of solar activity, are calculated. The boundary heights in the thermosphere above which the f-and γ-modes cannot exist due to dissipation are determined.