A Two-Dimensional Dynamic Model of the Diurnal Variation of the Thermosphere. Part I: Theory

Abstract

The main purpose of the paper is to develop a mathematical method for the calculation of the dynamics of the upper atmosphere including nonlinear terms with the aim of replacing the “second heat source” of the Harris-Priester model by taking into account horizontal wind systems. A system of hydrodynamic and thermodynamic equations is set up for a two-dimensional dynamic model of the upper atmosphere representing the diurnal behavior of the atmospheric parameters within the equatorial plane during the time of the equinox. An approximate WKB solution, taking into account heat conductivity, viscosity and external heat sources, leads to a generalized form of gravity waves with periods of one day. The solution of the one-dimensional quasi-static Harris-Priester model is treated explicitly. An estimate of the influence of horizontal winds on the heat balance suggests that a wind of the order 200 m sec⁻¹ can behave like a “second heat source” shifting phase and the amplitude of the calculated temperature, and by this, the density variation of the measured values. Nonlinear effects give rise to an average mechanical work done by the gas which decreases the internal energy and thus changes the heat balance within the thermosphere. An estimate of a further nonlinear effect, the phase difference between the diurnal variations of horizontal velocity and of ion drag, shows that it can set the whole upper atmosphere into a mean west to east rotation with a speed of the order 100 m sec⁻¹.