Barometric formula for non-isothermal atmosphere

A new barometric formula is derived for a non-isothermal atmosphere. It takes into account the dependence of the acceleration of gravity and gas temperature on the height z above the Earth’s surface. When deriving this formula, it was assumed that the dependence of the gas temperature on altitude is due to the heating of the Earth’s surface by the Sun and the subsequent heat transfer of energy from the Earth’s surface to the atmosphere. The proposed formula coincides with the classical barometric formula for an isothermal atmosphere at low altitudes z, takes into account the experimental linear decrease in the temperature of the atmosphere in its lower layers with increasing altitude z and gives a physically correct asymptotics for the pressure (and for concentration) of the gas as z -> oo, namely, the pressure (and concentration) of gas tends to zero faster than exponentially as z -> oo, which ensures the localization of a finite amount of gas near the Earth.

Two-frequency acoustic-gravitational waves, simulation of satellite measurements

The theory of acoustic gravity waves (AGW) considers free disturbances of the atmosphere within the framework of a single-frequency approach. In this case, the theory implies the existence of two separate types of waves with different natural frequencies - acoustic and gravitational. In the single-frequency approach, wave fluctuations of density, temperature, and velocity are related to each other through the spectral characteristics of the wave, and these relationships are unchanged. However, satellite observations of AGW parameters cannot always be explained within the framework of a single-frequency approach. This paper presents a two-frequency approach to the study of AGWs using the model of two coupled oscillators. It is shown that the perturbed movements of the elementary volume of the medium occur simultaneously at two natural frequencies. In this case, the connections between the wave fluctuations of the parameters are determined by the initial conditions, which can be arbitrary. Solutions in real functions for an isothermal atmosphere are obtained. The conditions under which single-frequency AGWs are obtained from the general two-frequency solution are investigated. The AGW waveforms measured from the satellite for velocities and displacements in single-frequency and dual-frequency modes are numerically simulated. The results of simulating two-frequency AGWs agree with the data of satellite measurements. Two-frequency AGWs are not always implemented at two different frequencies. It is shown that when the frequencies approach each other, the beat effect occurs and two closely related modes become indistinguishable. At the same wavelength, they have one center frequency and one phase velocity. The main feature of the two-frequency approach to the study of AGW is the expansion of the relationships between the wave parameters of the medium. This makes it possible to achieve satisfactory agreement of the model waveforms with the data of satellite measurements. Thus, the use of a two-frequency AGW treatment opens up new possibilities in the interpretation of experimental data.

Influence of vertical heterogeneity of the atmosphere temperature on the propagation of acoustic-gravity waves

A new approach to the study of acoustic-gravity waves (AGW) in the Earth’s atmosphere in the presence of a vertical temperature inhomogeneity is proposed. Using this approach, the local AGW dispersion equation is obtained for an atmosphere with a small vertical temperature gradient. The modification of acoustic and gravitational regions of freely propagating AGWs on the spectral plane is studied depending on the temperature gradient. It is shown that, the acoustic and gravitational regions approach each other with a positive temperature gradient and the distance between them increases with a negative gradient. On the spectral plane, the dispersion curves of non-divergent and anelastic horizontal wave modes are the indicators of location of the acoustic and the gravitational regions of freely propagating AGWs. The possibility of overlapping the acoustic and the gravitational regions of AGWs in non-isothermal atmosphere is investigated.

Modelling H 3 + in planetary atmospheres: effects of vertical gradients on observed quantities

Since its detection in the aurorae of Jupiter approximately 30 years ago, the H 3 + ion has served as an invaluable probe of giant planet upper atmospheres. However, the vast majority of monitoring of planetary H 3 + radiation has followed from observations that rely on deriving parameters from column-integrated paths through the emitting layer. Here, we investigate the effects of density and temperature gradients along such paths on the measured H 3 + spectrum and its resulting interpretation. In a non-isothermal atmosphere, H 3 + column densities retrieved from such observations are found to represent a lower limit, reduced by 20% or more from the true atmospheric value. Global simulations of Uranus' ionosphere reveal that measured H 3 + temperature variations are often attributable to well-understood solar zenith angle effects rather than indications of real atmospheric variability. Finally, based on these insights, a preliminary method of deriving vertical temperature structure is demonstrated at Jupiter using model reproductions of electron density and H 3 + measurements. The sheer diversity and uncertainty of conditions in planetary atmospheres prohibits this work from providing blanket quantitative correction factors; nonetheless, we illustrate a few simple ways in which the already formidable utility of H 3 + observations in understanding planetary atmospheres can be enhanced. This article is part of a discussion meeting issue ‘Advances in hydrogen molecular ions: H 3 + , H 5 + and beyond’.

Evanescent acoustic-gravity modes in the isothermal atmosphere: systematization and applications to the Earth and solar atmospheres

The objects of research in this work are evanescent wave modes in a gravitationally stratified atmosphere and their associated pseudo-modes. Whereas the former, according to the dispersion relation, rapidly decrease with distance from a certain surface, the latter, having the same dispersion law, differ from the first by the form of polarization and the nature of decrease from the surface. Within a linear hydrodynamic model, the propagation features of evanescent wave modes in an isothermal atmosphere are studied. Research is carried out for different assumptions about the properties of the disturbances. In this way, a new wave mode – anelastic evanescent wave mode – was discovered that satisfies the dispersion relation ω2=kxgγ-1. Also, the possibility of the existence of a pseudo-mode related to it is indicated. The case of two isothermal media differing in temperature at the interface is studied in detail. It is shown that a non-divergent pseudo-mode with a horizontal scale kx∼1/2H1 can be realized on the interface with dispersion ω2=kxg. Dispersion relation ω2=kxgγ-1 at the interface of two media is satisfied by the wave mode, which has different types of amplitude versus height dependencies at different horizontal scales kx. The applicability of the obtained results to clarify the properties of the f-mode observed on the Sun is analyzed.