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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.

The propagation of evanescent acoustic-gravity waves in the atmosphere with an arbitrary altitude temperature profile is investigated. The possibility of the existence of two types of evanescent wave modes in a vertically nonisothermal atmosphere is shown. The first type is the f-mode in which the dispersion does not depend on the altitude inhomogeneity of temperature and, therefore, is carried out at any altitude level of the nonisothermal atmosphere. The second type is a recently discovered $$\gamma $$ ‑mode in which the dispersion depends on the altitude temperature gradient and can be fulfilled only at certain altitude intervals. The possibility of realizing the f- and $$\gamma $$ - modes in the Earth’s atmosphere is considered, taking into account the model altitude temperature profile. It is shown that these modes can exist at the heights of local temperature extremes in the atmosphere. Moreover, they are realized only in a narrow range of spectral parameters for which the conditions for a decrease in the wave energy above and below the level of their propagation are satisfied. For the f-mode, this energy condition is fulfilled at the altitudes of the local temperature minima, while that for the $$\gamma $$ -mode is at the altitudes of the local maxima. Recommendations are given regarding the possibility of observing these modes in the atmosphere of the Earth and the Sun. In the Earth’s atmosphere, the f-mode can presumably be observed near the mesopause with the characteristic wavelength $${{\lambda }_{x}} \approx 75\,{\text{km}}$$ and in the solar atmosphere at the heights of the chromospheres with $${{\lambda }_{x}} \approx 1600\,{\text{km}}$$ . The period of the f‑mode propagating in the region of the temperature minimum slightly exceeds the Brent-Vaisala period at this altitude. In the Earth’s atmosphere, the $$\gamma $$ -mode can be realized in the regions of maximum temperature, for example, at the height of the stratopause with $${{\lambda }_{x}} \approx 100\,{\text{km}}$$ and a period slightly larger than the Brent-Vaisala period at the altitude of its propagation.

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

Within the model of a dissipative isothermal atmosphere, the attenuation of acoustic−gravity waves (AGWs) is studied on the basis of the modified Navier−Stokes and heat-transfer equations. Besides the usually considered velocity gradient, the modification of these equations takes into account the additional transfer of the momentum and energy induced by AGWs due to the density gradient. This results in that additional terms appear in the hydrodynamic equations of motion and heat transfer. Under these assumptions, the local dispersion equation for AGWs in an isothermal dissipative atmosphere, as well as an expression for the damping decrement, is obtained. In the limiting cases of high frequencies (sound waves) and low frequencies (gravitational waves), the nature of the attenuation allows a clear physical interpretation. Special aspects of the time-dependent attenuation for the evanescent acoustic−gravity modes of various types, including the Lamb waves and Brent−Vaisala oscillations, are also considered.

As is known from multiyear theoretical and experimental studies, acoustic−gravity waves (AGW) determine the dynamics and energy balance of the atmospheres of planets and the Sun to a considerable extent. Linear wave perturbations in the atmosphere can be described with a system of second-order equations for the vertical and horizontal components of the perturbed velocity. It follows from this system that small perturbations in the atmosphere may be considered as oscillations of coupled oscillators with two degrees of freedom. This suggests that it is worth studying more thoroughly the linear acoustic−gravitational wave modes in the atmosphere with well-developed methods of the theory of oscillations. To study small perturbations in the Earth’s atmosphere, the methods of the theory of coupled oscillatory systems were used. It has been shown that acoustic−gravity waves in an isothermal atmosphere can be considered as a superposition of oscillations that occur simultaneously at two natural frequencies—acoustic and gravitational. The equations for the natural frequencies of oscillations, as well as for the components of the perturbed velocity under specified initial conditions, were derived. From the analysis of temporal changes in the components of the perturbed velocity, new features in their behavior were found. All solutions are presented with the use of real quantities only. This representation is more convenient for comparison with observational data than the complex one commonly used in the theory of acoustic−gravity waves. The conditions under which the usual single-frequency oscillation mode can be realized in the atmosphere are analyzed. The results of the study can be used to explain some features in space-borne observations of wave perturbations in the Earth’s atmosphere that do not fit the framework of the known theoretical concepts.

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.

A simple method has been proposed to determine acoustic-gravity wave (AGW) characteristics at lower ionosphere (mesosphere) heights by measuring VLF radio signal amplitudes. For relatively short radio paths (less than ∼ 1500 km long) we obtained the simple relations for estimation of AGW neutral density fluctuation and for vertical displacement of an elementary volume of atmospheric gas. The proposed method has been verified by using VLF radio wave amplitude measurements on several radio paths. AGW properties based on these measurements are approximately calculated at heights of radio signal reflection. The relative fluctuation of 3%–6% of neutral particle concentration and elementary volume displacement of 0.6–1.2 km have been obtained. These results are in good agreement with AGW theory in the Earth atmosphere.

The peculiarities of acoustic-gravity waves propagating in inhomogeneous polar thermosphere flows have been investigated. It is shown that a spectrum filtration and a change in amplitudes of acoustic-gravity waves occur in the region of polar thermosphere circulation. As a result, the waves with horizontal lengths of 500–700 km and periods of ∼ 10 min are predominated in satellite observations. We have shown that such spectral properties correspond to the waves which are blocked in the counter flow. The amplitudes of the blocked waves are greatly enhanced due to their interaction with the non-uniform flow. A ground-based observer registers these waves with periods from 30 min to more than 1 h, depending on the flow velocity. Taking in to account the interaction of the waves with the flows we can explain the discrepancy between the results of satellite and ground-based observations of acoustic-gravity wave in the polar regions.

Based on satellite measurements, we investigated the properties of acoustic-gravity waves in different geographical areas of the Earth’s upper atmosphere. To study wave activity at high latitudes, we used the concentration of neutral particles measured by the low-altitude polar satellite Dynamic Explorer 2 and measurements from the equatorial satellite Atmosphere Explorer-E for analysis of waves at low latitudes. In the range of heights 250–400 km, there are observed latitudinal variations of amplitudes, together with variations in the morphological and spectral properties of acoustic-gravity waves. In the polar regions of thermosphere, the wave amplitudes amount to 3–10% in terms of relative variations of density and do not exceed 3% at low and middle latitudes. At low latitudes, regular fluctuations induced by the solar terminator are clearly seen with a predominant wave mode moving synchronously with terminator. Moreover, at low and middle latitudes, there are observed sporadic local wave packets of small amplitudes (1–2%) that can have origins of various natures. We also investigated the relation between some of the observed wave trains and the earthquakes.

The properties of acoustic-gravity waves in the polar regions of the Earth’s thermosphere have been studied. It has been shown that the change in AGW amplitudes occurs against the background of large-scale rotational movements of the medium in the polar thermosphere. The amplitudes of waves increase with AGW propagation against the motion of the medium and decrease when AGW propagate along rotation. An analytical expression for the gain coefficient of AGW perturbations is obtained; the wave’s amplification effect in the opposite wind given the characteristic parameters of the thermosphere is estimated. The results are consistent with the measurements of AGW parameters in the polar regions from the “Dynamic Explorer 2” satellite.)

We present a study correlating the spatial locations of young star clusters with those of molecular clouds in NGC~5194, in order to investigate the timescale over which clusters separate from their birth clouds. The star cluster catalogues are from the Legacy ExtraGalactic UV Survey (LEGUS) and the molecular clouds from the Plateau de Bure Interefrometer Arcsecond Whirpool Survey (PAWS). We find that younger star clusters are spatially closer to molecular clouds than older star clusters. The median ages for clusters associated with clouds is 4~Myr whereas it is 50~Myr for clusters that are sufficiently separated from a molecular cloud to be considered unassociated. After $\sim$6~Myr, the majority of the star clusters lose association with their molecular gas. Younger star clusters are also preferentially located in stellar spiral arms where they are hierarchically distributed in kpc-size regions for 50-100~Myr before dispersing. The youngest star clusters are more strongly clustered, yielding a two-point correlation function with $\alpha=-0.28\pm0.04$, than the GMCs ($\alpha=-0.09\pm0.03$) within the same PAWS field. However, the clustering strength of the most massive GMCs, supposedly the progenitors of the young clusters for a star formation efficiency of a few percent, is comparable ($\alpha=-0.35\pm0.05$) to that of the clusters. We find a galactocentric-dependence for the coherence of star formation, in which clusters located in the inner region of the galaxy reside in smaller star-forming complexes and display more homogeneous distributions than clusters further from the centre. This result suggests a correlation between the survival of a cluster complex and its environment., Comment: 17 pages, 12 figures. Accepted for publication in MNRAS

The dissipation of acoustic–gravity waves in the thermosphere due to molecular viscosity and thermal conductivity based on a modified system of hydrodynamic equations is studied. A modification of the system of equations consists in additional taking into account in the linearized Navier–Stokes equations and heat transfer additional terms describing the transfer of momentum and energy due to the background density gradient, except for the usually taken into account velocity gradient. Using these modified equations, the local dispersion equation of acoustic–gravity waves in an isothermal dissipative atmosphere is obtained. On this basis, new general expressions for the attenuation rates in time and in space for both acoustic and gravity waves in the entire spectral range are derived in the paper. The relationship between the rates of AGW temporal and spatial attenuation is analyzed. The results obtained are consistent with satellite-based observations of AGW at the heights of the thermosphere, indicating filtering of the wave spectrum due to viscosity and thermal conductivity.

Wave disturbances caused by moving solar terminator were studied using in situ satellite measurements. Neutral species densities measured by low-latitude satellite Atmosphere Explorer-E in the altitude range of 250–400 km were used for analysis. Wave disturbances of neutral species density with amplitudes of 2–4% were observed during few hours after passing the terminator, predominantly in time intervals of 6–9 LST and 20–23 LST. These disturbances were interpreted as the acoustic-gravity waves. Spatial scales of such waves range from few hundred to few thousand kilometers, major part of wave spectral power being concentrated in the horizontal wavelength range from 1000 km to 1200 km. It was shown that vertical and horizontal components of phase velocity of these waves coincide with vertical and horizontal components of terminator velocity, i.e. observed wave are synchronized with the terminator.

The article presents a summary of the main findings of the systematic study of acoustic-gravity waves (AGWs) in the polar thermosphere. This study was based on the in situ measurements made by the Dynamics Explorer 2 (DE2) spacecraft late in its mission when it descended low enough (250–400 km). It was found out that AGWs in the polar thermosphere are observed within a narrow frequency band close to the Brunt–Väisälä frequency and with horizontal wavelengths about 500–600 km. The broadband spectrum of travelling ionospheric disturbance (TID) frequencies observed by radars is caused by the Doppler effect. The AGW amplitudes do not depend on the altitude, but grow almost linearly with the wind velocity. They propagate towards the wind.

Recently acquired WFC3 UV (F275W and F336W) imaging mosaics under the Legacy Extragalactic UV Survey (LEGUS) combined with archival ACS data of M51 are used to study the young star cluster (YSC) population of this interacting system. Our newly extracted source catalogue contains 2834 cluster candidates, morphologically classified to be compact and uniform in colour, for which ages, masses and extinction are derived. In this first work we study the main properties of the YSC population of the whole galaxy, considering a mass-limited sample. Both luminosity and mass functions follow a power law shape with slope -2, but at high luminosities and masses a dearth of sources is observed. The analysis of the mass function suggests that it is best fitted by a Schechter function with slope -2 and a truncation mass at $1.00\pm0.12\times10^5\ M_\odot$. Through Monte Carlo simulations we confirm this result and link the shape of the luminosity function to the presence of a truncation in the mass function. A mass limited age function analysis, between 10 and 200 Myr, suggests that the cluster population is undergoing only moderate disruption. We observe little variation in the shape of the mass function at masses above $1\times10^4\ M_\odot$, over this age range. The fraction of star formation happening in the form of bound clusters in M51 is $\sim20\%$ in the age range 10 to 100 Myr and little variation is observed over the whole range from 1 to 200 Myr., Comment: 25 pages, 19 figures, 10 tables. Accepted for publication in MNRAS (14 Sep. 2017)

УДК 550.388, 551.520.32 Исследован отклик ионосферной плазмы на распространение акустико-гравитационных волн (АГВ) на основе измерений на спутнике Dynamics Explorer 2. Волновые возмущения проанализированы в интервале атмосферных высот 250 ÷350 км по данным одновременных измерений температур, концентраций, скоростей нейтральных частиц и ионов в высоких и средних широтах. Установлены следующие особенности ионосферных проявлений АГВ: 1) относительные вариации температур ионов и нейтральных частиц в этих широтах, за исключением областей авроральных овалов, примерно совпадают; 2) вариации общей концентрации плазмы противофазны вариациям концентрации нейтральных частиц, а их относительная амплитуда в среднем в несколько раз превышает амплитуду вариаций концентрации нейтральных частиц; 3) концентрация молекулярных ионов изменяется в фазе с концентрацией нейтральных частиц; 4) вертикальная скорость ионов в высоких широтах согласована с вертикальной скоростью нейтральных частиц, отражая их совместные движения вдоль силовых линий магнитного поля. Для отделения ионосферных проявлений АГВ от других типов возмущений в високих широтах нужен синхронный анализ различных параметров ионосферной плазмы. Ключевые слова: акустико-гравитационные волны, подвижные ионосферные возмущения, авроральный овал, ионосфера, атмосфера Статья поступила в редакцию 13.05.2014 Radio phys. radio astron. 2014, 19(3): 206-216 СПИСОК ЛИТЕРАТУРЫ 1. Бурмака В. П., Таран В. И., Черногор Л. Ф. Результаты исследования волновых возмущений в ионосфере методом некогерентного рассеяния // Успехи современной радиоэлектроники. – 2005. – № 3. – С. 4–35. 2. Лизунов Г. В., Федоренко А. К. Генерация атмосферных гравитационных волн солнечным терминатором по данным измерений на спутнике “Atmosphere Explorer-E” // Радиофизика и радиоастрономия. – 2006. – Т.11, № 1. – С. 49–62. 3. Федоренко А. К. Відтворення характеристик атмосферних гравітаційних хвиль в полярних регіонах на основі маспектрометричних супутникових вимірювань // Радиофизика и радиоастрономия. – 2009. – Т. 14, № 3. – С. 254–265. 4. Carignan G. R., Block B. P., Maurer J. C, Hedin A. E., Reber C. A., and Spencer N. W. The neutral mass Spectrometer on Dynamics Explorer // Space Sci. Instrum. – 1981. – Vol. 5. – P. 429–441. 5. Spencer N. W., Wharton L. E., Niemann H. B., Hedin A. E., Carignan G. R., and Maurer J. C. The Dynamics Explorer wind and temperature spectrometer // Space Sci. Instrum. – 1981. – Vol. 5. – P. 417–428. 6. Dudis J. J. and Reber C. A. Composition effects in thermospheric gravity waves // Geophys. Res. Lett. – 1976. – Vol. 3, No. 12. – P. 727–730. 7. Раклифф Дж. Введение в физику ионосферы и магнитосферы. – М.: Мир, 1975. – 295 с. 8. Брюнелли Б. Е., Намгаладзе А. А. Физика ионосферы. – М.: Наука, 1988. – 527 с. 9. Ляцкий В. Б., Мальцев Ю. П. Магнитосферно-ионосферное взаимодействие. – М.: Наука, 1983. – 191 с.

According to measurements on the Dynamic Explorer 2 satellite, features of the propagation of acoustic gravity waves (AGWs) in the multicomponent upper atmosphere have been investigated. In the altitude range 250–400 km in wave concentration variations of some atmospheric gases, amplitude and phase differences have been observed. Using the approach proposed in this paper, in different gases, AGW variations have been divided into components associated with elastic compression, adiabatic expansion, and the vertical background distribution. The amplitude and phase differences observed in different gases are explained on the basis of analyzing these components. It is shown how to use this effect in order to determine the wave propagation, the vertical displacement of the volume element, the wave frequency, and the spatial distribution of the wave energy density.

The relationship between the directions of polar acoustic gravity waves and a wind at 250–350 km altitudes has been studied based on an analysis of the Dynamics Explorer 2 satellite measurements. A method, which makes it possible to determine the direction of these waves relative to the satellite velocity vector based on one-point measurements of different neutral atmosphere parameters, is presented. It has been established that acoustic gravity waves observed over the polar caps systematically propagate upwind, which argues for their spatial wind filtering. In the polar regions, waves mainly propagate in two directions: toward magnetic noon and 15–16 MLT. Waves tend to move counterclockwise and clockwise over the northern and southern polar caps, respectively.

The dependence of energy transport by acoustic gravity waves (AGWs) on their spectral properties is studied. On the basis of the analysis of expressions for group velocities and energy fluxes of AGWs, it is shown that there exist separate frequencies and wavelengths at which the energy transport in space is most efficient. Comparison of the obtained results with the data of observations on board the Dynamic Explorer 2 satellite shows that, in the upper atmosphere of the Earth’s polar regions, AGWs with spectral parameters corresponding to the maximum of energy transport predominate.

The peculiarities of the distribution of medium-scale acoustic gravity waves (AGWs) in polar regions according to the data of measurements on board the Dynamics Explorer 2 satellite are studied. Over polar regions of both hemispheres at heights of 250–400 km, wave variations in neutral atmospheric parameters were systematically registered. These variations were identified as AGWs with horizontal wavelengths of 500–650 km. The relative amplitudes of polar AGWs in a neutral concentration reach 10%. Wave trains extend over the polar caps to thousands of kilometers and show a distinct spatial relationship with the auroral oval. A systematic direction is found in AGW propagation from the nighttime sector of the oval into the day-time sector, where wave activity is strictly limited. An assumption is formulated that this restriction is caused by dynamic interactions between AGWs and the zonal wind in the daytime sector of the auroral oval.

Wave disturbances of the Neutral Atmosphere above the polar caps are studied based on the Dynamic Explorer 2 satellite measurements. The characteristic spatial scales of these disturbances are 500— 600 km. Based on an analysis of the synchronous variations in different parameters, these disturbances were interpreted as propagating acoustic gravity waves (AGWs). The mass-spectrometer measurements of concentrations of individual atmospheric gases made it possible to determine the following AGW components: density of the acoustic compression, thermobaric, and average kinetic energies. It has been found out that the average (during the period) densities of the acoustic and thermobaric energies are approximately equal for polar AGWs. The results indicate that the contribution of these waves to the energy of the polar upper atmosphere is considerable.