Two-dimensional linearized hydrodynamic equations describing wave propagation in a stratified heavy gas are considered. The hydrodynamic equation system is reformulated as a single Schrödinger type operator equation. Waves with β = l_z/l_x≪ 1 are considered, where l_z and l_x are the characteristic vertical and horizontal scales, respectively, and study the asymptotic behavior of solutions as β→ 0 . It is shown that the set of solutions depending on β form two disjoint classes. For solutions from each of the selected classes, its own, asymptotic as β→ 0 , approximate equation system is proposed. The selected classes of solutions are acoustic and internal gravity waves. It is shown that the hydrodynamic variables of acoustic and gravity waves are related by certain stationary relationships, different for each class. This makes it possible to formulate the problem of separating the contributions of acoustic and gravity waves in the initial condition. The existence of a solution to this wave separation problem is shown. Examples of solving the problem of dividing the general problem into subproblems on the propagation of acoustic and gravity waves are given. Estimates for the division of the energy of the initial perturbation by wave type are obtained.

Using a high-resolution nonlinear numerical model, simulations are performed to study the propagation of acoustic-gravity waves (AGWs) from the troposphere into the upper atmosphere. These simulations take into account background wind profiles containing critical levels, where the horizontal wind velocity becomes equal to the horizontal AGW phase speed. According to conventional linear theories of atmospheric waves, the vertical wavelength approaches zero near critical levels, resulting in strong dissipation of AGWs propagating from the troposphere and preventing them from reaching the upper atmosphere. Our numerical simulations are carried out using wave sources in the form of plain wave perturbations of vertical velocity, propagating along the Earth's surface. Jet streams in the atmosphere are approximated by Gaussian profiles of the mean zonal wind with maxima located at altitudes of 110 km and 50 km. Calculations reveal that AGW amplitudes are significantly reduced above the high-altitude critical levels. For the critical levels at altitudes 30-70 km, part of wave energy can penetrate through them and propagate further into the upper atmosphere. In the nonlinear model, increased generation of secondary wave modes occur near the critical level. Therefore, modes with vertical wavelengths longer than that of the primary AGW dominate at altitudes exceeding 130 km, where amplitudes of these secondary waves may surpass the amplitudes of the primary AGW in the absence of middle atmosphere critical levels. (c) 2024 COSPAR. Published by Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

In this work, we investigate an ion-atom model describing the time-dependent evolution of electron density during the collision. For a S3+-H system, numerical simulations are based on classical trajectory calculations, and the electron density behaviour is described with the time-dependent Schr & ouml;dinger equation. We apply the finite difference method to obtain quantitative insights into the charge transfer dynamics, providing detailed information about the spatial and temporal evolution of the collision process. The results are given for representative examples of the collision, from eV to keV range of energies, in head-on collision as well as for different values of impact parameter. A validity and precision of the proposed model and interpretation of the particle collision in terms of eigenstates are also discussed. [GRAPHICS]

The derivation of a nonlinear Burgers-type equation for acoustic waves within the ray approximation for an inhomogeneous moving dissipative atmosphere is presented. The equation is applied to investigate the propagation of three-dimensional infrasonic waves, without using significant computational resources. By means of solving the obtained equation, the shapes of infrasonic signals recorded at distances of 295 km and 305 km from the explosion with energy of 30 kt THT were calculated. The observation point at the distance of 295 km (Tsimlyansk) was located in the western direction from the source. At this place, infrasonic signals were recorded corresponding to the sound propagation in the stratospheric and thermospheric acoustic waveguides. The presence of both two stratospheric and two thermospheric rays falling into the same observation point on the Earth's surface is a wave propagation feature result here. The recorded signals in Tsimlyansk also have a complex structure, both for stratospheric and thermospheric infrasonic arrivals. The registration point at a distance of 305 km (Saratov) was located north of the source. For this point, the calculations showed the presence of only thermospheric rays. The calculation results are compared with experimental data. A satisfactory agreement between the calculated and experimental data was obtained for both observation points in Saratov and Tsimlyansk. The calculated data in Tsimlyansk include manifestation features of the multipath structure of infrasound propagation and agree with the complex structure of infrasound signals recorded in Tsimlyansk.

Теоретически исследуются генерация акустико-гравитационных волн метеорологическими источниками тепла в тропосфере и распространение этих волн до высот верхней атмосферы. Выведены уравнения, описывающие по отдельности генерацию и распространение акустической и гравитационной волн локальным источником тепла. Тепловой источник волн представлен в виде парциальных источников гравитационных и акустических волн. Получена оценка мощности этих парциальных источников и показано, что их мощности различаются примерно вдвое, независимо от формы, размеров и частоты теплового источника. Показано, что генерация гравитационных волн не может происходить без соответствующей генерации акустических: эти волны генерируются только совместно. Разделение задачи о волнах от источника тепла на две отдельные (от гравитационного и акустического источников) проиллюстрировано прямым моделированием этих волн. Обсуждается применение полученных результатов к проблеме параметризации акустико-гравитационных волн в моделях общей циркуляции и климатических моделях.

Considerable attention has recently been paid to the study of so-called “secondary” acoustic-gravity waves (AGWs) that arise as a result of instability and nonlinear interactions of “primary” wave modes propagating from atmospheric sources, among themselves, and with the mean flow. In this paper, for the first time, the horizontal spatial spectra of primary and secondary AGWs are separated at fixed altitude levels in the middle and upper atmosphere at different time moments, which are simulated using a three-dimensional nonlinear high-resolution model AtmoSym. It is shown that in a short time after switching on the plane wave source at the lower boundary of the model, the spectrum consists of a peak corresponding to primary AGW and quasi-white noise generated by random atmospheric disturbances and the numerical model. Later, secondary peaks appear in the spectra at horizontal wave numbers, which are multiples of the wave numbers of primary AGW. The proposed separation of the spectra of primary and secondary AGWs makes it possible to estimate the relative contribution of secondary AGW at different altitudes, at different times, and with different stability of background temperature and wind profiles in the atmosphere.

The generation of acoustic-gravity waves by meteorological heat sources in the troposphere and the propagation of these waves to the heights of the upper atmosphere are studied theoretically. Equations that describe separately the generation and propagation of acoustic and gravity waves by a local heat source are derived. The heat source of the waves is divided into partial sources of gravity and acoustic waves (AWs). The power of these partial sources is estimated and it is shown that the power of the sources differs by about a factor of two, regardless of the shape, size, and frequency of the heat source. It is shown that in the case of heat sources of the waves, the generation of gravity waves cannot occur without the corresponding generation of AWs: these waves are generated only in pairs. The splitting of the problem of waves from a heat source into problems of waves from gravity and acoustic sources is illustrated by the direct modeling of these waves. The application of the obtained results to the problem of parametrization of acoustic-gravity waves in general circulation and climate models is discussed.

Using the method of different scales, formulas for the hydrodynamic fields of acoustic-gravity waves (AGWs) with vertical wavelengths that are small compared to the scales of changes in the background temperature and wind fields are derived. These formulas are equivalent to the conventional WKB approximation, but explicitly include the vertical gradients of the background fields. The conditions for the applicability of the formulas for describing the propagation of AGWs from the troposphere to the thermosphere are formulated and analyzed. The absence of singular points (critical levels) in the equations for wave modes in the analyzed height range is one of the conditions for the applicability of approximate formulas. For the wind from the empirical HWM model, singular points are often located below 200 km and are typical for internal gravity waves (IGWs) with lengths on the order of 10 km. As the wavelength increases, the number of singular points decreases. For IGWs with scales on the order of 300 km or more, there are usually no singular points. It is shown that IGWs with periods of less than 20 min propagating upward from tropospheric heights usually have one turning point in the altitude range from 100 to 130 km. The formulas are useful, in particular, for parametrizing the effects of AGWs in numerical models of atmospheric dynamics and energy.

The idea that a tropospheric heat source generating waves can be replaced with a surface source of pressure oscillations on the Earth's surface is proposed and analyzed. In the surface source, atmospheric pressure fluctuations caused by a tropospheric source are used. The discrepancies due to the replacement of the tropospheric heat source by the surface one are estimated using experiments with a high-resilution numerical model of acoustic-gravity waves. It is shown that at frequencies of infrasound, the wave amplitudes in the upper atmosphere are very close for both tropospheric heat and surface pressure sources. At frequencies of internal gravity waves, the time-spatial structure of the wave fields are close in the upper atmosphere, but wave amplitudes for the surface pressure generation could be larger (up to two times) than those for the respective tropospheric heat sources. This discrepancy is explained and some corrections to the surface pressure source are proposed, which provide better agreement and may be applied for modeling of waves from tropospheric sources, based on the data of atmospheric microbarometer measurements.

The consequences of the entry of a weak magnetic field into the upper chromosphere of the Sun are theoretically studied. It is assumed that the plasma at the initial moment is immobile and has everywhere a temperature of 50 000 K and that the field consists of two identical opposite-polarity magnetic regions adjacent to each other with a vertical contact zone. A completely self-consistent, two-dimensional system of nonlinear collisional equations of single-fluid, resistive magnetohydrodynamics is numerically solved with allowance for the Hall effect and thermal conductivity. It has been found that, during the coevolution of the field and plasma, the upward-directed boundary current more often takes the form of a thin current sheet and exists in this form longer than the boundary current directed downwards. However, with a downward current, the conversion of the magnetic field energy into the energy of regular flows of the chromospheric plasma proceeds more efficiently. Upon the assumption of a slow change in the values along the vertical, a range of parameter values is analytically found where, regardless of the general form of magnetic inhomogeneities, the downward currents degrade (are blurred), while a density of upward currents sharply increases. A fundamental difference in the behavior of currents arises when ohmic dissipation and the drift of field lines, due to their partial freezing-in, have a lesser effect on changes in the magnetic field than the Hall effect in the presence of a plasma density gradient created by the gravity. It is shown that the minimum height where such pure gradient-Hall evolution of the magnetic field occurs corresponds to the base of the corona. It is suggested that the ohmic dissipation of spontaneously formed concentrated currents contributes to the corona heating.

High-resolution numerical simulations of non-stationary, nonlinear acoustic–gravity waves (AGWs) propagating upwards from surface wave sources are performed for different temporal intervals relative to activation and deactivation times of the wave forcing. After activating surface wave sources, amplitudes of AGW spectral components reach a quasi-stationary state. Then the surface wave forcing is deactivated in the numerical model, and amplitudes of vertically traveling AGW modes quickly decrease at all altitudes due to discontinuations of the upward propagation of wave energy from the wave sources. However, later the standard deviation of residual and secondary wave perturbations experiences a slower quasi-exponential decrease. High-resolution simulations allowed, for the first time, for the estimation of the decay times of this wave noise produced by slow residual, quasi-standing and secondary AGW spectral components, which vary between 20 and 100 h depending on altitude and the rate of wave source activation and deactivation. The standard deviations of the wave noise are larger for the case of sharp activation and deactivation of the wave forcing compared to the steep processes. These results show that transient wave sources may create long-lived wave perturbations, which can form a background level of wave noise in the atmosphere. This should be taken into account in parameterizations of atmospheric AGW impacts.

The generation and propagation of waves from model tropospheric meteorologic heat sources are theoretically studied. The processes of gas heating/cooling in water phase transitions at tropospheric altitudes are assumed to be the wave sources. In an analytical part of the study, equations are derived which describe the generation and propagation of acoustic and internal gravity waves separately. It is shown that powers of partial sources of acoustic and internal gravity waves always approximately coincide, regardless of wave frequencies, and the generation of internal gravity waves cannot occur without the generation of acoustic waves, and vice versa. Explicit analytical expressions are obtained for the generated waves. Due to resonant properties of the atmosphere, the high-frequency sources generate predominantly acoustic waves. The low-frequency sources generate mainly internal gravity waves if the sources work long enough for the resonance properties of atmosphere to be manifested. Using numerical experiments, the issue of error is investigated which is introduced if a tropospheric source is replaced with a surface one in which the pressure fluctuations on the surface are the recorded pressure fluctuations caused by the tropospheric source. It is shown that, if a tropospheric source operates at the infrasonic wave frequencies, then the wave patterns generated in the upper atmosphere from the tropospheric source and from the surface pressure fluctuations are almost identical. In the case of a tropospheric source operating at frequencies of internal gravity waves, the amplitude of waves from the surface pressure may be overestimated no more than twice. It is shown that, based on pressure fluctuations on the Earth’s surface, some corrected surface pressure source can be constructed which takes into account the phase shifts of interfering waves that propagate into the upper atmosphere. This provides a significant improvement in the simulation of waves from meteorological sources based on data on atmospheric pressure fluctuations.

The effect background wind has on dynamic processes in the atmosphere caused by the propagation of waves with different periods from local tropospheric sources of heat is studied numerically using the high-resolution AtmoSym regional model of the atmosphere. Variations in the temperature field caused by the vertical propagation of acoustic and internal gravity waves are calculated, and the effects observed in the thermosphere are studied.

In this paper, we study, in theoretical terms, the structure of the spectrum of acoustic-gravity waves (AGWs) in the nonisothermal atmosphere having asymptotically constant temperature at high altitudes. A mathematical problem of wave propagation from arbitrary initial perturbations in the half-infinite nonisothermal atmosphere is formulated and analyzed for a system of linearized hydrodynamic equations for small-amplitude waves. Besides initial and lower boundary conditions at the ground, wave energy conservation requirements are applied. In this paper, we show that this mathematical problem belongs to the class of wave problems having self-adjoint evolution operators, which ensures the correctness and existence of solutions for a wide range of atmospheric temperature stratifications. A general solution of the problem can be built in the form of basic eigenfunction expansions of the evolution operator. The paper shows that wave frequencies considered as eigenvalues of the self-adjoint evolution operator are real and form two global branches corresponding to high- and low-frequency AGW modes. These two branches are separated since the Brunt–Vaisala frequency is smaller than the acoustic cutoff frequency at the upper boundary of the model. Wave modes belonging to the low-frequency global spectral branch have properties of internal gravity waves (IGWs) at all altitudes. Wave modes of the high-frequency spectral branch at different altitudes may have properties of IGWs or acoustic waves depending on local stratification. The results of simulations using a high-resolution nonlinear numerical model confirm possible changes of AGW properties at different altitudes in the nonisothermal atmosphere.

A mathematical apparatus for solving problems of X-ray wave propagation through complex optical systems, when the lens thickness can change with jumps, is developed and presented. The developed method is based on the use of the superposition of oriented Gaussian beams, which satisfy the Helmholtz equation with high accuracy. The wave propagation in air and through kinoform and ordinary lenses is considered. Focusing and imaging properties are compared for both types of X-ray optics. The diffraction effects arising due to thickness jumps in the kinoform lenses and the influence of these jumps on the X-ray focusing and imaging are investigated. The prospect of using the developed theory for X-ray optics applications is discussed.

A numerical model of the propagation of acoustic-gravity waves excited by pressure fluctuations on the Earth's surface is developed. Propagation of acoustic-gravity waves generated by instabilities of tropospheric fronts into the upper atmosphere is simulated. The experimental data on atmospheric pressure variations during 2016 year registered on a net of four microbarographs located in the Moscow region are processed. A case of very significant pressure fluctuations (up to 30 times larger than the average level) is selected, which were caused by an atmospheric front arrival. Observed surface pressure field variations for this field were approximated and used as the lower boundary condition for simulating the vertical wave propagation. The numerical simulations showed that just after the boundary source activation, the infrasonic waves in the upper atmosphere may have amplitudes of perturbations of temperature up to 100 K, and horizontal velocity up to 60 m/s. Internal gravity waves come into the upper atmosphere later and far horizontally away from the wave source. The influence of the limited dimensions of the computational domain on the simulation results is investigated. The conditions at the horizontal boundaries of the computational domain, which allow the runaway of waves beyond the domain are proposed. The frequency spectrum of waves in the non-isothermal atmosphere is analyzed.

The atmosphere and ionosphere are a complex dynamic system, which is affected by sources, caused both by internal processes and external ones. It is known that atmospheric waves propagating from the troposphere to the upper atmosphere make a significant contribution to the state of this system. One of the regular sources of such waves are various tropospheric disturbances caused, for example, by meteorological processes. Numerical modeling is an effective tool for studying these processes and the effects they cause. However, a number of problems arise, while setting up numerical experiments. The first is that most atmospheric models use hydrostatic approximation (which does not allow the resolution of small-scale perturbations) and work for a limited range of heights (which does not allow studying the relationship between the lower and upper atmosphere). This demands an accurate selection of the model in accordance with the stated research goals. The second problem is the difficulty of direct definition of the wave tropospheric sources, that was mentioned before, due to the lack of experimental information for their detailed description. The authors proposed, researched and tested a way to solve this problem. It was shown that the solution of the problem of waves propagation from a certain tropospheric source is completely determined by the pressure field at the surface of the Earth. This work is devoted to solving various problems using this approach.This study presents the results of calculations of the propagation of infrasound and internal gravity waves from tropospheric disturbances given by pressure variations at the surface of the Earth. The experimental data associated with various meteorological events and the passage of the solar terminator were obtained both directly - by a network of microbarographs in the studied region, and indirectly - based on the data from the LIDAR signal intensity and temperature changes in the coastal region. The calculations were done using the non-hydrostatic numerical model “AtmoSym”. The characteristics of atmospheric waves generated by such sources are estimated. The effect from a tropospheric sources on the state of the upper atmosphere and ionosphere is investigated. The physical processes that determine the change in atmospheric parameters are discussed. It is shown that the main contribution from wave disturbances generated by meteorological sources belongs to infrasound. Infrasound and internal gravity waves can be sources of travelling wave packets and can also cause a sporadic E-layer.The study was funded by RFBR and Kaliningrad region according to the research project 19-45-390005 (Y. Kurdyaeva) and RFBR to the research project 18-05-00184 (O. Borchevkina).

Numerical high-resolution modeling of nonlinear acoustic-gravity waves (AGWs) generated at the Earth's surface and propagating to the thermosphere shows that wave characteristics are depending on modifications in the mean density, temperature, molecular dissipation and composition due to variations of solar activity (SA). Amplitudes of temperature wave perturbations are generally larger at high SA at altitudes above 150 km, due to larger mean temperature and smaller molecular heat conductivity. Increasing kinematic coefficients of molecular heat conduction and viscosity result in stronger decreasing AGW amplitudes at altitudes larger 150 km at low SA. Dissipating AGWs generally produce heating at altitudes below 120 km. At larger heights, AGWs generally heat the thermosphere at low SA and cool it at high SA. Wave enthalpy fluxes are mainly upwards below 120 km altitude and downwards above 150 km at high SA, where they may have directions opposite to the upward wave energy fluxes. Downward wave enthalpy fluxes correspond to AGW cooling the upper atmosphere at high SA. Nonlinear dissipating AGWs may produce upward and downward transport of atmospheric mass. These mass flows may produce adiabatic heat influxes in the upper atmosphere. Mainly positive residual wave-induced mass flows at altitudes higher 150 km may contribute to the wave cooling of the upper atmosphere. Wave breaking and interactions between waves and the mean flow in the nonlinear model are stronger at higher amplitudes of AGW excitation at the ground, which lead to bigger energy losses for larger-amplitude waves. At high SA, resulting effects in the thermosphere depend on the balance between, on one hand, increases in wave amplitudes, caused by weaker molecular dissipation and smaller transfer of the wave energy to the wave-induced jet flows, and, on the other hand, decreases in the amplitudes due to higher density and larger AGW reflection. The thermal effects of waves in the upper atmosphere may depend on competitions between heating due to dissipation of the upward wave energy flux and cooling due to divergence of the downward wave entropy (or potential enthalpy) flux. At high SA, larger mean temperatures and larger temperature perturbations might increase magnitudes of downward wave entropy fluxes, which may result in more frequent downward wave enthalpy fluxes and wave cooling of the upper atmosphere.