A three-dimensional version of the AtmoSym high-resolution nonlinear numerical model is used to simulate the propagation of an atmospheric wave ahead of a strong surge of pressure during a squall in Moscow on May 29, 2017. The meteorological source of disturbances is specified on the basis of experimental observations by a network of four microbarographs in Moscow oblast. An estimate is made of wave disturbances in the upper atmosphere caused by the generation of internal gravity waves by the meteorological source.

The features of the propagation of nonlinear pulsed acoustic disturbances in the atmosphere are considered. Data are presented on the experimental observation of shock front formation and the transition of a shock wave into a low-intensity acoustic wave with transformation of the pulse shape and broadening of the front at distances greater than 1000 km under both spherical and cylindrical propagation conditions. The influence of Kelvin–Helmholtz instability during rapid gas compression on the formation of the shock front structure is discussed. Under atmospheric conditions, such instability significantly affects dissipative processes in the air and forms the front of a nonlinear wave.

A numerical simulation of atmospheric wave propagation ahead of a strong pressure spike during a squall in Moscow on May 29, 2017, was performed using a three-dimensional version of the high-resolution nonlinear numerical model AtmoSym. The meteorological source was specified based on experimental observations of a network of 4 microbarographs located in the Moscow region. Wave perturbations in the upper atmosphere caused by the generation of internal gravity waves by the meteorological source were estimated.

A new decomposition method (decomposition into N and U-waves) of infrasonic signals corresponding to partial reflection of N-wave sounding pulses from anisotropic atmospheric layers and recorded in areas of geometric shadow at large distances from explosions and volcanic eruptions is presented. The decomposition method makes it possible to determine the vertical gradients of the effective sound speed (sound speed plus wind speed in the direction of propagation) that are not available for determination by other methods.

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 empirical approximations of atmospheric pressure-field oscillations were constructed based on observational data on atmospheric pressure variations at the land surface, which were obtained at the network of four microbarographs located in the Moscow region during the passage of an atmospheric front. The approximating functions were used as a lower boundary condition to numerically calculate the propagation of acoustic-gravity waves into the upper atmosphere from their source in the lower troposphere. The amplitude of upper atmosphere temperature disturbances caused by acoustic-gravity waves from the atmospheric front was estimated at about 170 K, while the amplitude of upper atmosphere temperature disturbances caused by background pressure variations at the land surface was estimated at 4–5 K.

Data on internal gravity and infrasound waves recorded during the passage of both warm and cold fronts throughout Moscow, which are associated with the atmospheric storm of May 29, 2017, are given. These waves were recorded by four microbarographs located in the city of Moscow and Moscow region (and marked IFA, MGU, MSR, and ZNS in Fig. 1) and the data obtained were compared with data on infrasound waves recorded at the IS43 station in the town of Dubna. Time variations in the characteristics of internal gravity and infrasound waves (coherence, propagation azimuths, phase velocities, characteristic periods, and frequency spectra) during the passage of both warm and cold fronts are studied. The transition from the gravity to acoustic dispersive branch of acoustic-gravity waves due to increasing frequency and the temporal modulation of the phase velocity of infrasound waves due to internal gravity waves (IGWs) are also studied. Data on both aerosol (PM10) and gas (NO2) concentrations measured at different Moscow stations during the approaching atmospheric storm are given. The possibility of detecting wave precursors of atmospheric storms in simultaneous variations in atmospheric pressure, wind velocity, and pollutant concentrations is studied.

Internal gravity wave (IGW) data obtained during the passage of atmospheric fronts over the Moscow region in June–July 2015 is analyzed. IGWs were recorded using a group of four microbarographs (developed at the Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences) located at distances of 7 to 54 km between them. Regularities of variations in IGW parameters (spatial coherence, characteristic scales, propagation direction, horizontal propagation velocity, and amplitudes) before, during, and after the passage of an atmospheric front over the observation network, when the observation network finds itself inside the cyclone and outside the front, are studied. The results may be useful in studying the relationships between IGW effects in different physical fields at different atmospheric heights. It is shown that, within periods exceeding 30 min, IGWs are coherent between observation points horizontally spaced at distances of about 60 km (coherence coefficient is 0.6–0.9). It is also shown that there is coherence between wave fluctuations in atmospheric pressure and fluctuations in horizontal wind velocity within the height range 60–200 m. A joint analysis of both atmospheric pressure and horizontal wind fluctuations has revealed the presence of characteristic dominant periods, within which cross coherences between fluctuations in atmospheric pressure and wind velocity have local maxima. These periods are within approximate ranges of 20–29, 37–47, 62–72, and 100–110 min. The corresponding (to these dominant periods) phase propagation velocities of IGWs lie within an interval of 15–25 m/s, and the horizontal wavelengths vary from 52 to 99 km within periods of 35 to 110 min, respectively.

Currently there are many international microbarograph networks for high-resolution recording of wave pressure variations on the Earth's surface. This arouses interest in wave propagation in the atmosphere generated by atmospheric pressure variations. A full system of nonlinear hydrodynamic equations for atmospheric gases with lower boundary conditions in the form of wavelike pressure variations on the Earth's surface is considered. Since the wave amplitudes near the Earth's surface are small, linearized equations are used in the analysis of well-posedness of the problem. With the help of a wave energy functional method, it is shown that in the non-dissipative case the solution to the boundary value problem is uniquely determined by the variable pressure field on the Earth's surface. The corresponding dissipative problem is well-posed if, in addition to the pressure field, appropriate conditions on the velocity and temperature on the Earth's surface are given. In the case of an isothermal atmosphere, the problem admits analytical solutions that are harmonic in the variables x and t. A good agreement between the numerical and analytical solutions is obtained. The study shows that the temperature and density can rapidly vary at the lower boundary of the boundary value problem. An example of solving the three-dimensional problem with variable pressure on the Earth's surface taken from experimental observations is given. The developed algorithms and computer programs can be used to simulate atmospheric waves generated by pressure variations on the Earth's surface.

The results of studying variations in the fine layered structure of the upper atmosphere (heights of 20–140 km) according to data obtained from acoustic sounding within the range of infrasonic waves are given. The sources of infrasounds were surface explosions equivalent to 10 kg to 70 t of TNT. These explosions were set off in different seasons in different regions of Russia. Experimental data obtained in 1981–2011 have been analyzed. It has been found that the fine structure in the form of vertically distributed layered formations occurs in the upper atmosphere in all seasons. Moreover, the vertical distribution of both air-temperature and wind-velocity inhomogeneities in the upper atmosphere may be invariable over a time interval of no less than several hours. It has also been found that, throughout the entire atmospheric thickness from the stratopause to the lower thermosphere heights (up to 140 km), the instantaneous height distribution of layered air-temperature and wind-velocity inhomogeneities may remain almost unchanged during a time interval of no less than 20 min.

Nonlinear effects manifested in infrasonic signals passing through different atmospheric heights and recorded in the region of a geometric shadow have been studied. The source of infrasound was a surface explosion equivalent to 20–70 t of TNT. The frequencies of the spectral maxima of infrasonic signals, which correspond to the reflections of acoustic pulses from atmospheric inhomogeneities at different heights within the stratosphere-mesosphere-lower thermosphere layer, were calculated using the nonlinear-theory method. A satisfactory agreement between experimental and calculated data was obtained.