This paper considers the breakup of liquid drops at the large Weber number within the framework of Kolmogorov’s scenario of breakup. The population balances equation for droplet radius distribution is written to be an invariant under the group of scaling transformations. It is shown that due to this symmetry, the long-time limit solution of this equation is a power function. When the standard deviation of droplet radius strongly increases and, consequently, the characteristic length scale disappears, the power asymptotic solution can be viewed as a further evolution of Kolmogorov’s log-normal distribution. This new universality appears to be consistent with the experimental observation of fractal properties of droplets produced by air-blast breakup. The scaling properties of Kolmogorov’s model at later times are also demonstrated in the case where the breakup frequency is a power function of instantaneous radius. The model completes the Liouville equation for distribution function of liquid particles in the phase space of droplet position, velocity, and radius. The numerical scheme is proposed for stochastic modeling of droplets production. Lagrangian simulation of the spray under air-blast atomization is performed using KIVA II code, which is a frequently used code for computation of turbulent flows with sprays. The qualitative agreement of simulation with measurements is demonstrated.

On the basis of a recently discovered collision group [V. L. Saveliev, in Rarefied Gas Dynamics: 22nd International Symposium, edited by T. J. Bartel and M. Gallis, AIP Conf. Proc. No. 585 (AIP, Melville, NY, 2001), p. 101], the Boltzmann collision integral is exactly rewritten in two parts. The first part describes the scattering of particles with small angles. In this part the infinity due to the infinite cross sections is extracted from the Boltzmann collision integral. Moreover, the Boltzmann collision integral is represented as a divergence of the flow in velocity space. Owing to this, the role of collisions in the kinetic equation can be interpreted in terms of the nonlocal friction force that depends on the distribution function.

Using an approach developed earlier for renormalization of the Boltzmann collision integral [Saveliev and Nanbu, Phys. Rev. E 65, 051205 (2002)], we derive an exact divergence form for the fragmentation operator. Then we reduce the fragmentation equation to the continuity equation in size space, with the flux given explicitly. This allows us to obtain self-similar solutions and to find the integral of motion for these solutions (we call it the bare flux). We show how these solutions can be applied as a description of cascade processes in three- and two-dimensional turbulence. We also suggested an empirical cascade model of impact fragmentation of brittle materials.

After the explosive eruption of the Hunga Tonga volcano on 15 January 2022, disturbances were observed at a distance of about 12,000 km in Northern Tien Shan and regarded variations in the atmospheric pressure, in telluric current, and in the Doppler frequency shift of ionospheric signal. At 16:00:55 UTC, a pulse of atmospheric pressure was detected there, with peak amplitude of 1.3 hPa and propagation speed of 0.3056 km/s, equal to the velocity of Lamb waves. In the variations in the Doppler frequency shift, disturbances of two types were registered on the 3212 km and 2969 km long inclined radio paths, one of which arose as a response to the passage of a Lamb wave (0.3059 km/s) through the reflection point of the radio wave and another as reaction to an acoustic-gravity wave (0.2602 km/s). Two successive perturbations were also detected in the records of telluric current at the arrival times of the Lamb and acoustic-gravity waves at the registration point. According to the parameters of the Lamb wave, the energy transfer into the atmosphere upon the explosion of the Hunga Tonga volcano was roughly estimated to be 2000 Mt of TNT equivalent.

The article describes in detail the equipment and method for measuring the Doppler frequency shift (DFS) on an inclined radio path, based on the principle of the phase-locked loop using an SDR receiver for the investigation of seismogenic and man-made disturbances in the ionosphere. During the two M7.8 earthquakes in Nepal (25 April 2015) and Turkey (6 February 2023), a Doppler ionosonde detected co-seismic and pre-seismic effects in the ionosphere, the appearances of which are connected with the various propagation mechanisms of seismogenic disturbance from the lithosphere up to the ionosphere. One day before the earthquake in Nepal and 90 min prior to the main shock, an increase in the intensity of Doppler bursts was detected, which reflected the disturbance of the ionosphere. A channel of geophysical interaction in the system of lithosphere–atmosphere–ionosphere coupling was traced based on the comprehensive monitoring of the DFS of the ionospheric signal, as well as of the flux of gamma rays in subsoil layers of rocks and in the ground-level atmosphere. The concept of lithosphere–atmosphere–ionosphere coupling, where the key role is assigned to ionization of the atmospheric boundary layer, was confirmed by a retrospective analysis of the DFS records of an ionospheric signal made during underground nuclear explosions at the Semipalatinsk test site. A simple formula for reconstructing the velocity profile of the acoustic pulse from a Dopplerogram was obtained, which depends on only two parameters, one of which is the dimension of length and the other the dimension of time. The reconstructed profiles of the acoustic pulses from the two underground nuclear explosions, which reached the height of the reflection point of the sounding radio wave, are presented.