Том 54, № 3 (2018)

In 1934, A.N. Kolmogorov considered the random walks of the 6D vector X, U of velocities generated by the Markov process and corresponding coordinates. The Fokker–Planck type equation using the scales of mean squares of velocity and coordinates as solutions was proposed to describe the time evolution of probability density of random process p(X, U, t). In 1959, A.M. Obukhov excluded time from these scales and obtained formulas in the form of asymptotes for the small-scale turbulence formulated in 1941. However, these results allow deeper insight into a wider range of phenomena, such as the size distribution of lithospheric plates (Bird [6]); the fetch laws describing wind wave growth (Toba [15]); and other phenomena (see specifically (Golitsyn [25]) considering the scales manifested in galaxies). Random accelerations and their integration set the velocities, which, being integrated, set the coordinates of particle ensembles. All these factors promote the energy input into the system increasing with time, whose growth rate ε is the doubled diffusion coefficient in the space of velocities, according to the Kolmogorov equation. It was found that the mean square velocity obtained upon solving the Fokker–Planck equation grows with time—theoretical physicists have long been aware of this result.

Statistical properties of different finite-dimensional approximations of two-dimensional ideal fluid equations are studied. A special class of approximations introduced by A.M. Obukhov (systems of hydrodynamic type) is considered. Vorticity distributions over area and quasi-equilibrium coherent structures are studied. These coherent structures are compared to structures occurring in a viscous fluid with random forcing.

A two-zone model of the atmospheric circulation over the hemisphere is considered. The geographic latitude φ of the boundary between the Rossby circulation regime zone at middle and high latitudes and the Hadley circulation regime zone at low latitudes serves as a model variable. The closeness between the actual and reference (exponential) air-mass distribution over the hemisphere, with respect to Ertel’s modified potential vorticity (MPV), is accounted for. The informational entropy of the statistical MPV distribution in the hemispheric atmosphere and the informational entropy of the eddy regime in the basic storm-track zone are used to determine a statistically (climatically) equilibrium value of φ. The question of atmospheric blocking over the hemisphere is considered using the proposed statistical–dynamical model.

On September 23, 1968, the Cosmos-243 satellite was launched into orbit with four radio telescopes directed to the nadir on board. They were designed to measure the microwave radiation of the Earth’s surface and its atmosphere at wavelengths of 0.8, 1.35, 3.4, and 8.5 cm. The onboard infrared radiometer measured radiation in the band of 10–11 µm in the same solid angle as the radio telescopes. This experiment, which was initiated by scientists from the Institute of Radioengineering and Electronics (IRE) and Institute of Atmospheric Physics (IAP) and, in particular, academicians V.A. Kotel’nikov and A.M. Obukhov, broke new ground in the remote sensing of the Earth from space, which is being actively developed.

Results obtained from simulating the propagation of infrasonic waves from the Chelyabinsk meteoroid explosion observed on February 15, 2013, are given. The pseudodifferential parabolic equation (PDPE) method has been used for calculations. Data on infrasonic waves recorded at the IS31 station (Aktyubinsk, Kazakhstan), located 542.7 km from the likely location of the explosion, have been analyzed. Six infrasonic arrivals (isolated clearly defined pulse signals) were recorded. It is shown that the first “fast” arrival (F) corresponds to the propagation of infrasound in a surface acoustic waveguide. The rest of the arrivals (T1–T5) are thermospheric. The agreement between the results of calculations based on the PDPE method and experimental data is satisfactory. The energy E of the explosion has been estimated using two methods. One of these methods is based on the law of conservation of the acoustic pulse I, which is a product of the wave profile area S/2 of the signal under analysis and the distance to its source E_I [kt] = 1.38 × 10^–10 (I [kg/s])^1.482. The other method is based on the relation between the energy of explosion and the dominant period T of recorded signal E_T [kt] = 1.02 × (T [s]²/σ)^3/2, where σ is the dimensionless distance determining the degree of nonlinear effects during the propagation of sound along ray trajectories. According to the data, the explosion energy E_I,T ranges from 1.87 to 32 kt TNT.