The evolution of the correlation characteristics in homogeneous helical turbulence is studied. Additional Kármán-Howarth-type equations describing the evolution of the mixed correlation tensor of the

The results of direct observations of fine mineral dust aerosol (0.15–15 μm) were carried out on extensive sand areas in desertificated lands of Kalmykia in 2007, 2009, and 2010 under conditions of weak wind and strong heating of the surface, almost in the absence of saltation processes. These results show that the fine mineral dust aerosol (0.15–0.5 μm) in the region under consideration contributes considerably to the total aerosol content of the atmospheric surface layer. Data on the mass concentrations of fine aerosol are treated on the basis of physical model estimates obtained for fluid dynamic parameters in the viscous thermal boundary layer near the ground surface. Deviations of these mass concentrations from their background values are related to a temperature drop in the thermal layer at the surface and from the values of friction velocity. For small and moderate values of friction velocity, these mass concentrations increase proportionally to a temperature drop with an exponent of about 0.5, and, for high friction velocities, this exponent becomes negative (~−0.5), which implies a decrease in these concentrations with an increase in a temperature drop.

The influence of helicity on the stability of scaling regimes, on the effective diffusivity, and on the anomalous scaling of structure functions of a passive scalar advected by a Gaussian solenoidal velocity field with finite correlation time is investigated by the field theoretic renormalization group and operator-product expansion within the two-loop approximation. The influence of helicity on the scaling regimes is discussed and shown in the plane of exponents $\epsilon \text{−}\eta$, where $\epsilon$ characterizes the energy spectrum of the velocity field in the inertial range $E\propto k^{1-2\epsilon }$, and $\eta$ is related to the correlation time at the wave number $k$, which is scaled as $k^{-2+\eta }$. The restrictions given by nonzero helicity on the regions with stable fixed points that correspond to the scaling regimes are analyzed in detail. The dependence of the effective diffusivity on the helicity parameter is discussed. The anomalous exponents of the structure functions of the passive scalar field which define their anomalous scaling are calculated and it is shown that, although the separate composite operators which define them strongly depend on the helicity parameter, the resulting two-loop contributions to the critical dimensions of the structure functions are independent of helicity. Details of calculations are shown.

The average monthly profiles of the dust extinction coefficient (ε) were analyzed according to the CALIOP lidar data from 2006–2021 for 24 cells (size of 2° × 5°) in the Aral-Caspian arid region (ACAR; 38–48°N, 50–70°E). Using the NOAA HYSPLIT_4 trajectory model and the NCEP GDAS1 gridded (resolution of 1° × 1°) archive of meteorological data, the array of >1 million 10-day forward trajectories (FTs) of air particles that started from the centers of the ACAR cells was calculated. On the basis of the FT array, the average seasonal heights of the mixed layer (ML) for the ACAR cells were reconstructed. Estimates of the average seasonal dust optical depth (DOD) were obtained for ACAR’s lower troposphere, for ACAR’s ML (“dust emission layer” (EL)), and for the lower troposphere above the ML (“dust transit layer” (TL)) above each of the ACAR cells. Using the example of ACAR, it is shown that the analysis of DOD for the EL, TL and the surface layer (SL; the first 200 m AGL) makes it possible to identify dusty surfaces that are not detected on DOD diagrams for the entire atmospheric column, as well as regions where the regular transport of aged dust from remote sources can generate false sources. Based on FT array, the fields of the potential contribution of both the ACAR’s dust transit and the ACAR’s dust emission layers as well as of the entire ACAR’s lower troposphere into the DOD of the surrounding and remote regions are retrieved using the original method of potential impact of a three-dimensional source (3D-PSI). It has been found out that ACAR dust spreads over almost the entire Northern Hemisphere; the south and southeast regions of the ACAR are subject to the maximum impact of the ACAR dust. Quantitative estimates of the potential contribution of ACAR dust to the regional DODs are given for a number of control sites in the Northern Hemisphere. The results could be useful for climatological studies.