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-eta, where epsilon characterizes the energy spectrum of the velocity field in the inertial range E proportional to k(1-2epsilon), 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.
Abstract. 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 2007Kalmykia in , 2009Kalmykia in , 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 linear mechanism of generation of gravity waves by potential vorticity (PV) disturbances in flows with constant horizontal and vertical shears is studied. The case of the initial singular distribution of PV, in which the PV is localized in one coordinate and is periodic with respect to other coordinates, is considered. In a stratified rotating medium, such a distribution induces a vortex wave (continuous mode), the propagation of which is accompanied by the emission of gravity waves. To find the emission characteristics, a linearized system of dynamical equations is reduced to wave equations with sources that are proportional to the initial distributions of PV. The asymptotic solutions of the equations are constructed for small Rossby numbers (horizontal shear) and large Richardson numbers (vertical shear). When passing through the inertial levels symmetrically located with respect to a vortex source, the behavior of the solutions for wave amplitudes radically changes. Directly in the vicinity of the source, the solutions are of monotonic character, corresponding to a quasigeostrophic vortex wave. At long distances from the source, the solutions oscillate. The horizontal momentum flux and the Eliassen–Palm flux are estimated using asymptotic solutions. It is found that, within the indicated range of both Rossby and Richardson numbers, these fluxes are exponentially small: that is, the emission of waves is weak.
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