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The investigation was fulfilled on the basis of the Navier-Stokes equations for viscous heat-conducting gas. The
Helmholtz decomposition of the velocity field into a potential part and a solenoidal one was used. We considered initial
vorticity to be small. So the results refer only to weak turbulence. The solution has been represented in the form of power
series over the initial vorticity, the coefficients being multiple integrals. In such a manner the system of the Navier-
Stokes equations was reduced to a parabolic system with constant coefficients at high derivatives. The first terms of the
series are the main ones that determine the properties of acoustic radiation at small vorticity. We modelled turbulence
with the aid of an ensemble of vortical structures (vortical rings). Two problems have been considered : (i) density
oscillations (and therefore the oscillations of the refractive index) in the case of a single vortex ring; (ii) oscillations in
the case of an ensemble of vortex rings (ten in number). We considered vortex rings with helicity, too. The calculations
were fulfilled for a wide range of vortex sizes (radii from 0.1 mm to several cm). As shown, density oscillations arise.
High-frequency oscillations are modulated by a low-frequency signal. The value of the high frequency remains constant
during the whole process excluding its final stage. The amplitude of the low-frequency oscillations grows with time as
compared to the high-frequency ones. The low frequency lies within the spectrum of atmospheric turbulent fluctuations,
if the radius of the vortex ring is equal to several cm. The value of the high frequency oscillations corresponds
satisfactorily to experimental data. The results of the calculations may be used for the modelling of the Gaussian beam
propagation through turbulence (including beam distortion, scintillation, beam wandering). A method is set forth which
describes the propagation of non-paraxial beams. The method admits generalization to the case of inhomogeneous
medium.
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