Laser beam propagation through an ensemble of vortex rings in air

The problem of the evolution of an ensemble of vortex rings in air is considerd. The full system of the Navier -Stokes equations is analyzed. The parametrix method was applied. The calculations were performed for a wide range of the ring parameters (various diameters of the rings, their initial vorticy). The initial value problem is as follows. The vorticity has non-zero value only inside the rings at the initial instant, the density and the temperature being constant everywhere at t=0. If the density is known, then it is possible to find the refractive index. The solution to the Navier-Stokes equations is an oscillating one. Thus the refractive index is an oscillating function with respect to time. These results enable to model turbulence in an adequate way without using the Taylor frozen turbulence hypothesis. The evolution of the frequency spectrum of the density fluctuations was obtained. These results were compared with Tatarskii's data. The intensity of a laser beam propagating through the ensemble of vortex rings in air was found with the aid of the parabolic equation method. A numerical procedure is set forth which allows to solve the problems of super-resolution without using regularization methods. The task is as follows. There is a set of experimental data and an instrument function (with some error). We change the domain in such a manner that the corresponding MTF has nowhere zero values. The procedure enables to solve problems of focusing in the turbulent atmosphere.