Density oscillations generated by vortex rings and their effect on scintillation of a Gaussian beam

Abstract

Density oscillations in the vicinity of vortex rings in air have been investigated. The calculations were fulfilled on the basis of the Navier-Stokes equations. We used series expansions of unknown functions in powers of a parameter which characterizes vorticity. As a result, we got a non-uniform system of parabolic differential equations with constant coefficients. The frequency of oscillations depends only on the dimensions and the shape of the ring in the case of small vorticity (weak turbulence). We analyzed oscillations generated by rings with circular cross-section. The size of the rings varied in a wide range. It includes inertial range and dissipation range. It is interesting to note that first of all the amplitude of oscillations increases, reaches its maximum and then decreases up to zero. These data can be used for modeling the propagation of a Gaussian beam through the turbulent atmosphere. We analyzed intensity fluctuations (scintillations) of the beam after the passage through the non-uniform region which contains vortex rings. We considered an ill-posed problem (that of super-resolution) connected with image restoration. In such cases if the input data are slightly changed, the solution may vary considerably. The proposed procedure is as follows. We change the instrument function in such a manner that it will be reversible one within the limits of accuracy. The procedure enables to solve some problems referring to the turbulent atmosphere. Ke