Characterization of a laser beam propagating through the turbulent atmosphere

The method is proposed in order to model the propagation of a laser beam through turbulence. Two kinds of beams are under consideration: (i) beams of small power; (ii) high-power beams with effect of self-focusing (including ultra-short laser pulses). Turbulent atmosphere can be modeled with the aid of the full Navier-Stokes equations. As known, turbulent fluctuations decay in isolated system due to dissipation. To prevent decay, energy transfer from outside must exist. So we introduced an additional term into the equation of energy. The amplitude of arising disturbances has been investigated. The Navier-Stokes equations were reduced to integral ones and solved by iterative procedure. The comparison of the subsequent iterations demonstrates rapid convergence. The nonlinear solution has an important feature: the dispersion law depends on coordinates and time. The range of applicability of the numerical method has no restrictions on the value of the Reynolds number. Turbulent properties can be found by averaging over initial data. Some theoretical results were confirmed by experiments relating to grid turbulence. We have also considered the 3D objecttargeting problem. Some examples are given.