On a bending of the wave front surface in randomly inhomogeneous medium with velocity fluctuations

Many papers have been devoted to the investigation of features of rays´ propagation in randomly inhomogeneous media with refractive index fluctuations. Chaotic bending of the wave front caused by random inhomogeneities of dielectric permittivity and velocity fluctuations leads to displacement of the rays. Transversal shift of rays, angles of arrival and dispersion of phase fluctuations are important statistical characteristics of radiation propagating in nonstationary media. Although they are basically geometry optical characteristics, the area of their application is beyond the scope of (ray-) optics approximation. A new method of calculation of dispersion of geometrical rays shifting is suggested in this paper. It is based on the stochastic kinematic equation describing evolution of the curvature of the wave front in nonstationary inhomogeneous medium with velocity fluctuations randomly varying in space and time. This method is universal and is valid for arbitrary nonstationary media. It does not impose any restrictions both on the distance passing by the wave and characteristic scale of random inhomogeneities. This method is important for investigation of chaotic bending of the phase front of wave beams due to heating spread in random media. For simplicity we consider 2D case.