Abstract <p>The paper theoretically studies the propagation regimes of narrow (millimeter) laser beams in a Kerr-nonlinear turbulent medium, which simulates the evolution of light inhomogeneities generated under multiple filamentation of high-power laser pulses in corresponding media, by methods of diffraction-beam tubes and diffraction rays. Three propagation regimes are found: self-focusing with generation of a nonlinear focus (beam collapse), self-channeling over a limited distance, and turbulent propagation. An equation for squared beam effective radius is derived, which is of interest for practical applications in nonlinear atmospheric optics.</p>