Various approaches to numerical modeling of free (without wall layers) hydrodynamic turbulence are described, including direct modeling, as well as modeling using phenomenological theories. The main algorithms of EGAK method for modeling of two-dimensional and three-dimensional hydrodynamic flows with turbulent mixing are considered. The results of calculations of a number of one-dimensional, two-dimensional and three-dimensional turbulent currents obtained using this method are given. The book is intended both for researchers engaged in research in the field of turbulent mixing of gases and liquids, and for students of the departments of applied mathematics and mechanics.