Equations for describing a family of self-similar solutions of the far field of a round submerged jet

The flow of a turbulent round submerged jet in far field has been considered. The modified Navier−Stokes equations have been derived with the aid of known self-similar properties of the time-mean flow as well as the spatial and temporal characteristics of the entire spectrum of the scales of turbulent fluctuations. A technique has been proposed for the numerical computation of these equations to describe a family of self-similar solutions in a cylindrical region with periodic boundary conditions in the longitudinal direction, and the velocity of the jet expansion enters the obtained equations explicitly as a parameter.