Using a mathematical model, which includes the averaged motion equations, differential transport equations of normal Reynolds stresses and dissipation rate, we carried out numerical modeling of evolution of a swirling turbulent wake with nonzero total excess momentum and angular momentum. The calculations were done to very large distances from the body. For small distances from the body the calculated profiles of averaged motion velocities and intensities of turbulent fluctuations of the longitudinal velocity component are in good agreement with the known experimental data of the Lavrent’ev Institute of Hydrodynamics, SB RAS. A simplified model of the flow is constructed.