The system of averaged equations of motion, continuity, and transport equations for normal Reynolds stresses and dissipation rate of turbulent kinetic energy is employed in the thin shear layer approximation to describe a flow in swirling turbulent jets. The turbulent shear stresses are determined from the non-equilibrium algebraic relations of Rodi. The numerical realization of the model is based on the application of a finite-difference algorithm on moving grids, preserving the laws of momentum and angular momentum conservation. As an example to model a swirling turbulent jet, numerical simulation of swirling turbulent wake flows with varied total momentum and angular momentum is performed. A modification of diffusion terms in the transport equations is considered, based on the improved algebraic Ilyushin approximations of third-order moments that take into account the flow swirl. The computation results are in satisfactory agreement with the known experimental data of Lavrentyev Institute of Hydrodynamics of the Siberian Branch of the Russian Academy of Sciences (LIH SB RAS). A numerical analysis of the self-similarity of decay for the far turbulent wake with zero excess momentum and nonzero angular momentum is made. The computation results for swirling turbulent wake behind a towed sphere are presented.