The flow in swirling turbulent wakes with varying total excessmomentum and angular momentum is described using two second-ordermathematical models. The first one includes averaged equations ofmomenta, turbulence energy balance, and dissipation rate in the far-wakeapproximation. The closure of the mathematical model relies on Rodi’salgebraic model for Reynolds stresses. The second model is based onsimplified representations of the turbulent viscosity coefficients. Forsmall distances, the calculated profiles of averaged motion velocitiesand turbulence energy are in good agreement with the experimental dataof Lavrent’ev Institute of Hydrodynamics of SB RAS. At large distances,numerical experiments have yielded a self-similar solution of problemsof dynamics of turbulent wake behind a self-propelled body andmomentumless swirling turbulent wake. Group-theoretical analysis of thesimplified mathematical model has been done. The model had been reducedto a system of ordinary differential equations, which was solvednumerically using asymptotic expansions. The solution obtained wascompared with the self-similar solution found by direct numericalintegration of the differential equations of the model at largedistances from the body, and good agreement was observed. In addition,the problem of asymptotic behavior of swirling turbulent wake behind asphere with non-zero values of total excess momentum and angularmomentum was considered. The group-theoretical analysis has shown theabsence of physically meaningful self-similar solutions to the equationsof the turbulence model under consideration.