Semi-empirical three-dimensional model of turbulence in the approximation of the far turbulent wake behind a self-propelled body in a passively stratied medium is considered. The sought quantities are the kinetic
turbulent energy, kinetic energy dissipation rate, averaged density defect and
uctuation variance. The full group of transformations admitted by
this model is found. The governing equations are reduced into ordinary differential equations by similarity reduction and method of the B-determining
equations (BDEs). This system of ordinary dierential equations satisfying
natural boundary conditions was solved numerically. The obtained solutions
agree with experimental data.