Non-invariant solutions of the three-dimensional semi-empirical model of the far turbulent wake

A semi-empirical three-dimensional model of turbulence in the approximation of the far turbulent wake behind a self-propelled body in a passive stratified medium is considered. The sought quantities are the kinetic turbulent energy, kinetic energy dissipation rate, averaged density defect and density fluctuation variance. The full group of transformations admitted by this model is found. The model is reduced to a system of ordinary differential equations using symmetry groups and B-determining equations method. This system of ordinary differential equations satisfying natural boundary conditions was solved numerically. The obtained solutions agree with experimental data.