Local equilibrium approach in the problem of the dynamics of a plane turbulent wake in a passively stratified medium

To study the flow in a far plane turbulent wake in a passively stratified medium, we use a mathematical model that includes differential equations for the balance of turbulence energy, the transfer of its dissipation rate, shear turbulent stress, a defect of the density of the liquid, and the vertical component of the mass flux vector. Algebraic truncation of the last equation leads to a well-known gradient relation for the vertical component of the mass flux vector. It is established that under a certain constraint on the values of empirical constants in the mathematical model and the law of time scale growth consistent with the mathematical model, this relation is a differential constraint for the model. The equivalence of the local equilibrium approach for the vertical component of the mass flux vector and the zero Poisson bracket for the dimensionless turbulent diffusion coefficient and the averaged density is shown. The results of numerical experiments illustrating the theoretical results are presented.