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 amathematical model that includes differential equations for the balance of turbulence energy, thetransfer of its dissipation rate, shear turbulent stress, a defect of the density of the liquid, and thevertical component of the mass flux vector. Algebraic truncation of the last equation leads to awell-known gradient relation for the vertical component of the mass flux vector. It is establishedthat under a certain constraint on the values of empirical constants in the mathematical modeland the law of time scale growth consistent with the mathematical model, this relation is adifferential constraint for the model. The equivalence of the local equilibrium approach for thevertical component of the mass flux vector and the zero Poisson bracket for the dimensionlessturbulent diffusion coefficient and the averaged density is shown. The results of numericalexperiments illustrating the theoretical results are presented.