Local equilibrium approximation in the mathematical model of the far turbulent wake behind a body of revolution

The flow in the far turbulent wake behind a body of revolution is studied with the use of a three-parameter turbulence model, which includes differential equations of the turbulent energy balance, transfer equation for the turbulent energy dissipation rate, and turbulent shear stress equation. Local equilibrium algebraic truncation of the transfer equation for the turbulent shear stress yields the known Kolmogorov–Prandtl relation. Under a certain restriction on the values of the empirical constants and for the law of time scale growth consistent with the mathematical model, this relation is a differential constraint of the model or an invariant manifold in the phase space of the corresponding dynamic system. The equivalence of the local equilibrium approximation and the condition of the zero value of Poisson’s bracket for the normalized turbulent diffusion coefficient and defect of the averaged streamwise component of velocity is demonstrated. Results of numerical experiments are reported; they are found to be in good agreement with theoretical predictions.