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, transport equation for the turbulent energy dissipation rate, and turbulent shear stress equation. Local equilibrium algebraic truncation of the transport equation for the turbulent shear stress yields the known Kolmogorov–Prandtl equation. Under a certain constraint on the values of the empirical constants and for the law of time scale growth consistent with the mathematical model, this equation 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 the Poisson bracket for the normalized turbulent diffusion coefficient and defect of the longitudinal component of velocity is demonstrated. Results of numerical experiments are reported; they are found to be in good agreement with theoretical predictions.