Abstract
The problem above marked as resolved is more than a hundred years known as the closure problem of turbulence. Extending its name follows from below presented knowledge that to be its solution successful it is necessary to find an effective averaging tool enabling one to describe and smooth down any random turbulent field without any phenomenological limitations. To convince of necessity of such tool author in the article previously proved the nondifferentiability of random fields of measurable turbulence characteristics. But the decisive momentum of his solution strategy arose from the idea that randomness is an autonomous factor of physical processes and, therefore, this property can be utilized as a property of independent variables of the governing PDEs. To realize this idea author picked random frequences of turbulent fluctuations. Author then postulated the dual property as well as bifunctionality hypothesis and found suitable constitutive equations enabling him: (i) to express the instantaneous behaving of any random vector and scalar turbulent fields; (ii) to average the non-linear N–S system for the thermally known turbulent flow over the characteristic domains in the 5–D random space; (iii) to close the averaged equations systems with the set of four relationships named the Energy Distribution Equations (EDE) as the key result of the closure process. The energy invariance principle was used to find a closing equation for the energy distribution factor. The resultant EDEs were successfully verified meanwhile by comparing them with data from four independent sources of experiments made in boundary layers of wind tunnel flows of high anisotropy. This closure problem solution was obtained without the use of any auxiliary parameters or assumptions of phenomenological or experimental origin. From the nature of EDEs it follows that all turbulent mean flows are always 3–Dimensional. The use of randomness autonomy as the property of independent variables at describing turbulent flows is not limited upon Newtonian fluids.