The mathematical theory of turbulent flows is far from being achieved. Begun at the end of the last century, the theory was mainly developped as a branch of theoretical and experimental physics, the mathematical frame of which remained heuristic. This development is based on the assumption that the statistical averages of the physical entities (velocities, energy, energy-spectrum, two point velocity-conclations, etc) have some definite spatial properties determined by the physical nature of the envisaged flow. Therefore in order to build a rigorous mathematical framework for the statistical theory of turbulence one ought to supplement the Navier-Stokes equations with some random factors, write the new equations, etc.