Abstract

The phenomenon of hydrodynamic turbulence has puzzled mathematicians, physicists and engineers since the beginning of the 20th century. Mathematicians are fascinated by the solvability of the corresponding Navier-Stokes system of partial differential equations, physicists in the statistical behaviour as related to statistical mechanics of turbulence and engineers ask questions like: What are the heat transfer properties of a turbulent flow? What are the forces applied by a fluid to its boundary?

In a turbulent flow, many physical quantities undergo rapid, random and very chaotic changes, proving an obstacle in the analysis of the Navier-Stokes equations. All this leads to the need of statistical description of a turbulent flow, the concept of statistical solutions of the Navier-Stokes equations and the use of probability theory in the study of the Navier-Stokes equations.