Progress in the Statistical Theory of Turbulence

The fundamental notion of statistical mean values in fluid mechanics was first introduced by Reynolds. His most important contributions were the definition of the mean values for the so-called Reynolds' stresses and the recognition of the analogy between the transfer of momentum, heat and matter in the turbulent motion. In the decades following Reynolds' discoveries, the turbulence theory was directed toward finding semi-empirical laws for the mean motion by methods loaned from the kinetic theory of gases. Prandtl's ideas on momentum transfer and Taylor's suggestions concerning vorticity transfer belonged to the most important contributions of this period. I believe that my formulation of the problem by the application of the similarity principle has the merit to be more general and independent of the methods of the kinetic theory of gases. This theory led to the discovery of the logarithmic law of velocity distribution in shear motion for the case of homologous turbulence.