On the lognormality of the small-scale structure of turbulence

Higher-order moments of turbulent velocity gradients and their behavior with Reynolds number were measured in the nearly isotropic turbulent field generated by a square-mesh grid and in a turbulent boundary layer along a flat plate with zero pressure gradient. Hot-wire anemometry and instrumentation combining analog and digital methods were used to measure moments up to the fourteenth order. Measurements of such high-order moments required that particular attention be given to their validity. Involved herein was the evaluation of such effects as nonlinearity, averaging intervals, and the adequacy of the statistics for the tails of the probability density distributions. The results obtained are compared with those of other investigators for a variety of flow configurations in the laboratory as well as in the atmosphere. The concept of the intermittency of the small-scale structure and the theoretical approach involving lognormality of the probability density distribution of the dissipation rate are evaluated.