Scaling of small-scale wall turbulence

Abstract

In the vicinity of walls, turbulence is anisotropic. Since the classical hypotheses of Kolmogorov (Dokl. Akad. Nauk SSSR, vol. 30, 1941, pp. 299–303), Obukhov (Izv. Akad. Nauk SSSR Geogr. Geofiz, vol. 13, 1949, pp. 58–69) and Corrsin (J. Appl. Phys., vol. 22, 1951, pp. 469–473) require small-scale turbulence to be isotropic, they have only limited relevance to wall-bounded turbulent flows. Here, we put forward a hypothesis whereby small-scale near-wall statistics, when suitably normalized, are independent of the type of flow as well as of the Reynolds and Péclet numbers. The relatively large amount of available wall turbulence direct numerical simulations data, related mainly to second-order statistics, in a channel flow and a boundary layer provides good support for the independence with respect to the Reynolds number. To fully validate the hypothesis, more data are required for higher-order statistics as well as for other wall flows and for different surface conditions.