Scaling properties in the production range of shear dominated flows

Abstract

Recent developments in turbulence are focused on the effect of large scale anisotropy on the small scale statistics of velocity increments. According to Kolmogorov, isotropy is recovered in the large Reynolds number limit as the scale is reduced and, in the so-called inertial range, universal features -namely the scaling exponents of structure functions - emerge clearly. However this picture is violated in a number of cases, typically in the high shear region of wall bounded flows. The common opinion ascribes this effect to the contamination of the inertial range by the larger anisotropic scales, i.e. the residual anisotropy is assumed as a weak perturbation of an otherwise isotropic dynamics. In this case, given the rotational invariance of the Navier-Stokes equations, the isotropic component of the structure functions keeps the same exponents of isotropic turbulence. This kind of reasoning fails when the anisotropic effects are strong as in the production range of shear dominated flows. This regime is analyzed here by means of both numerical and experimental data for a homogeneous shear flow. A well defined scaling behavior is found to exist, with exponents which differ substantially from those of classical isotropic turbulence. Contrary to what predicted by the perturbation approach, such a deep alteration concerns the isotropic sector itself. The general validity of these results is discussed in the context of turbulence near solid walls, where more appropriate closure models for the coarse grained Navier-Stokes equations would be advisable.