Large-scale anisotropy effect on small-scale statistics over rough wall turbulent boundary layers

Abstract

According to the local isotropy hypothesis presented by Kolmogorov, small-scale velocity fluctuations should be universal in any kind of turbulent flow when the Reynolds number is sufficiently large. This is one of the key assumptions in turbulence phenomena. At this stage, the question is not whether this assumption is correct or not, but rather how the local isotropy works as a good approximation depending on the nature of the large-scale anisotropy. In this paper, we report on how the large-scale anisotropy penetrates the small scales. Based on the experiments performed in the strong mean shear flow on the rough-wall boundary layer, we consider how the local isotropy is restored. The anisotropic parameter S* is defined as a ratio of the time scale caused by the mean velocity gradient and the Kolmogorov time scale. It is found that the local isotropy is achieved in the dissipation range even in S*≃0.1. On the other hand, there is no clear evidence of isotropy in the inertial range. Due to the strong mean shear, the second-order structure functions do not satisfy the exact power-law relation but they indicate the convex shape plotted in the logarithmic coordinate. Computing the local slope and the curvature of structure functions, we found they are a strong function of anisotropic parameter.