Structure functions and flatness of streamwise velocity in a turbulent channel flow

Abstract

In this article, we present a multiscale characterization of the streamwise velocity of a turbulent channel flow. We study the 2nd and 4th order structure functions and the flatness for scales ranging from the dissipative to the integral domains and for a wide range of distances to the walls spanning four distinct regions of the channel. We characterize the impact of the shear stress induced by the walls on these statistics. Far from the walls, in the outer layer, the impact of the boundaries on the flow is negligible and the flow statistics follow the Kolmogorov-Obukhov theory. In the viscous, buffer and logarithmic regions, the inertial domain can be split in two subdomains of scales with two different statistical behaviors. In the logarithmic region, the scaling of the structure functions agrees with the model of Davidson et al. 2006 but the scaling of the flatness seems to better correspond to the characterization of intermittency proposed by Kolmogorov and Obukhov in 1962. The structure functions and flatness of the streamwise velocity in the buffer and viscous regions are studied for the first time. We show the strong non-Gaussianity of the velocity flow at any scale in the viscous layer with strong intermittent events that may correspond to high shear-induced dissipation.