Scaling of mixed structure functions in turbulent boundary layers

Abstract

We address the issue of the scaling of the anisotropic components of the hierarchy of correlation tensors in the logarithmic region of a turbulent boundary layer over a flat plate, at Reθ≈15000. We isolate the anisotropic observables by means of decomposition tools based on the SO(3) symmetry group of rotations. By employing a dataset made of velocity signals detected by two X probes, we demonstrate that the behavior of the anisotropic fluctuations throughout the boundary layer may be understood in terms of the superposition of two distinct regimes. The transition is controlled by the magnitude of the mean shear and occurs in correspondence with the shear scale. Below the shear scale, an isotropy-recovering behavior occurs, which is characterized by a set of universal exponents which roughly match dimensional predictions based on Lumley’s argument [J. L. Lumley, Phys. Fluids 8, 1056 (1965)]. Above the shear scale, the competition between energy production and transfer mechanisms gives rise to a completely different scenario with strong alterations of the observed scaling laws. This aspect has significant implications for the correct parametrization of the anisotropy behavior in the near wall region since, approaching the wall, an increasingly larger fraction of the scaling interval tends to conform to the shear-dominated power laws.