Scale-by-scale approach to isotropy in homogeneous turbulent flows

Kolmogorov's local isotropy hypothesis suggests that the increasingly smaller lengths scales in turbulent flows become increasingly independent of the large scales, and at small enough scales the turbulence attains a universal isotropic state. However, within the last 25 years, several researchers have presented evidence for the persistence of anisotropy at scales for which the assumption of local isotropy would be expected to hold. We thus report results from an investigation into the approach to the isotropy on a scale-by-scale basis. We quantify the level of anisotropy at each length scale by analyzing DNS data for homogeneous uniformly-sheared turbulence for several different mean shear rates. Vorticity and strain rate orientations are examined for each wavenumber to provide insight into the physical mechanisms involved in the approach to isotropy.