A Scale-Dependent Analysis of the Return to Isotropy from Anisotropic Homogeneous Turbulent Shear Flow

Using results obtained from direct numerical simulations, the current work studies the return to isotropy from anisotropic homogeneous turbulent shear flow as well as from imposed polarization anisotropy. A wavelet-based scale-dependent decomposition of the velocity fields is performed and the Reynolds stress anisotropy tensor is used to quantify the anisotropy features of the total flow fields as well as the fields at different scales of the turbulent motion. In the case of homogeneous turbulent shear flow, the larger scales of the turbulent motion contribute more strongly to the anisotropy of the flow, but even the smaller scales hold lower levels of anisotropy. The return towards isotropy from anisotropic states due to shear and polarization anisotropy is most pronounced at the smallest scales of the turbulent motion, while anisotropy remains present for multiple eddy-turnover time scales at the larger scales of the turbulent motion.