Isotropy vs anisotropy in small-scale turbulence

The decay of large-scale anisotropies in small-scale turbulent flow is investigated. By introducing two different kinds of estimators we discuss the relation between the presence of a hierarchy for the isotropic and the anisotropic scaling exponents and the persistence of anisotropies. By direct measurements on a channel flow numerical simulation we show that the presence of a hierarchy for the isotropic and the anisotropic scaling exponent is not in contradiction with the persistence of anisotropies at small scales.