Scaling exponents saturate in three-dimensional isotropic turbulence

That a range of scales is unaffected by every detail of a turbulent flow except the energy flux across scales has been fundamental to quantifying turbulence. However, it holds only for turbulent fluctuations of middle magnitudes. One manifestation is the anomalous scaling of structure functions (the scaling exponents depart from Kolmogorov scaling for high and low moment orders). Here we show that the anomaly varies by velocity component, and that scaling exponents of the transverse structure functions saturate with moment order, ruling out a unique inertial-range scaling, even an anomalous one.