Intermittency of longitudinal and transverse velocity gradients in turbulence and their relation to inertial range exponents

A defining feature of fluid turbulence is small-scale intermittency--the occurrence of intense, sporadic fluctuations that lead to strong deviations from Gaussian statistics, and necessatiting anomalous corrections to mean-field descriptions. In the dissipation range, intermittency can be quantified, for instance, through Reynolds number scaling of velocity gradient moments, whereas in the inertial range, through anomalous scaling of velocity increment moments (or structure functions) . Classical intermittency theories, notably based on multifractal models, provide a framework that links these two regimes. While the description works remarkably well for longitudinal components, persistent discrepancies remain in the behavior of transverse components. In this work, we revisit this open problem using theory and data from high-resolution direct numerical simulations (DNS) of isotropic turbulence. By utilizing a joint multifractal description, we show that while scaling of longitudinal gradients can be solely prescribed by inertial range exponents of longitudinal structure functions, scaling of transverse moments requires consideration of mixed structure functions. When utilizing such a joint description, the intermittency of both transverse and longitudinal gradients can be reconciled with inertial range scaling exponents.