Bridging inertial range scaling exponents of Lagrangian and Eulerian structure functions in high Reynolds number turbulence

A central question in turbulence theory concerns the inertial range scaling exponents of structure functions, which are known to depart from Kolmogorov's 1941 mean-field description due to small scale intermittency. This anomalous scaling can be studied from the Eulerian viewpoint capturing spatial intermittency, or the Lagrangian viewpoint capturing temporal intermittency. Bridging these two approaches has been a major challenge, primarily due to lack of reliable data. Using state-of-the-art direct numerical simulations (DNS) of isotropic turbulence at Taylor-scale Reynolds number of up to 1300, we extract inertial range scaling exponents for both Lagrangian and Eulerian structure functions. For the Eulerian case, we demonstrate that scaling exponents for longitudinal and transverse directions are different for high moments orders, in essential agreement with many past studies. It is further shown that the transverse Eulerian exponents saturate at ≈ 2.1 for moment orders p ≥10. The Lagrangian exponents likewise saturate at ≈ 2 for p ≥ 8. It is further shown that Lagrangian and Eulerian transverse exponents can be related by the same multifractal spectrum, which is different from that for Eulrian longitudinal exponents. Our results suggest that Lagrangian intermittency can be solely characterized by Eulerian transverse intermittency, and not by the longitudinal or a combination of both, as previously believed. Implications for extending multifractal predictions to dissipation range are also discussed, especially for Lagrangian acceleration.