Linking Eulerian and Lagrangian structure functions' scaling exponents in turbulence

In fully developed turbulence, intermittency is classically characterized by ζE(q), the Eulerian scaling exponent of structure functions. The same approach can be used in a Lagrangian framework, using ζL(q) to characterize the temporal intermittency of the velocity of a particle advected by a turbulent intermittent field. An interesting question is then to know how to relate the scaling functions and explore the links between ζL(q) and ζE(q). We first provide different transformations between these functions, associated to different transformations linking space and time scales. We test these relations using experimental estimates for the two functions. For small and medium order of moments they are both close to data. For larger moments, experimental estimates have still too much scatter to conclude. The present paper underlines the need of more precise estimates and provides a methodology for future comparisons of Eulerian and Lagrangian scaling exponents.