The Lagrangian nature of turbulent energy cascade

We study the spatial and temporal evolution of energy flux at different scales using direct numerical simulations of isotropic turbulence. We compute the correlation coefficient at different times, between energy dissipation and local energy fluxes across inertial-range scales, in both Eulerian and Lagrangian frames. For the latter, we use a backward particle-tracking method. The Eulerian correlation coefficients decay monotonically, backward in time. However, the Lagrangian correlation coefficients between flux at adjacent scales peak after a certain time delay, which scales as the local turnover time. This result provides strong evidence of the Lagrangian nature of turbulent energy cascade. We present results on similar correlations in the two-dimensional inverse energy cascade range, and discuss the differences with three- dimensional forward energy cascade.