Dissipation-energy flux correlations as evidence for the Lagrangian energy cascade in turbulence

We study the spatial and temporal evolution of kinetic energy flux at different scales using direct numerical simulations of isotropic turbulence. The correlation coefficients at different times, between the molecular energy dissipation and local energy fluxes across inertial-range scales, are computed in both Eulerian and Lagrangian frames. The Eulerian correlation coefficients are found to decay monotonically backward in time. However, the Lagrangian correlation coefficients peak after a certain time delay. The peak time delay is found to be proportional to the local eddy turnover time (it scales with wave number k according to k(-2/3)), consistent with Kolmogorov's theory. Conditional sampling is used to isolate effects of strong rotation. The results presented provide strong evidence of the Lagrangian nature of turbulent energy cascade. 2010 American Institute of Physics. [doi:10.1063/1.3447887]MechanicsPhysics, Fluids & PlasmasSCI(E)EI7ARTICLE61-42