On the Lagrangian nature of the turbulence energy cascade

The spatial and temporal evolution of turbulence kinetic energy at different scales is studied using direct numerical simulations of isotropic turbulence. To explicitly follow the energy during the cascade process in physical space, a Lagrangian correlation coefficient between local kinetic energy at different scales is computed. This correlation is found to peak only after a Lagrangian time delay that is an increasing function of the scale separation. It is shown that a characteristic length reduction of a factor of 2 is achieved approximately after the local eddy-turnover time scale. The results show that the view of spatially localized eddy structures transferring their kinetic energy to smaller scales appears to be, on average, quite realistic.