The spatial and temporal evolution of turbulence kinetic energy at dif
ferent scales is studied using direct numerical simulations of isotrop
ic turbulence. To explicitly follow the energy during the cascade proc
ess in physical space, a Lagrangian correlation coefficient between lo
cal kinetic energy at different scales is computed. This correlation i
s found to peak only after a Lagrangian time delay that is an increasi
ng 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 spa
tially localized eddy structures transferring their kinetic energy to
smaller scales appears to be, on average, quite realistic.