The temporal evolution of the energy flux across scales in homogeneous turbulence

A temporal study of energy transfer across length scales is performed in 3D numerical simulations of homogeneous shear flow and isotropic turbulence. The average time taken by perturbations in the energy flux to travel between scales is measured and shown to be additive. Our data suggests that the propagation of disturbances in the energy flux is independent of the forcing and that it defines a `velocity' that determines the energy flux itself. These results support that the cascade is, on average, a scale-local process where energy is continuously transmitted from one scale to the next in order of decreasing size.