Paths of energy in wall-turbulent flows

The paper describes the energy fluxes simultaneously occurring in the space of scales and in the physical space of wall-turbulent flows. The unexpected behavior of the energy fluxes consists of spiral-like paths in the combined physical/scale space where the contro- versial reverse energy cascade plays a central role. Two dynamical processes are identified as driving mechanisms for the fluxes, one in the near wall region and a second one fur- ther away from the wall. The former, stronger one is related to the dynamics involved in the near-wall turbulence regeneration cycle. The second suggests an outer self-sustaining mechanism which is asymptotically expected to take place in the eventual log-layer and could explain the debated mixed inner/outer scaling of the near-wall statistics. The ob- served behavior conflicts with the classical notion of Richardson cascade, and may have strong repercussions on both theoretical and modeling approaches to wall-turbulence, as anticipated by a simple model which is shown able to capture most of the rich dynamics of the shear dominated region of the flow.