Turbulent cascade in fully developed turbulent channel flow

We show that Kolmogorov scale-by-scale equilibrium in the intermediate layer of a fully developed turbulent channel flow is only achieved asymptotically around the Taylor length and, therefore, not in an inertial range. Furthermore, we analyse scale-by-scale turbulence production and interscale turbulence energy transfer in terms of alignments/anti-alignments of fluctuating velocities, straining/compressive relative motions, forward/inverse interscale transfer/cascade and homogeneous/non-homogeneous interscale transfer rate contributions. We also propose leading order scalings for second-and third-order two-point statistics, including the extremum interscale turbulence energy transfer rate and a second-order anisotropic structure function, which acts as a scale-by-scale Reynolds shear stress and determines the scale-by-scale (two-point) turbulence production rate.