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The transport equations for velocity variances are investigated using datafrom DNS of incompressible channel flows at $Re_\tau$ up to 5200. Each term inthe transport equation has been spectrally decomposed to expose thecontribution of turbulence at different length scales to the processesgoverning the flow of energy in the wall-normal direction, in scale and amongcomponents.  The outer-layer turbulence is dominated by very large-scale streamwiseelongated modes. Away from the wall, production occurs primarily in theselarge-scale streamwise-elongated modes in the streamwise velocity, butdissipation occurs nearly isotropically in both velocity components and scale.For this to happen, the energy is transferred from the streamwise elongatedmodes to modes with a range of orientations through non-linear interactions,and then transferred to other velocity components. This allows energy to betransferred more-or-less isotropically from these large scales to the smallscales at which dissipation occurs. The VLSMs also transfer energy to thewall-region resulting in a modulation of the autonomous near-wall dynamics.  The near-wall energy flows are consistent with the well-known autonomousnear-wall dynamics. Through the overlap region between outer and inner layerturbulence, there is a self-similar structure to the energy flows. The VLSMproduction occurs at spanwise scales that grow with $y$. There is transport ofenergy away from the wall over a range of scales that grows with $y$. And,there is transfer of energy to small dissipative scales which grow like$y^{1/4}$. Finally, the small-scale near-wall processes characterised bywavelengths less than 1000 wall units are largely Reynolds number independent,while the larger-scale outer layer process are strongly Reynolds numberdependent. The interaction between them appears to be relatively simple.

Spectral analysis of the budget equation in turbulent channel flows at high Re