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It has long been surmised that the mean-velocity profile (MVP) of a pipe flowis closely related to the spectrum of turbulent energy. Here we perform aspectral analysis to identify the eddies that dominate the production of shearstress via momentum transfer. This analysis allows us to express the MVP as afunctional of the spectrum. Each part of the MVP relates to a specific spectralrange: the buffer layer to the dissipative range, the log layer to the inertialrange, and the wake to the energetic range. The parameters of the spectrum setthe thickness of the viscous layer, the amplitude of the buffer layer, and theamplitude of the wake.

The turbulent mean-velocity profile: it is all in the spectrum