A theory for the streamwise turbulent fluctuations in high Reynolds number pipe flow

A new theory for the streamwise turbulent fluctuations in fully developed pipe flow is proposed. The theory extends the similarities between the mean flow and the streamwise turbulence fluctuations, as observed in experimental high Reynolds number data, to also include the theoretical derivation. Connecting the derivation of the fluctuations to that of the mean velocity at finite Reynolds number as introduced by Wosnik, Castillo & George (J. Fluid Mech., vol. 421, 2000, pp. 115–145) can explain the logarithmic behaviour as well as the coefficient of the logarithm. The slope of the logarithm, for the fluctuations, depends on the increase of the fluctuations with Reynolds number, which is shown to agree very well with the experimental data. A mesolayer, similar to that introduced by Wosnik et al., exists for the fluctuations for $300\gt {y}^{+ } \gt 800$ , which coincides with the mesolayer for the mean velocities. In the mesolayer, the flow is still affected by viscosity, which shows up as a decrease in the fluctuations.