Friction-Based Scaling of Streamwise Turbulence Intensity in Zero-Pressure-Gradient and Pipe Flows

We explore the analogy between the asymptotic (high Reynolds number) scaling of two canonical wall-bounded turbulent flows, namely zero-pressure-gradient (ZPG) and pipe flows. We find that the two flows can be characterised using similar scaling laws that relate the streamwise turbulence intensity to friction: the product of the dimensionless drag and the square root of a dimensionless boundary-layer thickness for ZPG flow plays the role of the streamwise turbulence intensity for pipe flow, and the two flows are linked through a Reynolds-number-dependent correction term derived from the logarithmic mean-velocity profile. As a consequence, the squared product scales as the friction factor. Establishing a common, friction-based turbulence intensity scaling for ZPG and pipe flows is of interest both for fundamental studies of canonical wall-bounded flows and for the specification of the turbulence intensity in computational fluid dynamics simulations.