Emergence of the four layer dynamical regime in turbulent pipe flow

Direct numerical simulations of fully developed turbulent pipe flow that span the Reynolds number range 90 ! δ+ ! 1000 are used to investigate the evolution of the mean momentum field in and beyond the transitional regime. It is estimated that the four layer regime for pipe flow is nominally established for δ+ ≥ 180, which is also close to the value found for channel flow. Primary attention is paid to the magnitude ordering and scaling behaviors of the terms in the mean momentum equation. Once the ordering underlying the existence of four distinct balance layers is attained, this ordering is sustained for all subsequent increases in Reynolds number. Comparisons indicate that pipe flow develops toward the four layer regime in a manner similar to that for channel flow, but distinct from that for the boundary layer. Small but discernible differences are observed in the mean momentum field development in pipes and channels. These are tentatively attributed to variations in the manner by which the outer region mean vorticity field develops in these two flows. C © 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3702897]