Emergence of the four layer dynamical regime in turbulent pipe flow

Abstract

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 develo..