Eddy viscosity and complete log-law for turbulent pipe flow at high Reynolds numbers

Junke Guo

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Turbulent pipe flow velocity distribution at high Reynolds numbers is described by Coles' log-wake law for which the wake component is purely empirical. This research innovates Coles' wake law with another log-function, and thus combines the log- and the wake-laws into a single (complete) log-law, for which the von Kármán constant (0.39) is the only fit parameter. Specifically, the symmetrical velocity distribution about the centreline requires a symmetrical eddy viscosity model which is approximated by a quartic polynomial, leading to a complete log-law including the effects of the bottom and top walls as well as their interactions. The complete log-law is confirmed with data from both smooth and rough pipes; it also results in an accurate and explicit friction law for smooth pipe flow. Furthermore, the complete log-law is preliminarily tested with data from channels and boundary layers; the quartic eddy viscosity may be extended for ice-covered river flow in future studies.

Original languageEnglish (US)
Pages (from-to)27-39
Number of pages13
JournalJournal of Hydraulic Research
Issue number1
StatePublished - Jan 2 2017


  • Eddy viscosity
  • friction factor
  • log-law
  • pipe flow
  • velocity distribution
  • wall-bounded flow

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Water Science and Technology


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