On the invariant mean velocity profile for compressible turbulent boundary layers

Bin Wu, Weitao Bi, Fazle Hussain, Zhen Su She

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


An invariant mean velocity profile is derived and validated by direct numerical simulations of compressible turbulent boundary layers (CTBL) for a range of Reynolds number, Mach number and wall temperature. Near the wall, we reveal an invariance of the mean momentum equation, which derives and clarifies the semi-local scaling of the wall-normal coordinate. A near-wall multilayered modeling of the invariant spatial coordinate yields an invariant mean velocity for the inner flow. In the outer flow, an explicit invariant velocity is derived, based on a symmetry-based analytic description of the mixing length in the CTBL bulk. Thus, a whole invariant mean velocity profile is constructed, and validated to be superior to previous transformations.

Original languageEnglish (US)
Pages (from-to)186-202
Number of pages17
JournalJournal of Turbulence
Issue number2
StatePublished - Feb 1 2017


  • Compressible turbulent boundary layers
  • mean velocity scaling
  • multi-layer structure

ASJC Scopus subject areas

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Physics and Astronomy(all)


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