The log behaviour of the Reynolds shear stress in accelerating turbulent boundary layers

Guillermo Araya, Luciano Castillo, Fazle Hussain

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


Direct numerical simulation of highly accelerated turbulent boundary layers (TBLs) reveals that the Reynolds shear stress, u′ v′+, monotonically decreases downstream and exhibits a logarithmic behaviour (e.g. -u′ v′+ = -(1/Auv) ln y+ + Buv) in the mesolayer region (e.g. 50 ≤ y+ ≤ 170). The thickness of the log layer of u′ v′+ increases with the streamwise distance and with the pressure gradient strength, extending over a large portion of the TBL thickness (up to 55 %). Simulations reveal that V+ ∂ U+/∂y+ ∼ 1/y+ ∼ ∂u′ v′+/∂y+, resulting in a logarithmic u′ v′+ profile. Also, V+ ∼ -y+ is no longer negligible as in zero-pressure-gradient (ZPG) flows. Other experimental/numerical data at similar favourable-pressure-gradient (FPG) strengths also show the presence of a log region in u′ v′+. This log region in u′ v′+ is larger in sink flows than in other spatially developing FPG flows. The latter flows exhibit the presence of a small power-law region in u′ v′+, which is non-existent in sink flows.

Original languageEnglish (US)
Pages (from-to)189-200
Number of pages12
JournalJournal of Fluid Mechanics
StatePublished - Jun 19 2015


  • turbulence simulation
  • turbulent boundary layers
  • turbulent flows

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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