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

18 Scopus citations


Direct numerical simulation of highly accelerated turbulent boundary layers (TBLs) reveals that the Reynolds shear stress, u′ v′<sup>+</sup>, monotonically decreases downstream and exhibits a logarithmic behaviour (e.g. -u′ v′<sup>+</sup> = -(1/A<inf>uv</inf>) ln y<sup>+</sup> + B<inf>uv</inf>) in the mesolayer region (e.g. 50 ≤ y<sup>+</sup> ≤ 170). The thickness of the log layer of u′ v′<sup>+</sup> 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<sup>+</sup> ∂ U<sup>+</sup>/∂y<sup>+</sup> ∼ 1/y<sup>+</sup> ∼ ∂u′ v′<sup>+</sup>/∂y<sup>+</sup>, resulting in a logarithmic u′ v′<sup>+</sup> profile. Also, V<sup>+</sup> ∼ -y<sup>+</sup> 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′<sup>+</sup>. This log region in u′ v′<sup>+</sup> 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′<sup>+</sup>, 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

  • Mechanical Engineering
  • Mechanics of Materials
  • Condensed Matter Physics


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