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A stochastic flow approach to model the mean velocity profile of wall-bounded flows

Benoît Pinier 1, 2, * Etienne Mémin 2, 1 Sylvain Laizet 3 Roger Lewandowski 1, 2 
* Corresponding author
2 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences
IRMAR - Institut de Recherche Mathématique de Rennes, IRSTEA - Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture, Inria Rennes – Bretagne Atlantique
Abstract : There is no satisfactory model to explain the mean velocity profile of the whole turbulent layer in canonical wall-bounded flows. In this paper, a mean velocity profile expression is proposed for wall-bounded turbulent flows based on a recently proposed stochastic representation of fluid flows dynamics. This original approach, called modeling under location uncertainty introduces in a rigorous way a subgrid term generalizing the eddy-viscosity assumption and an eddy-induced advection term resulting from turbulence inhomogeneity. This latter term gives rise to a theoreti- cally well-grounded model for the transitional zone between the viscous sublayer and the turbulent sublayer. An expression of the small-scale velocity component is also provided in the viscous zone. Numerical assessments of the results are provided for turbulent boundary layer flows, pipe flows and channel flows at various Reynolds numbers.
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Submitted on : Tuesday, May 21, 2019 - 10:31:43 AM
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Benoît Pinier, Etienne Mémin, Sylvain Laizet, Roger Lewandowski. A stochastic flow approach to model the mean velocity profile of wall-bounded flows. Physical Review E , American Physical Society (APS), 2019, 99 (6), pp.063101. ⟨10.1103/PhysRevE.99.063101⟩. ⟨hal-01947662v4⟩



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