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To date no satisfying model exists to explain the mean velocity profilewithin the whole turbulent layer of canonical wall bounded flows. We propose amodification of the velocity profile expression that ensues from a recentlyproposed stochastic representation of fluid flows dynamics. This modeling,called modeling under location uncertainty introduces in a rigorous way asubgrid term generalizing the eddy-viscosity assumption and an eddy-inducedadvection term resulting from turbulence inhomogeneity. This latter term givesrise to a theoretically well-grounded model for the transitional zone betweenthe viscous sublayer and the turbulent sublayer. An expression of thesmall-scale velocity component is also provided in the viscous zone. Numericalassessment of the results are provided for turbulent boundary layer flows, forpipe flows and channel flows at various Reynolds numbers.

A model under location uncertainty to predict the mean velocity in wall bounded flows