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

## TL;DR

This paper introduces a novel stochastic model incorporating location uncertainty to better predict the mean velocity profile across the entire turbulent layer in wall-bounded flows, addressing a longstanding modeling challenge.

## Contribution

It proposes a new modeling framework that includes subgrid terms and eddy-induced advection, improving the understanding of transitional zones in turbulent flows.

## Key findings

- Model captures the transitional zone between viscous and turbulent sublayers.
- Numerical results agree with experimental data for various flow types.
- Provides a small-scale velocity expression in the viscous zone.

## Abstract

To date no satisfying model exists to explain the mean velocity profile within the whole turbulent layer of canonical wall bounded flows. We propose a modification of the velocity profile expression that ensues from a recently proposed stochastic representation of fluid flows dynamics. This modeling, 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 theoretically 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 assessment of the results are provided for turbulent boundary layer flows, for pipe flows and channel flows at various Reynolds numbers.