# Non-equilibrium three-dimensional boundary layers at moderate Reynolds numbers

## TL;DR

This study investigates non-equilibrium three-dimensional boundary layers at moderate Reynolds numbers, revealing a self-similar reduction in Reynolds stress due to flow displacement and pressure-strain effects, with implications for turbulence modeling.

## Contribution

It introduces a multiscale model explaining Reynolds stress reduction in non-equilibrium 3D turbulence, validated through direct numerical simulations at Reynolds numbers up to 1,000.

## Key findings

- Reynolds stress decreases with 3D strain and flow displacement.
- Flow regimes follow a self-similar evolution pattern.
- Pressure-strain correlation reduction inhibits Reynolds stress generation.

## Abstract

Non-equilibrium wall turbulence with mean-flow three-dimensionality is ubiquitous in geophysical and engineering flows. Under these conditions, turbulence may experience a counter-intuitive depletion of the turbulent stresses, which has important implications for modelling and control. Yet, current turbulence theories have been established mainly for statistically two-dimensional equilibrium flows and are unable to predict the reduction in the Reynolds stress magnitude. In the present work, we propose a multiscale model which explains the response of non-equilibrium wall-bounded turbulence under the imposition of three-dimensional strain. The analysis is performed via direct numerical simulation of transient three-dimensional turbulent channels subjected to a sudden lateral pressure gradient at friction Reynolds numbers up to 1,000. We show that the flow regimes and scaling properties of the Reynolds stress are consistent with a model comprising momentum-carrying eddies with sizes and time scales proportional to their distance to the wall. We further demonstrate that the reduction in Reynolds stress follows a spatially and temporally self-similar evolution caused by the relative horizontal displacement between the core of the momentum-carrying eddies and the flow layer underneath. Inspection of the flow energetics reveals that this mechanism is associated with lower levels of pressure-strain correlation which ultimately inhibits the generation of Reynolds stress. Finally, we assess the ability of the state-of-the-art wall-modelled large-eddy simulation to predict non-equilibrium, three-dimensional flows.