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

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.

typos corrected

References in corpus (13)

• Direct numerical simulation of turbulent channel flow up to $R{e}_{\tau }\approx 5200$
• Coherent structures in wall-bounded turbulence
• The Significance of Simple Invariant Solutions in Turbulent Flows
• Turbulence and secondary motions in square duct flow
• On a self-sustained process at large scale in the turbulent channel flow
• Wall-attached structures of velocity fluctuations in a turbulent boundary layer
• Dynamic slip wall model for large-eddy simulation
• Self-sustaining process of minimal attached eddies in turbulent channel flow
• Causality of energy-containing eddies in wall turbulence
• Characteristic scales of Townsend's wall attached eddies
• A statistical state dynamics-based study of the structure and mechanism of large-scale motions in plane Poiseuille flow
• Two-dimensional energy spectra in high Reynolds number turbulent boundary layers
• Intense structures of different momentum fluxes in turbulent channels

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