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

Published online by Cambridge University Press:  25 November 2019

Adrián Lozano-Durán Open the ORCID record for Adrián Lozano-Durán [Opens in a new window] ,
Marco G. Giometto ,
George Ilhwan Park  and
Parviz Moin
Adrián Lozano-Durán*
Affiliation:
Center for Turbulence Research, Stanford University, CA 94305, USA
Marco G. Giometto
Affiliation:
Department of Civil Engineering and Engineering Mechanics, Columbia University, NY 10027, USA
George Ilhwan Park
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA
Parviz Moin
Affiliation:
Center for Turbulence Research, Stanford University, CA 94305, USA
*
†Email address for correspondence: adrianld@stanford.edu
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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 that captures 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 1000. 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, consistent with previous works. Finally, we assess the ability of the state-of-the-art wall-modelled large-eddy simulation to predict non-equilibrium three-dimensional flows.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulence theory Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 883 , 25 January 2020 , A20
Copyright
© 2019 Cambridge University Press

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