Journal
JOURNAL OF FLUID MECHANICS
Volume 883, Issue -, Pages -Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2019.869
Keywords
turbulence simulation; turbulence theory; turbulent boundary layers
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Funding
- Office of Naval Research (ONR) [N000141712310]
- U.S. Department of Defense (DOD) [N000141712310] Funding Source: U.S. Department of Defense (DOD)
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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.
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