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 pressurestrain 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.

Direct numerical simulation of a non-equilibrium three-dimensional turbulent boundary layer over a flat plate

“…Note that the reduced is not observed in the 3-D channel DNS of Lozano-Durán et al . (2020) at a low Reynolds number (i.e. Re τ = 180), although in both the present and their simulations, propagates from the near-wall region to the outer layer.…”

“…The primary Reynolds shear stress () also decreases with increasing , as observed in the recent DNS work by Lozano-Durán et al . (2020) in a turbulent channel flow with a sudden spanwise pressure gradient. Not only the inactive motion ( and ) but also the active motion ( and ) are changed in a 3DTBL.…”

“…The latter behaviour was also reported in the recent temporally developing DNS work of Lozano-Durán et al . (2020).

Figure 13.Distributions of , and as functions of : ( a ) ; ( b ) for with and 2; ( c ) for , 600 and 900 with ; and ( d ) for with and 2.

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“…In particular, we investigate if the spanwise length scales increase linearly with distance from the wall in the present 3DTBL, and follow the attached-eddy hypothesis (Townsend 1976) given that Lozano-Durán et al . (2020) recently reported a self-similar response of a non-equilibrium 3DTBL in their 3-D channel with a sudden imposition of mean spanwise pressure gradient. In the recovery region, attention is given to what extent the present 3DTBL recovers to a ZPG TBL state after turning off in light of the seminal work of Antonia & Luxton (1971) on the sudden change of surface condition in a TBL.…”

“…The recent 3DTBL DNS of Lozano-Durán et al . (2020) in a turbulent channel flow with a sudden imposition of a spanwise mean pressure gradient is of note. They performed simulations at and 1000, and noted 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.…”