Causal dynamics of turbulent structures in adverse-pressure-gradient turbulent boundary layers

Abstract

Abstract This study investigates the causal dynamics of turbulent boundary layers subjected to adverse pressure gradients (APGs), using direct numerical simulation (DNS) data from canonical zero-pressure-gradient (ZPG) and non-equilibrium APG cases. The causal links between outer-layer turbulence and inner-layer activity, as well as those within the inner layer itself, are analyzed using the Synergistic, Unique, Redundant Decomposition (SURD) of causality framework. Results reveal a one-way causal influence from outer to inner layers across all cases, with the strength of this interaction decreasing as the pressure gradient intensifies. A universal time scale for the outer-to-inner interaction delay is identified, formed by the boundary layer thickness and the outer-layer velocity scale proposed by Ma et al. (Phys. Fluids, 36(6), 2024), which incorporates pressuregradient history. Within the inner layer, persistent causal links from streamwise to wall-normal velocity fluctuations and uv fluctuations confirm the continued activity of the near-wall turbulence cycle under strong APG conditions. These findings support the hypothesis that the near-wall cycle is masked, rather than disrupted, by dominant outer-layer structures. The study also highlights the sensitivity of the SURD method to signal length, emphasizing the need for careful application to ensure reliable causal inference.