Experimental investigation of the structure of plane turbulent wall jets. Part 2. Structural analysis

Building on the hypothesis of wall and jet structural modes proposed in Part 1 (Choudhary et al. 2024), this study reports coherent patterns and vortical structures associated with the jet mode by further analysing our experimental particle image velocimetry datasets. Instantaneous velocity fields are binned based on dominant streamwise Fourier modes, focusing on submodes with wavelengths $\lambda _x\approx 5{z_{T}}$ (submode 1) and $\lambda _x\approx 2.5{z_{T}}$ (submode 2); $z_{T}$ is outer length scale of the flow. Two-point correlations of streamwise velocity fluctuations for the total and modal fields reveal near-periodic coherent patterns inclined backwards (∼ $14^{\circ }$ ) in the outer region and forwards (∼ $9^{\circ }$ ) in the inner region. Vortical structures in conditionally averaged velocity fluctuation vector fields are examined using linear stochastic estimation (LSE) with anticlockwise vorticity (prograde) at the outer energy site as the condition. The vortical structure of submode 1 is a three-vortex system with (i) a robust clockwise vortex in the inner region and (ii) a saddle-point topology in the outer region. The vortical structure of submode 2 is a backward-leaning vortex packet. The LSE fields indicate Q1–Q3 events in the inner region contributed by ‘non-local’ eddies through the interaction of outer and inner submode 1 vortices. Quadrant analysis reveals that Q1–Q3 events due to ‘non-local’ eddies outweigh Q2–Q4 contributions of ‘local’ eddies, producing counter-gradient momentum diffusion below mean velocity maximum. These findings further substantiate the hypothesis of wall and jet structural modes and indicate that the region below mean velocity maximum in wall jets significantly differs from a turbulent boundary layer.