Scale effects on the evolution of embedded synthetic streamwise vortices in turbulent boundary layers

Low-friction-Reynolds-number ( italic Re Subscript tau Baseline almost equals 235 minus 300 Re τ ≈ 235 − 300 Re_τ ≈ 235 - 300 and italic Re Subscript tau Baseline almost equals 400 minus 480 Re τ ≈ 400 − 480 Re_τ ≈ 400 - 480 ) turbulent boundary layers (TBLs) perturbed by small, mesoscale and relatively large synthetic streamwise vortices are investigated using planar particle image velocimetry (PIV) measurements and wall-resolved large-eddy simulation (LES). To better understand how these varying size streamwise vortices evolve in TBLs, synthetic streamwise vortex pairs are generated from a family of geometrically self-similar miniature vortex generators of viscous-scaled heights h Superscript plus Baseline almost equals 24 comma 48 comma 96 h + ≈ 24 , 48 , 96 h⁺ ≈ 24, 48, 96 in experiments and h Superscript plus Baseline almost equals 24 comma 30 comma 48 h + ≈ 24 , 30 , 48 h⁺ ≈ 24, 30, 48 in simulations. Analyses employing a triple decomposition of velocity found that the wall-normal domains of influence of these vortices are distinct and show dependence on the wall-normal peak location of the primary Reynolds shear stress component. It is found that the evolution of the synthetic vortices in TBLs is scale-dependent and characterised by the interplay between the positive (momentum source) and negative (momentum sink) components of the turbulent inertia, and additional inertia induced by the vortices. The ratio of the gradient of the viscous stress (of a canonical TBL) to the turbulent inertia acts as a diagnostic for estimating the wall-normal domain of influence of the synthetic vortices. Analyses of wall-normal domains of influence suggest that synthetic vortices of sufficient size ‘escape’ from the near-wall region. This scale effect on the evolution of embedded streamwise vortices is closely connected to the spread of time-invariant spatial fluctuations associated with secondary flows in TBLs. Estimation of the ‘escape’ scale provides insights into how the near-field mean dynamics of these vortices is related to their resulting dynamical signatures in the far field.