Vortical structures in the turbulent boundary layer: a possible route to a universal representation

A study of streamwise oriented vortical structures embedded in turbulent boundary layers is performed by investigating an experimental database acquired by stereoscopic particle image velocimetry (SPIV) in a plane normal both to the mean flow and the wall. The characteristics of the experimental data allow us to focus on the spatial organization within the logarithmic region for Reynolds numbers Re-theta up to 15000. On the basis of the now accepted hairpin model, relationships and interaction between streamwise vortices are first investigated via computation of two-point spatial correlations and the use of linear stochastic estimation (LSE). These analyses confirm that the shape of the most probable coherent structures corresponds to an asymmetric one-legged hairpin vortex. Moreover, two regions of different dynamics can be distinguished: the near-wall region below y(+) = 150, densely populated with strongly interacting vortices; and the region above y(+) = 150 where interactions between eddies happen less frequently. Characteristics of the detected eddies, such as probability density functions of their radius and intensity, are then studied. It appears that Reynolds number as well as wall-normal independences of these quantities are achieved when scaling with the local Kolmogorov scales. The most probable size of the detected vortices is found to be about 10 times the Kolmogorov length scale. These results lead us to revisit the equation for the mean square vorticity fluctuations, and to propose a new balance of this equation in the near-wall region. This analysis and the above results allow us to propose a new description of the near-wall region, leading to a new scaling which seems to have a good universality in the Reynolds-number range investigated. The possibility of reaching a universal scaling at high enough Reynolds number, based on the external velocity and the Kolmogorov length scale is suggested.